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Consolidation properties of phosphatic clays from automated slurry consolidometer and centrifugal model tests

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Title:
Consolidation properties of phosphatic clays from automated slurry consolidometer and centrifugal model tests
Creator:
Martinez, Ramon E., 1951-
Publication Date:
Language:
English
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xiv, 327 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Calibration ( jstor )
Centrifugation ( jstor )
Computer printers ( jstor )
Modeling ( jstor )
Ponds ( jstor )
Slurries ( jstor )
Specimens ( jstor )
Stress tests ( jstor )
Transducers ( jstor )
Void ratio ( jstor )
Sedimentation analysis ( lcsh )
Slurry ( lcsh )
Soil consolidation test ( lcsh )
City of Gainesville ( local )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1987.
Bibliography:
Includes bibliographical references (leaves 320-325).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Ramon E. Martinez.

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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19109802 ( OCLC )

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CONSOLIDATION PROPERTIES OF PHOSPHATIC CLAYS
FROM AUTOMATED SLURRY CONSOLIDOMETER
AND CENTRIFUGAL MODEL TESTS













By

RAMON E. MARTINEZ


A DISSERTATION PRESENTED TO THE GRADUATE
SCHOOL OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1987




























DEDICATED WITH ALL MY LOVE TO MY WIFE,

VIRGINIA, AND MY SON, JUAN RAMON,

FOR THEIR DEVOTED LOVE AND PATIENCE.



AND TO MY PARENTS, DAMASO AND CATALINA,

FOR THEIR SUPPORT, ENCOURAGEMENT, AND

PRAYERS.



GOD BLESS THEM ALL.















ACKNOWLEDGMENTS

I would like to express my deepest gratitude to the

members of my supervisory committee. Foremost, I am

grateful to Dr. Frank C. Townsend for serving as chairman of

the committee. However, Dr. Townsend's support included far

more than his experience and knowledge on the subject of

phosphatic clay consolidation. His personal interest,

friendship, and love for Panama will outlast in my memory

the technical aspects of my career.

I am also very thankful to Dr. Michael C. McVay for

serving on the committee and for his valuable assistance and

always appropriate comments throughout the development of my

doctoral research. My gratitude is extended to Dr. John L.

Davidson, not only for being on the committee, but also for

giving me the opportunity to observe what an excellent

teacher should be; I will definitely try to imitate him.

Special thanks are expressed to Dr. Gustavo Antonini, of the

Latin American Center, for taking the time and interest of

serving as the external member of the committee.

I have intentionally left Dr. David Bloomquist to the

end of the list of committee members. I can not emphasize

enough my gratitude to "Dave," as he prefers to be called.

Dave was a key element in the development of all the

equipment reported in this research. Most of what I now

know about laboratory equipment and instrumentation I

iii








learned from him. But Dave's most valuable qualification is

his attitude toward work. He enjoys so much his work around

the lab that, while working with him, you also enjoy yours.

I extend my gratitude to Dr. J. Schaub, chairman of the

Civil Engineering Department. It is because of all these

faculty members that I will remember my stay at UF not only

as a profitable experience, but also as an enjoyable one.

I also must express my gratitude to the Universidad

Tecnol6gica de Panama for supporting me during the pursuit

of this degree. I want to specially thank Ings. H6ctor

Montemayor and Jorge L. Rodriguez, dean and vicedean of the

Civil Engineering College, and Dr. Victor Levi S., the

university president.

The friendship and support of many colleague graduate

students is also recognized. I want to make a special

recognition to Pedro Zuloaga, whose friendship I am sure

will continue after my return to Panama. The list of other

good friends who were part of my long career at UF includes,

but is not limited to, Sarah Zalzman, Charles Moore, Jeff

Beriswill, Hwee-Yen Kheng, Kwasi Badu-Tweneboah, Nick

Papadopoulos, Charlie Manzione, John Gill, and my panamanian

colleague, Javier Navarro.

The financial support of the Florida Institute for

Phosphate Research was instrumental in the development of

the research and is acknowledged here. I also want to

recognized Randy Bushey of the Florida Department of Natural

Resources for providing financial support for this research.
















TABLE OF CONTENTS

Page


ACKNOWLEDGMENTS ...................... ..................... iii

LIST OF TABLES ......................... ................... viii

LIST OF FIGURES ......................................... ix

A BSTRA CT ................................................ x iii

CHAPTERS

I INTRODUCTION ...................................... 1

Problem Statement ................................. 1
Purpose and Scope of the Study..................... 4

II BACKGROUND AND LITERATURE REVIEW................... 6

Introduction ...................................... 6
Slurry Consolidation Laboratory Tests.............. 7
Settling Column Tests ............................. 11
CRD Slurry Consolidation Tests..................... 12
Centrifugal Modelling........................ ...... 20
Constitutive Properties ........................... 22


III AUTOMATED SLURRY CONSOLIDOMETER--EQUIPMENT AND
TEST PROCEDURE .................................... 27

Introduction ...................................... 27
The Test Chamber .................................. 27
The Stepping Motor ................................ 36
The Computer and Data Acquisition/Control System.. 39
The Controlling Program ........................... 45
Test Procedure .................................... 47

IV AUTOMATED SLURRY CONSOLIDOMETER--DATA REDUCTION... 55

Introduction ...................................... 55
Determination of Void Ratio........................ 56
Determination of Effective Stress.................. 59
Determination of Permeability..................... .. 62

V AUTOMATED SLURRY CONSOLIDOMETER--TEST RESULTS...... 68









Testing Program ................................... 68
CRD Tests Results ................................. 69
CHG Tests Results ................................. 93
Testing Influence ................................. 109

VI CENTRIFUGE TESTING--EQUIPMENT, PROCEDURE, AND
DATA REDUCTION .................................... 120

Introduction ...................................... 120
Test Equipment and Procedure ...................... 122
Method of Data Reduction .......................... 131

VII CENTRIFUGE TESTING RESULTS ........................ 142

Testing Program ................................... 142
Determination of Constitutive Relationships....... 143
Comparison of CRD and Centrifuge Test Results...... 178
Effect of Surcharge on Pore Pressure Response...... 182
Some Comments on the Time Scaling Exponent........ 191

VIII COMPARISON OF CENTRIFUGAL AND
NUMERICAL PREDICTIONS ............................. 202

Introduction ...................................... 202
The Constitutive Relationships...................... 204
Predictions of Ponds KC80-6/0 and KC80-10.5/0...... 206
Predictions of Ponds CT-1, CT-2/3, and CT-5....... 211

IX CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH... 231

Summary and Conclusions ........................... 231
Suggestions for Future Research..................... 237

APPENDICES

A TIME SCALING RELATIONSHIP ......................... 240

Introduction ...................................... 240
Permeability Scaling Factor ....................... 241
Governing Equation in the Centrifuge............... 242

B LVDT-PIVOTING ARM CALIBRATION...................... 244

C ANALYSIS OF NOISE EFFECT IN THE TRANSDUCERS
R ESPON SE .......................................... 24 7

D AUTOMATED SLURRY CONSOLIDOMETER CONTROLLING
AND MONITORING PROGRAM SLURRYY) .................. 254

SLURRY1 Flowchart ................................. 254
Listing of SLURRY1 ................................ 260

E AUTOMATED SLURRY CONSOLIDOMETER
DATA REDUCTION PROGRAM (SLURRY2) .................... 270









F TRANSDUCER CALIBRATION IN THE CENTRIFUGE

G CENTRIFUGE MONITORING PROGRAM...........


281

286


H CENTRIFUGE DATA REDUCTION PROGRAM
AND OUTPUT LISTINGS ............................... 289

Data Reduction Program ............................ 289
Data Reduction Output of Test CT-1.................. 295
Data Reduction Output of Test CT-2................. 299

I NUMERICAL PREDICTION PROGRAM AND
EXAMPLE OUTPUT LISTINGS ........................... 304

Listing of Program YONG-TP......................... 304
Prediction of Pond KC80-6/0 ....................... 315

BIBLIOGRAPHY ............................................ 320

BIOGRAPHICAL SKETCH ..................................... 326


vii















LIST OF TABLES


Table Page

2-1. Kingsford Clay Parameters ......................... .. 23

3-1. Slurry Consolidometer Transducer Information ...... 35

3-2. Deformation Rates in CRD Tests..................... 45

3-3. Valve Positions for Vacuum System.................. 49

3-4. Verification of Transducer Calibration............. 53

5-1. Conditions of Eight Tests Conducted................. 69

5-2. Summary of CRD Tests Results ....................... 85

5-3. Summary of CHG Tests Results....................... 99

6-1. Centrifuge Test Transducer Information............. 126

7-1. Centrifuge Testing Program ........................ 142

7-2. Partial Output of the Analysis of Test CT-1....... 158

7-3. Partial Output of the Analysis of Test CT-2....... 172

7-4. Modelling of Model Results (Bloomquist and
Townsend 1984) ................................... 196

7-5. Time Scaling Exponent Obtained from Data
in Table 7-4 ...................................... 196

7-6. Modelling of Models on Tests CT-2 and CT-3 ........ 201

C-1. Summary of Transducers Response Using
Various Filtering Techniques....................... 251

F-1. Calibration Data for Transducer No. 1. ............. 283

F-2. Calibration Data for Transducer No. 2 ............. 284

F-3. Calibration Data for Transducer No. 3 ............. 285


viii


















LIST OF FIGURES




Schematic of Automated Slurry Consolidometer..

Schematic of Slurry Consolidometer Chamber....

Pore Pressure Transducer PDCR 81 ..............

Photograph of Slurry Consolidometer Chamber...

Motor Translator, Gear Box, and Stepper Motor.

Schematic of Motor Translator Connections .....

Entire Slurry Consolidometer Assembly .........

Computer and Data Acquisition/Control System..

Vacuum System .................................

Phase Diagrams ................................


4.2 Variation of Effective Stress with


- Results of Test CRD-l ........

- Results of Test CRD-2 ........

- Duplication of Test CRD-1 ....

- Results of Test CRD-3 ........

- Results of Test CRD-4 ........

- Pore Pressure and Effective S
with Depth for Test CRD-l....

- Summary of CRD Tests .........

- Results of Test CHG-l ........

- Results of Test CHG-2 ........

- Results of Test CHG-3 ........

- Results of Test CHG-4 ........


....



..,...

.....

o..o


tress
o.....



.....




....


Depth .........

. .

. .

. .

..............

..............

Distributions
. .

. .

. .

. .

. .

. .


Figure

3.1 -

3.2 -

3.3 -

3.4 -

3.5 -

3.6 -

3.7 -

3.8 -

3.9 -

4.1 -


Page

28

29

32

34

37

38

40

42

49

57


5. 1

5. 2

5. 3

5.4

5.5 5

5 .6



5.7

5.8

5.9

5.10

5.11


61

71

75

78

81

83



86

88

94

97

100

102









5.12 Pore Pressure and Effective Stress Distributions
with Depth for Test CHG-2 ........................

5.13 Summary of CHG Tests .............................

5.14 Deformation Rate and Hydraulic Gradient with
Time for Tests CRD-2 and CHG-3. ...................


5.15

5.16


6.1

6.2

6. 3

6.4

6. 5

6. 6

6.7

7.1

7 .2

7 .3

7.4

7 .5


- Comparison of CRD and CHG Tests Results ..........

- Constitutive Relationships Proposed for
Kingsford Clay ...................................

- Schematic of Centrifuge and Camera Set-up ........

- Centrifuge Bucket ................................

- Sampler for Solids Content Distribution ..........

- Effect of Stopping and Re-starting Centrifuge....

- Variation of Void Ratio with Depth. ...............

- Location of Material Node i.......................

- Excess Pore Pressure Distribution.................

- Height-Time Relationship for Test CT-1 ...........

- Solids Content Profiles for Test CT-I ............

- Evaporation Effect on Excess Pore Pressure .......

- Evaporation Correction for Test CT-1 .............

- Pore Pressure with Time for Test CT-1 ............


7.6 Pore Pressure Profiles for Test CT-1 .............

7.7 Parabolic Distribution Excess Pore Pressure
at t 2 hours for Test CT-1.......................

7.8 Constitutive Relationships from Centrifuge
T e s t CT -1 . .

7.9 Height-Time Relationship for Test CT-2 ...........

7.10 Solids Content Profiles for Test CT-2 ............

7.11 Evaporation Correction for Test CT-2 .............

7-12 Pore Pressure with Time for Test CT-2 ............

7.13 Pore Pressure Profiles for Test CT-2 .............

x


105

106


110

112


117

123

125

128

130

134

137

139

145

146

148

150

151

153


156


161

165

166

168

169

170









7.14 Constitutive Relationships from Centrifuge
Test CT -2 ........................................ 173

7.15 Comparison of CT-1 and CT-2 Results............... 176

7.16 Comparison of CRD and Centrifuge Test Results.... 179

7.17 Pore Pressure Profiles for Test CT-4. ............. 184

7.18 Bucket Used in Centrifuge Surcharge Tests ......... 186

7.19 Height-Time Relationship for Test CT-5 ........... 188

7.20 Pore Pressure Profiles for Test CT-5 ............. 189

7.21 Pore Pressure with Time for Test CT-5 ............ 190

7.22 Modelling of Models using Bloomquist and
Townsend (1984) Data ............................. 198

7.23 Modelling of Models using Tests CT-2 and CT-3 .... 200

8.1 Prediction of Pond KC80-6/0 using Constitutive
Relationships obtained from Test CRD-1 ........... 207

8.2 Comparison of YONG-TP, UF-McGS, and
QSUS Outputs ..................................... 209

8.3 Prediction of Pond KC80-10.5/0 using Constitutive
Relationships obtained from Test CRD-1. ........... 210

8.4 Prediction of Pond CT-1 using Constitutive
Relationships obtained from Test CRD-1. ........... 212

8.5 Prediction of Pond CT-2/3 using Constitutive
Relationships obtained from Test CRD-1. ........... 213

8.6 Comparison of Centrifuge Tests KC80-10.5/0
an d CT -6 ............................. ............ 215

8.7 Prediction of Pond CT-1 using Centrifuge
Test Parameters .................................. 216

8.8 Measured and Predicted Void Ratio Profiles
for Pond CT -1 .................................... 218

8.9 Predicted Excess Pore Pressure Profiles
for Pond CT -1 .................................... 219

8.10 Measured and Predicted Excess Pore Pressure
Profiles at a Model Time of 2 hours for
Pond CT -1 ........................................ 221









8.11 Prediction of Pond CT-2/3 using Centrifuge
Test Parameters ..................................

8.12 Measured and Predicted Void Ratio Profiles
for Pond CT -2/3 ..................................

8.13 Prediction of Pond CT-6 using Centrifuge
Test Parameters ..................................

8.14 Prediction of Pond CT-5 using Centrifuge
Test Parameters ..................................

8.15 Measured and Predicted Excess Pore Pressure
Profiles for Test CT-5 ...........................

8.16 Measured and Predicted Void Ratio Profiles
for Pond CT -5 ....................................


- Two Positions of Pivoting Arm ..........

- Initial Inclination of Pivoting Arm....

- Response of Pressure Transducer No. 1..

- Response of Load Cell...................

- Radii rI and r2 for Transducer No. 1...

- Calibration Plot for Transducer No. 1..

- Radii rl and r2 for Transducer No. 2...

- Calibration Plot for Transducer No. 2..

- Radii rl and r2 for Transducer No. 3...

- Calibration Plot for Transducer No. 3..


.......... 244

.......... 24 5

. .. .. 2 52

.......... 253

.. .. .. 28 3

.......... 283

.......... 284

.......... 284

.......... 285

... ....... 285


xii


222


224


226


227


228


230


B.1

B.2

C. 1

C. 2

F. 1

F. 2

F. 3

F. 4

F. 5

F. 6















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



CONSOLIDATION PROPERTIES OF PHOSPHATIC CLAYS
FROM AUTOMATED SLURRY CONSOLIDOMETER
AND CENTRIFUGAL MODEL TESTS

By

RAMON E. MARTINEZ

December 1987



Chairman: Dr. Frank C. Townsend
Major Department: Civil Engineering



As a by-product of phosphate mining and other indus-

trial processes, a very dilute fine-grained slurry is pro-

duced, which consolidates over long periods of time in large

retention ponds. Numerical prediction of the magnitude and

time rate of settlement of these slurries requires a knowl-

edge of the effective stress-void ratio and the permeabil-

ity-void relationships of the material. The purpose of this

research was to develop equipment and techniques for deter-

mining these relationships by (1) performing automated

slurry consolidation experiments and (2) centrifugal model

tests.

An automated slurry consolidometer, which is fully

controlled by a computer-data acquisition system that


xiii









monitors load, pore pressure, total stress, and deformation,

was developed. The load is applied by a stepping motor.

Results from the tests conducted show the effectiveness of

the apparatus. The Constant Rate of Deformation test was

found to have several advantages over the Controlled

Hydraulic Gradient test and is recommended for future

applications; the results from both tests were consistent.

A "pseudo-preconsolidation" effect, attributed to the

initial remolded condition of the specimen, was observed in

both constitutive relationships. Thus, the curves are not

unique but depend upon the initial solids content. However,

different curves approach what seems to be a "virgin zone."

The compressibility relationship also was found to be

dependent upon the rate of deformation.

The technique using centrifugal modelling is based on

the measurement of pore pressure and void ratio profiles

with time, and the use of a material representation of the

specimen. The compressibility relationship obtained was in

good agreement with the results of CRD tests performed at a

slow rate of deformation. The permeability relationship

plotted parallel to the CRD curves, however, permeability

values were approximately a half order of magnitude higher.

Further research is required to explain this difference.

The constitutive relationships obtained in the study

were used to predict the behavior of hypothetical ponds

modelled in the centrifuge. A good agreement between

centrifugal and numerical models was found.


xiv















CHAPTER I
INTRODUCTION



Problem Statement

The production of phosphate fertilizers from Florida's

mines involves the excavation of approximately 300 million

cubic yards of material (overburden and matrix containing

the phosphate) annually. This is roughly equal to the

entire volume excavated during the construction of the

Panama Canal (Carrier, 1987). During the phosphate benefi-

ciation process, large amounts of water are used to wash the

matrix in order to separate the phosphate from the sand and

clay forming that layer. As a by-product of the process, a

very dilute fine-grained slurry is produced with very low

solids contents (weight of solids + total weight).

Florida's phosphate mines produce more than 50 million tons

of such waste clays annually (Carrier et al., 1983).

Disposal of these waste clays is accomplished by

storing them in large containment areas or ponds, and allow-

ing them to settle/consolidate over long periods of time.

During the initial sedimentation phase, the slurry reaches a

solids content on the order of 10-15% within a few weeks or

months, depending on several physio-chemical properties of

the material (Bromwell, 1984; Bromwell and Carrier, 1979;

Scott et al., 1985). Subsequently, a very slow process of








2

self-weight consolidation begins, which can require several

decades to achieve a final average solids content of

approximately 20-25%. Because of this time delay, research

efforts have been concentrated on the consolidation behavior

rather than the sedimentation phase of these slurries.

The design of the disposal areas, as well as the

estimate of time required for reclamation thereof, presents

a challenging problem to geotechnical engineers, who must

estimate the magnitude and time rate of settlement of the

slurry, as well as the final pond conditions. It has been

well established that conventional linear consolidation

theory is inappropriate for these materials (Bromwell, 1984;

Cargill, 1983; Croce et al., 1984; McVay et al., 1986).

This is primarily the result of the significant changes in

permeability and compressibility that occur as these

slurries consolidate to very large strains (Bromwell and

Carrier, 1979). Accordingly, large-strain nonlinear

consolidation theory has been used to model the self-weight

consolidation process of these soft, very compressible soil

deposits (see e.g. McVay et al., 1986), and several computer

codes have been written to predict their behavior applying

this theory (Cargill, 1982; Somogyi, 1979, Yong et al.,

1983; Zuloaga, 1986).

The use of large-strain consolidation theory requires a

clear definition of two constitutive relationships of the

slurry, namely, the effective stress-void ratio relation and

the permeability-void ratio relation. Unfortunately, our







3

capability of measuring accurately these soil properties has

not advanced as fast as our ability to represent the physi-

cal process by a mathematical model. The results of the

numerical predictions are very susceptible to these input

material properties, primarily the permeability relationship

(Hernandez, 1985; McVay et al., 1986). Comparison of

centrifugal and numerical predictions has found good agree-

ment on the magnitude of settlement. However, good predic-

tions of the rate of settlement require improvement in

laboratory input data, primarily the permeability relation-

ship (Carrier et al., 1983; Townsend et al., 1987).

Traditional consolidation tests are not suitable for

the study of the consolidation properties of highly com-

pressible clays, mainly because they rely on curve fitting

methods and small strain theory to characterize the consoli-

dation process. Although several attempts to develop large

deformation consolidation tests are reported in the litera-

ture, the Slurry Consolidation Test has emerged as one of

the most popular (Ardaman and Assoc., 1984; Bromwell and

Carrier, 1979; Carrier and Bromwell, 1980; Scott et al.,

1985). Unfortunately, the test, which is essentially a

large-scale version of the standard oedometer, suffers from

some drawbacks, among them its extremely long duration of

several months.

Alternative tests are being developed. These include

settling column tests, constant rate of deformation consoli-

dation tests, and others. Chapter II will discuss the








4

details of these tests. To date, however, there is no

standard approach that satisfactorily measures the compres-

sibility and permeability of very soft soils and soil-like

materials.



Purpose and Scope of the Study

The purpose of this research is to develop a technique

to determine accurately the compressibility and permeability

relationships of phosphatic clays and other slurries. To

achieve this objective, two approaches are followed. The

first one involves testing in a newly developed automated

slurry consolidometer, while the second involves centrifuge

testing. The automated slurry consolidometer should be

capable of (1) accommodating a relatively large volume of

slurry, (2) producing large strains in the specimen, (3)

allowing different loading conditions, (4) monitoring and/or

controlling load, deformation, pore pressures, and other

parameters, and (5) testing a wide range of solids content.

A major concern in the development of this consoli-

dometer was to avoid the use of any assumptions concerning

the theoretical behavior of the slurry in analyzing the

data. Instead, the adopted test method measures directly

many of the required parameters and computes others from

well accepted soil mechanics principles, such as the

effective stress principle and Darcy's law. This approach

to the problem is different from those attempted by others,

as will be discussed in Chapter II (literature review).








5

Chapter III describes in detail the test equipment and

procedure while Chapter IV presents the proposed method of

analysis of the test data. Chapter V presents the results

of several tests conducted on a Florida phosphatic clay.

The second approach used to obtain constitutive

relationships of the material is centrifugal testing. This

involves measuring pore pressure and solids content profiles

in a centrifuge model with time. The use of updated Lagran-

gian coordinates for a number of points along the specimen,

in conjunction with the previously described data, allows

the determination of the compressibility and permeability of

the slurry. Chapter VI describes the test procedure,

instrumentation, and method of data reduction. Chapter VII

presents the results of several centrifuge tests on the same

clay used in the slurry consolidation tests. A comparison

of the results of both approaches is also presented in this

chapter.

One of the main applications of centrifuge testing is

to validate the results of computer predictions (McVay et

al., 1986; Scully et al., 1984). In Chapter VIII the

constitutive relationships obtained in this research are

used to predict the behavior of a hypothetical pond. These

predictions are compared with the results of centrifugal

modelling. Finally, Chapter IX presents the conclusions and

suggestions for future research.















CHAPTER II
BACKGROUND AND LITERATURE REVIEW



Introduction

The main reasons for performing a consolidation

analysis are (1) to determine the final height of the

deposit (theoretically at t -) and (2) to evaluate the

time rate of settlement. Other information, such as pore

pressure or void ratio distributions at any time, can also

be obtained from the analysis. Of course, such an analysis

requires the determination of several consolidation proper-

ties of the soil. In traditional consolidation analysis,

the first of the two objectives is accomplished by knowing

the preconsolidation pressure and the compression index.

The second objective requires the determination of the

coefficient of consolidation.

Along with the development of his classical one-

dimensional consolidation theory, Terzaghi (1927) proposed

the first consolidation test, known today with minor

modifications as the step loading test and standardized as

ASTM D 2435-80. Since its first introduction, several

procedures have been proposed to analyze the data in order

to solve for the material properties; this is usually accom-

plished by a curve fitting procedure. The test has several

drawbacks, among them that it is time consuming and the








7

results are highly influenced by the load increment ratio

(Znidarcic, 1982). To overcome some of the limitations of

the step loading test, other testing techniques have been

proposed. Among the most popular are the Constant Rate of

Deformation test (Crawford, 1964; Hamilton and Crawford,

1959) and the Controlled Hydraulic Gradient test (Lowe et

al., 1969). The analysis procedure for these tests relies

on small strain theory to obtain the material properties.

Znidarcic et al. (1984) present a very good description of

these and other consolidation tests, with emphasis on their

different methods of analysis. They conclude that these

tests are limited to problems where linear or constant

material properties are good approximations of the real soil

behavior.

Consequently, conventional consolidation tests are not

suitable for very soft soils or slurries, which will undergo

large strains and exhibit highly nonlinear behavior. In

large strain theory the soil is characterized by two

constitutive relationships, namely, the effective stress-

void ratio relation and the permeability-void ratio rela-

tion, and not by single parameters such as the coefficient

of consolidation or the compression index.



Slurry Consolidation Laboratory Tests

Accordingly, there is a definite need to develop

testing techniques appropriate to study the consolidation

properties of soft soils and sediments. Lee (1979)








8

describes a number of early efforts (1964-1976) to develop

large deformation consolidation tests. He developed a

fairly complicated step loading oedometer, which monitored

the load, pore pressures, and deformation of a 4-inch

diameter and 6-inch high specimen. Interpretation of his

test data was based on a linearized form of the finite

strain consolidation theory, using a curve fitting construc-

tion analogous to the square root of time method in the

conventional oedometer. The test provided the stress-strain

relationship compressibilityy) and a coefficient of consol-

idation, which is assumed to be constant for a given load

increment. Permeability values could be obtained from this

coefficient of consolidation.

Lee introduced, in a special test, the use of a flow

restrictor in order to reduce the pore pressure gradient

across the specimen and approximate this to a uniform

condition. This allowed him to make direct computations of

the permeability. The test program conducted by Lee was on

specimens with initial void ratios in the order of 6.

Although some of the characteristics of Lee's apparatus are

valuable, the overall approach is probably not appropriate

for testing dilute slurries with initial void ratios of 15

or more.

A very popular test, most probably due to its relative

simplicity, developed specifically for testing very dilute

fine-grained sediments is the Slurry Consolidation Test

(Ardaman and Assoc., 1984; Bromwell and Carrier, 1979;








9

Carrier and Bromwell, 1980; Keshian et al., 1977; Roma,

1976; Scott et al., 1985; Wissa et al. 1983). The test is

essentially a large-scale version of the standard oedometer,

using a much larger volume of soil to allow the measurement

of large strains. The specimen diameter is usually in the

order of 10-20 cm and its initial height is 30 to 45 cm.

Slurry consolidation tests are usually conducted on speci-

mens with initial solids content near the end of sedimenta-

tion. The specimen is first allowed to consolidate under

its own weight, recording the height of the specimen

periodically. The average void ratio at any time is

computed from this height and the initial conditions.

Subsequent to self-weight consolidation, the specimen

is incrementally loaded and allowed to consolidate fully

under each load. Typical loading stresses begin as low as

0.001 kg/cm2 and increase, using a load increment ratio of

2, to values usually less than 1 kg/cm2 (Ardaman and Assoc.,

1984; Bromwell and Carrier, 1979). At the end of each load

increment, average values of void ratio and effective stress

are computed, leading to the compressibility relationship.

A typical test will last several months.

To determine the permeability relationship several

approaches can be used. First, a constant head permeability

test can be conducted at the end of each load increment.

However, in doing this, care must taken to minimize seepage-

induced consolidation, which is commonly accomplished by

applying very small gradients (Ardaman and Assoc., 1984;








10

Wissa et al., 1983), or by reducing the applied load to

counterbalance the tendency of the effective stress to

increase (Scott et al. 1985).

In a different approach, the coefficient of permeabil-

ity, k, at the end of each load increment is computed from

the coefficient of consolidation at 90% consolidation,

obtained from a square root of time method similar to the

conventional oedometer; this is given by (Carrier and

Bromwell, 1980)

k cy av Yw (2.1)
1 + ef



with cv T h(2.2)
t90

where ef = final void ratio

av = coefficient of compressibility de/dU'

hf = final height of specimen

t90 = elapsed time to 90% consolidation

T factor similar to the standard time factor, which

depends on the void ratio; typically 0.85 to 1.2.

Such an approach is based on a modified form of

Terzaghi's theory, obtained from finite strain computer

simulations of the slurry consolidation test (Carrier et

al., 1983; Carrier and Keshian, 1979). In some instances

(e.g. Ardaman and Assoc., 1984; Keshian et al., 1977; Wissa

et al., 1983), Terzaghi's classical theory is used directly

to backcalculate the permeability.

In a third approach, used during the self-weight phase

of the test, the permeability is obtained from the








11

self-imposed hydraulic gradient (Bromwell and Carrier,

1979). Of course, this approach requires very accurate

measurements of pore pressure, which is not a standard part

of the test; for example, for a 45-cm height specimen of a

typical phosphatic clay, with initial solids content of 16%,

the initial maximum excess pore is only about 0.07 psi.

In summary, the slurry consolidation test is a rela-

tively simple procedure to obtain the constitutive relation-

ships of diluted soils. However, it suffers from two major

drawbacks, specifically, its extremely long duration of up

to 6 to 7 months (Carrier et al., 1983) and the shortcoming

of partially relying on small strain theory to interpret the

test results.



Settling Column Tests

Several variations of self-weight settling column tests

have been used to study the settlement behavior of slurries.

Relatively small specimens have been used to study the end

of sedimentation conditions of very dilute sediments

(Ardaman and Assoc., 1984), to define the compressibility

relation of the material at low effective stresses (Cargill,

1983; Scully et al., 1984; Wissa et al. 1983) and the

highest possible void ratio of the material as a soil, i.e.

the fluid limit, (Scully et al., 1984), and in some cases,

even the permeability relationship (Poindexter, 1987). In

these tests, the compressibility relationship is readily

obtained from water content measurements with depth at the








12

end of the consolidation process. Determination of the

permeability, on the other hand, requires curve fitting

methods using a linearized version of the finite strain

consolidation theory.

Larger settling tests with specimen heights of up to 10

meters (Been and Sills, 1981; Lin and Lo, 1984; Scott et

al., 1985) are perhaps the best approach to study the

sedimentation/consolidation behavior of sediments. If

properly monitored, such tests can provide all the needed

characteristics of the slurry. Proper monitoring of the

test includes measurements of pore pressure and density

profiles with time. The approach, however, has major

limitations. Specifically, those tests on small and very

dilute samples only cover a small range of effective stress,

while the tests with large specimens would take so long that

they become impractical for any purpose other than research.



CRD Slurry Consolidation Tests

Perhaps, one of the most promising tests to study the

consolidation properties of slurries and very soft soils is

the constant rate of deformation (CRD) consolidation test.

The test is applicable over a wide range of initial void

ratios (ei 10-20) (Scully et al. 1984). Very large

strains can be achieved (up to 80%) and, compared to other

tests, it can be performed in a relatively short period of

time (in the order of one week) (Schiffman and Ko, 1981).

The test allows automatic and continuous monitoring and with








13

the right approach it can provide both, the compressibility

and permeability relationships, over a wide range of void

ratios.

To interpret the results of CRD tests, two different

philosophies can be followed. In one case, one could choose

to measure experimentally only those variables needed to

solve the inversion problem, i.e. obtain the material

characteristics from the governing equation, usually after

some simplifications, knowing the solution observed experi-

mentally; this would be the equivalent of the curve fitting

methods in conventional tests. For example, in the conven-

tional approach only the specimen height is monitored in the

test. By curve fitting techniques and the solution of the

governing equation, the coefficient of consolidation and

other properties, including compressibility and permeabil-

ity, are computed.

Alternatively, one could try to measure directly as

many parameters as possible and avoid the use of the

governing equation, reducing the number of assumptions

concerning the theoretical behavior of the material. For

example, measuring the pore pressure distribution in a

conventional oedometer could lead to the compressibility

curve by only using the effective stress principle. With

the rapid development in the areas of electronics and

instrumentation the use and acceptance of this last approach

will definitely grow.







14

The University of Colorado's CRD test (Schiffman and

Ko, 1981; Scully et al., 1984; Znidarcic, 1982) can be

classified in the first one of these categories. The test

uses a single-drained 2-inch specimen. The analysis

procedure neglects the self-weight of the material and

assumes the function g(e) to be piecewise linear in order to

simplify the governing equation (Znidarcic, 1982; Znidarcic

et al., 1986); this is given by


g(e) = k da' (2.3)
Yw(l+e) de

where 7w is the unit weight of water, e is the void ratio,

and the other terms have been previously defined.

The test only measures the total stress and pore

pressure at both ends of the specimen, as well as its

deformation. An iterative procedure using the solution of

the linearized differential equation, in terms of the void

ratio, yields the void ratio-effective stress relationship.

The permeability-void ratio relation can then be computed

from the definition of g(e). However, Znidarcic (1982)

found that this approach produced a 15%-30% error in the

computed values of g(e), and therefore the permeability;

this was for a case where the compressibility relationship

was accurate within 2%.

In an alternative method suggested to overcome the

above problem, the solution of the linearized governing

equation is used as before to obtain the compressibility

relationship. From the theoretical distribution of excess

pore pressure, the hydraulic gradient, i, at the drained







15

boundary can be determined. With this value the coefficient

of permeability is readily obtained from

k -v- (2.4)


where v is the apparent relative velocity at the boundary,

equal to the imposed test velocity; in this form, k is not

directly affected by errors in the calculated values of

g(e).

Due to the limitations of using consolidation tests to

obtain the permeability, Znidarcic (1982) stressed the

importance of a direct measurement using the flow pump test.

In this technique a known rate of flow is forced, by the

movement of a piston, through the sample and the generated

gradient is measured. This induced gradient must be small

(less than 2) in order to minimize seepage-induced consoli-

dation (Scully et al., 1984).

The flow pump test is used in conjunction with a step

loading test to generate the permeability-void ratio

relationship. This technique, however, is more appropriate

in the case of very stiff and permeable samples (Znidarcic,

1982), where no significant excess pore pressures would be

developed. It has been used for slurries at relatively low

void ratios (e < 8) (Scully et al., 1984), and soft samples

of kaolinite (e < 2.8) (Croce et al., 1984).

Znidarcic (1982) has also proposed the use of a

simplified analysis procedure to obtain the permeability

from a CRD test. If the void ratio and therefore the

coefficient of permeability are assumed uniform within the







16

specimen, then the pore pressure distribution is found to be

parabolic. This is justified in those cases where the test

produces very small but measurable pore pressures at the

undrained boundary. From here, the hydraulic gradient and

permeability are easily computed.

An important parameter in any CRD consolidation test is

the rate of deformation. This will determine the amount of

excess pore pressure that builds up in the specimen. Most

analysis procedures assume that the void ratio within the

sample is uniform. However, even when the weight of the

material is negligible, the pore pressure and the effective

stress are not uniform, due to the boundary conditions.

Thus, the assumption of uniform void ratio could never be

met. Nevertheless, it is desirable to keep the hydraulic

gradient small in order to minimize the error introduced by

the assumption. This can be achieved by running the test at

the lowest possible velocity. In the case of the small

strain controlled rate of strain consolidation theory (ASTM

D 4186), an estimate strain rate of 0.0001 %/minute is sug-

gested for soils with high liquid limits of 120%-140%; the

liquid limit of a typical phosphatic clay is even higher.

The test procedure specifies that the strain rate should be

selected such that the generated excess pore pressure be

between 3% and 20% of the applied vertical stress at any

time during the test. Unfortunately, there are no equi-

valent recommendations for the case of large deformation

consolidation tests. It has been suggested that an







17

acceptable deformation rate should produce a maximum excess

pore pressure of up to 30%-50% of the applied stress

(Znidarcic, 1982).

A variation of the CRD consolidation test was developed

at the U.S. Army Engineer Waterways Experiment Station (WES)

for testing soft, fine-grained materials (Cargill, 1986) and

to replace the use of the standard oedometer as the tool to

obtain the compressibility and permeability relationship of

dredged materials (Cargill, 1983). In this test, denoted

large strain, controlled rate of strain (LSCRS) test, a 6-

inch in diameter specimen of slurry is loaded under a

controlled, but variable, strain rate; the specimen height

can be up to 12 inches. The main reason for selecting a

controlled and not a constant rate of strain was to minimize

testing time to, typically, 12-16 hours (Poindexter, 1987).

The WES test monitors the pore pressure at 12 ports

along the specimen using 3 pressure transducers and a system

of lines and valves, with the associated problems of system

compliance and dearing. The effective stress at each end of

the specimen as well as its deformation are also measured

with time.

Analysis of the LSCRS data requires the use of the

results obtained from the small self-weight consolidation

test (Poindexter, 1987) in order to generate the compres-

sibility and permeability relationships. In the approach,

the first void ratio distribution in the specimen is

computed from the measured effective stress, using the








18

value of the compression index, Cc, obtained from the self-

weight test; at point i the void ratio is given by

ei eref Cc log(i/ref) (2.5)

where eref reference void ratio on the previously

determined e-a' curve

aref value of effective stress at eref

a' = effective stress for which ei is being

calculated

Between any two points where the void ratio is being

computed, the volume of solids, li, is given by

li = hi/(l + ei) (2.6)

where hi actual thickness of the increment

ei = average void ratio of the increment

Since the total volume of solids is constant throughout the

test, the calculated void ratio distribution is adjusted to

satisfy this condition. After this adjustment is done, the

compressibility curve is extended further by using the

average values of effective stress and void ratio of points

next to the moving end as the next reference point. The

process is repeated using the new measured data at increas-

ing loads.

Determination of the coefficient of permeability at the

moving boundary of LSCRS test is obtained from Darcy's law

using an expression equivalent to equation 2.4. In addi-

tion, the approach obtains the permeability at interior

points from an estimate of the apparent fluid velocity,








19

obtained from the equation of fluid continuity (Poindexter,

1987).

Many deficiencies have been found in the LSCRS test.

Because of the rapid rate of deformation, consolidation does

not occur uniformly throughout the specimen and a filter

cake of material forms at the drained boundary. Additional-

ly, the analysis of the test data requires a trial and error

procedure which depends on the results of a self-weight test

to provide a starting point. Last, but not least, the test

equipment is extremely complicated and requires frequent

manual adjustment and monitoring. WES is currently working

on the development of a new test device and procedure

(Poindexter, 1987) to replace the LSCRS test; it will be a

constant rate of strain apparatus and the test is expected

to last from 5 to 10 days. Automatic controlling and

monitoring, through a computer/data acquisition system, will

be incorporated in the test.

Conventional consolidation tests, such as the step

loading test or the CRSC test are very frequently used to

complement the results of large-deformation consolidometers

(Ardaman and Assoc., 1984; Cargill, 1983; Poindexter, 1987;

Wissa et al., 1983). In some cases, conventional testing

methods and analysis procedures have been used exclusively

(Cargill, 1983). These tests are usually conducted on

preconsolidated specimens to facilitate handling and trim-

ming. Such tests will provide information on the behavior








20

of the material at relatively low void ratios (e < 7)

(Ardaman and Assoc., 1984).



Centrifugal Modelling

Centrifugal modelling has been used quite extensively

to predict the consolidation behavior of slurries under

different disposal schemes (Beriswell, 1987; Bloomquist and

Townsend, 1984; McClimans, 1984; Mikasa and Takada, 1984;

Townsend et al., 1987). Several attempts have been made to

determined the soil's constitutive relationships from

centrifuge testing (Croce et al., 1984; McClimans, 1984;

Townsend and Bloomquist, 1983) with relatively good results

obtained in the case of effective stress-void ratio rela-

tion. Perhaps, one of the most valuable applications of

centrifugal modelling is to validate computer predictions

(Hernandez, 1985; McVay et al., 1986; Scully et al., 1984).

The main advantages of centrifugal modelling in the

study of the consolidation behavior of slurries are (1) the

duplication in the model of the stress level existing in the

prototype and (2) the significant reduction in the time

required to achieve a given degree of consolidation in the

model. This is given by

tm tp/nx (2.8)

where tm elapsed time in the model

tp = elapsed time in the prototype

n acceleration level in number of g's

x time scaling exponent







21

A major problem with centrifugal modelling is the

determination of the time scaling exponent, x. Theoretical-

ly, this exponent is 1.0 for sedimentation and 2.0 for

consolidation. In Appendix A a proof is presented where the

governing equation of the finite strain self-weight consoli-

dation theory holds in the model if and only if x = 2. A

different proof of this result, based on mechanical simila-

rity, is given by Croce et al. (1984).

However, experimental results based on modelling of

models and reported by several researchers indicate somewhat

contradictory conclusions. An exponent of 2.0 has been

confirmed for the centrifugal modelling of the consolidation

of soft kaolinite clay with a relatively low initial void

ratio of 2.86 (Croce et al., 1984). Scully et al. (1984)

found that the time scale exponent varied from 1.90 to 2.3

for a slurry with initial void ratio of 15; they concluded

that the exponent could be assumed to be 2.0 and that

sedimentation probably did not occur in the tests.

By contrast, the results of Bloomquist and Townsend

(1984) show that starting with an initial void ratio of 16,

the scaling factor progresses from 1.6 to 2.0. They

attributed these values to the existence of two zones in the

slurry, hindered settlement and consolidation. As these

zones approach, consolidation predominates and the theoreti-

cal exponent of 2.0 is achieved; this occurred at an average

solids content of 20.9% (e = 10.3), practically at the end

of the test.







22

Constitutive Properties

One of the basic assumptions of any of the formulations

of large strain consolidation theory is that the soil's

constitutive relationships are of the general form (e.g.

Cargill, 1982)

a' = ao'(e) (2.7a)

k = k(e) (2.7b)

and that they are unique for a given material. Equation

2.7a determines how much consolidation will take place,

while equation 2.7b describes how fast this will happen.

Roma (1976) reported that the best compressibility

relationship for phosphatic clays was a power curve of the

form

e A.(a')B (2.8)

Likewise, the permeability relationship was expressed by the

function

k = C.(e)D (2.9)

Traditionally, it has been accepted that phosphatic clays

can be characterized by these relationships (Ardaman and

Assoc., 1984; Carrier and Bromwell, 1980; Somogyi, 1979),

and very little effort, if any, has been dedicated to

corroborate the validity of such relationships. This may be

attributed, in part, to the convenience presented by the

simplicity of the expressions and, just maybe, to the bad

habit or tradition of geotechnical engineers to stay with

the "status-quo."







23

The parameters A,B,C,D obtained by several studies for

Kingsford phosphatic clay are presented in Table 2-1.


Source

Ardaman and

Somogyi et

Carrier et

McClimans (

Townsend/Bl


Table 2-1. Kingsford Clay Parameters

A B

Assoc. (1984) 26.81 -0.269 7.

al. (1984) 23.00 -0.237 1.

al. (1983) 24.36 -0.290 1.

1984) 19.11 -0.187 7.5

oomquist (1983) 22.30 -0.230 2.


These parameters are for a' in psf and k in ft/day.

Ardaman and Assoc.'s parameters are based on slurry consoli-

dation tests and conventional CRSC and incremental loading

tests. Somogyi et al. parameters were obtained from

laboratory slurry consolidation tests and CRSC tests, as

well as field data.

The parameters attributed to Carrier et al. (1983) were

obtained from the constitutive relationships proposed by

them in terms of the Atterberg limits of the clay, as

preliminary design properties. These relationships, for a

specific gravity of the solids of 2.7, are given by

e = (0.48PI)(a')-0.29 (2.10a)

k (2.57PI)-4.29(e)4.29/(l+e) (2.10b)

where PI is the plasticity index in percentage, a' is in

kPa, and k is in m/sec. Using a plasticity index of 156%

reported for this clay (Ardaman and Assoc., 1984; McClimans,


C

74E- 7

03E-6

34E-6

9E-14

03E-9


D

3.56

4.19

3.41

11.12

7.15








24

1984), a number of data points with void ratios between 5

and 15 were generated. A log-log linear regression, with

very high correlation coefficients, led to the parameters

given in Table 2-1 after the necessary units conversion.

Finally, McClimans' and Townsend and Bloomquist's parameters

were obtained by back-calculations from selected centrifugal

tests.

Table 2-1 shows a tremendous discrepancy in the parame-

ters defining the constitutive relationships, mainly in

those corresponding to the permeability-void ratio relation.

This can be the result of improper testing techniques, the

relationships not being unique, or both.

The use of the power functions in computer predictions

introduces an important inconsistency. Under quiescent

conditions, for example, the slurry is deposited at a known

and usually constant solids content. According to equation

2.8, the material must have an initial effective stress

throughout its depth. This implies two things; first, the

initial excess pore pressure will be less than the buoyant

stress and, second, the points at the surface will have an

effective stress which does not exist. The computer

programs overcome this inconsistency by imposing on the pond

a dummy surcharge equal to the initial effective stress

(Somogyi, 1979; Zuloaga, 1986).

The results of several studies suggest that the

constitutive relationships of slurried soils not only are

not power curves, but also are not unique. Specifically,








25

variations in the compressibility relations have been

observed in different soils, especially at low effective

stresses (Been and Sills, 1981; Cargill, 1983; Imai, 1981;

Mikasa and Takada, 1984; Scully et al., 1984; Umehara and

Zen, 1982; Znidarcic et al., 1986). These variations have

been attributed by some to the effect of the initial void

ratio.

Scully et al. (1984) reported the existence of a

"preconsolidation" effect in the compressibility curves

obtained from CRD tests; they concluded that this effect was

most probably the result of the initial void ratio. Similar

results on the permeability-void ratio relation have not

been specifically reported. However, the curves presented

by several researchers suggest the existence of a zone

similar to the apparent preconsolidation effect observed in

compressibility curves (Scully et al., 1984; Znidarcic,

1986).

Another important aspect that may be conclusive to

better understand the consolidation behavior of slurries is

their initial conditions when they are first deposited.

Scott et al. (1985) found in their large settling column

tests that, when the material was first placed in the

cylinders, the pore pressures were equal to the total

stresses over the full height. A similar response was

observed in samples with initial solids content of 10% and

31%. In the case of the denser specimen, a uniform decrease

in pore pressure was observed in 30 days, when no







26

significant consolidation had taken place; this was attri-

buted to the appearance of an effective stress by

thixotropy. Thus, these results indicate that the slurry

has no effective stress when deposited, regardless of its

initial solids content. If this is the case, the compressi-

bility relationship can not be unique, at least initially.















CHAPTER III
AUTOMATED SLURRY CONSOLIDOMETER--
EQUIPMENT AND TEST PROCEDURE



Introduction

This chapter describes the test equipment and procedure

of a new automated slurry consolidation test, developed

specifically to obtain the compressibility and permeability

relationships of slurries and very soft soils. Figure 3.1

shows a schematic arrangement of the equipment, which con-

sists of the following components:

1) test chamber,

2) stepping motor,

3) data acquisition/control system.

The following sections describe in detail each one of these

components. At the end of the chapter, the test procedure

is presented.



The Test Chamber

The specimen of slurry is contained in an acrylic

cylinder with a diameter of 0.2 meters (8 inches) and 0.35

meters (14 inches) height. Figure 3.2 is a schematic of the

test chamber. The initial height of the specimen can be

varied between 0.10 and 0.20 meters (4-8 inches).

A double-plate piston is used to apply the load on the

specimen; the two plates, 3.75 inches apart, help prevent

27









Motor Motor
Power Supply Manual Control
1- --LT


Gear Box
Stepping
-Motor


Figure 3.1 Schematic of Automated Slurry Consolidometer


Load Cell
Pivoting Arm
Loading -
Piston
T
LVDT
Power Connection T
Suppl Box T


T: Transducer



































I I ., LVDT







Su0y suPPLY J SI
to t I- IF= =












DIMENSIONS IN INCHES

Figure 3.2 Schematic of Slurry Consolidometer Chamber








30

tilting of the piston. At the bottom of the piston, a

porous plastic plate allows top drainage of the specimen. A

filter cloth, wrapped around the bottom plate, closes the

small, nonuniform gap between the piston and the walls of

the cylinder, while allowing water to drain freely.

Originally, this gap was filled with a rubber 0-ring around

the bottom plate; however later, it was found that the

filter cloth served the function better and reduced the

piston friction.

Located directly on top of the piston rod, a load cell

measures the load acting on the specimen at any time. Two

load cells, 200-lb and 1000-lb range, both manufactured by

Transducers, Inc. have been used in this research.

Along the side of the acrylic cylinder, two 1-bar (1

bar 100 kPa = 14.5 psi) and one 20-psi miniature pressure

transducers are used to monitor the excess pore pressure in

the specimen. Transducer No. 1 is located 1.235 centimeters

from the bottom of the chamber. Transducers No. 2 and No. 3

are placed 5 centimeters above the previous one. An add-

itional 350-mbar (5 psi) transducer (No. 4), located on the

moving piston, is used to detect any excess pore pressure

building up at the supposedly free-drainage boundary. The

transducers were mounted inside an 0-ring sealed brass

fitting, which threads directly onto the wall of the

chamber. Locating the transducers directly in contact with

the specimen eliminates the problems of tubing, valves, and

system dearing.








31

All the pressure transducers used in the test are model

PDCR 81, manufactured by Druck Incorporated, of England.

They consist of a single crystal silicon diaphragm with a

fully active strain gauge bridge diffused into the surface.

These transducers are gage transducers, thus eliminating the

potential problem of variations in atmospheric pressure,

with a combined nonlinearity and hysteresis of 0.2% of the

best straight line. To resist the effective stress of the

soil, i.e. only measure pore pressure, a porous filter plate

or stone is placed in front of the diaphragm. The standard

porous stone is made of ceramic with a filter size of 1-3

microns; a 9-12 microns sintered bronze stone is also

available. Figure 3.3 shows a photograph of the PDCR 81 and

a sketch indicating its dimensions.

At the bottom of the specimen another pressure trans-

ducer (3-bar range), without the porous stone, is used to

measure the total vertical stress at this point. This

measurement, coupled with the load cell readings, makes it

possible to determine the magnitude of the side friction

along the specimen.

A major objective during the design phase of the

equipment was to make it fully automatic. This presented an

obstacle when trying to define the best way to measure the

specimen deformation, which was anticipated to be up to 4-6

inches. The problem was solved using a Direct Current

Linear Variable Differential Transformer (LVDT) and the

pivoting arm arrangement shown in Figure 3.2. The LVDT,







































(a)


DIMENSIONS: MM


POROUS ELECTRICAL CONNECTION
DISC RED: SUPPLY POSITIVE
BLUE: SUPPLY NEGATIVE
YELLOW: OUTPUT POSITIVE
GREEN: OUTPUT NEGATIVE


(b)

Figure 3.3 Pore Pressure Transducer PDCR81. a) Photograph;
b) Sketch Showing Dimensions







33

model GCD-121-1000 and manufactured by Schaevitz, has a

nominal range of 1 inch and linearity of 0.25% at full

range.

The horizontal distances from the pivoting point of the

arm to the center of the specimen and to the LVDT tip were

accurately measured as 121.2 mm and 35.6 mm, respectively,

which resulted in an arm ratio of 1:3.40. This arrangement

allows measuring specimen deformations over 6 inches. The

factory calibration of the LVDT was converted using the arm

ratio to yield directly the deformation of the specimen.

Appendix B evaluates the converted calibration of the LVDT

and proves that computations of the deformation are indepen-

dent of the initial inclination of the arm.

Figure 3.4 is a photograph of the test chamber showing

the pressure transducers, the loading piston, the LVDT, and

the pivoting arm. Table 3.1 summarizes the information on

the different devices. The recommended excitation for

these transducers is 5 VDC, but this was increased to 10

VDC, the maximum allowed, to improve the transducer sensi-

tivity. Although the 200-lb load cell was used in most of

the tests, the information on the 1000-lb load cell is also

included since this was used in some tests where the load

was expected to be large.






















































Figure 3.4 Photograph of Slurry Consolidometer Chamber


































00 )00 )0
00 rr40 00









--4 -4 -4








W 4 -1-4



0V


00 Lt) 14-4
(71%0'0C% -
CJeCs'Cc*i


0000
0QQQ
PL|CL A AL


-4 -4

E 2





00 C\ r-4
ON- -4


0 0


0'C

0'
In~ .
U U















C-4
00








-4 ~
04 40 1









~0C\J I1




I~0



C\C'J C1
-4 0-0 1=




0 F


r--( CN M * u u

:L4 P64 C4 a
:3: 1-- :: ::
P14 rW a4 OL4







36

The Stepping Motor

The load applied to the specimen is produced by a

computer-controlled stepping motor and a variable speed

transmission arrangement, located as shown in Figure 3.1.

The stepping motor is a key element of the apparatus; its

versatility is crucial in allowing different types of

loading conditions.

The stepping motor is manufactured by Bodine Electric

Company, model 2105, type 34T3FEHD. It operates under 2.4

VDC and 5.5 amps/phase. The motor has a minimum holding

torque of 450 oz-in and a SLEW (dynamic) torque of 400 oz-

in, producing 200 steps per revolution or 1.8 degree per

step.

The motor is driven by a THD-1830E Modular Translator,

model No. 2902, also made by Bodine. The translator uses

and external 24 VDC power supply. The photograph of Figure

3.5 shows the front panel of the translator (left), and the

stepper motor (right), while Figure 3.6 presents a schematic

diagram of the back of the instrument with the cover

removed, showing the connections to the stepping motor. For

this configuration, the following resistances are required

Suppression Resistor: R1 13 ohms @ 18W

Series Resistors (2): R2 3.6 ohms @ 175W

Logic Resistor: R3 15 ohms @ 2W

All control line connections to the stepping motor control

card are made through a 15 pin "D" connector, located on the

side of the translator. For manual (front panel) control of





















































Figure 3.5 Motor Translator, Gear Box, and Stepper Motor


















LLU


Cl
w
I
...
...

O








39

the motor, pins 6 and 13 of the connecter are jumped. A

switch that allows this jumping was installed next to the

translator. In this way the control of the motor can be

easily switched between manual and computer. Manual

operation of the motor is very important during setting up

and dismantling of the test.

The variable speed transmission (gear box), made by

Graham, converts the motor rotation into vertical movement

of a threaded rod, which acts directly on the loading piston

(Figure 3.5). Even if the motor is running at full speed,

the gear box allows minute movement of the loading piston.

During the testing program, the speed control of the gear

box was set at its maximum, producing a vertical displace-

ment in the order of 3E-05 mm/step. Figure 3.5 also shows

the load cell at the bottom of the threaded rod.

Figure 3.7 shows a photograph of the entire test

assembly. The equipment was mounted on a steel frame.



The Computer and Data Acquisition/Control System

Figure 3.8 shows a photograph of the computer system

used to control and monitor the test. The computer is a

Hewlett Packard, model 86B, with 512 KB of memory and a

build-in BASIC Interpreter.

The data acquisition/control system has two components:

an HP-3497A and an HP-6940B, both manufactured by Hewlett

Packard. The HP-3497A, a state-of-the-art data acquisition

and control unit, is used to monitor the pressure



















































Figure 3.7 Entire Slurry Consolidometer Assembly







41

transducers, load cell, and LVDT outputs. The unit can be

remotely operated from the computer or through the front

panel display and keyboard.

The 3497A Digital Voltmeter (DVM) installed in the unit

is a 5 digit, 1 microvolt sensitive voltmeter. Its

assembly is fully guarded and uses an integrating A/D

conversion technique, which yields excellent noise rejec-

tion. Its high sensitivity, together with autoranging and

noise rejection features, makes it ideal for measuring the

low level outputs of thermocouples, strain gauges and other

transducers. The DVM includes a programmable current source

for high accuracy resistance measurements when used simulta-

neously with the voltmeter.

The 3497A DVM assembly is very flexible and can be

configured to meet almost any measurement configuration. It

may be programmed to obtain a maximum of 50 readings per

second in 5 digit mode or 300 readings per second in 3

digit mode. The 3497A DVM may be programmed to delay before

taking a reading to eliminate any problem with settling

times. Similarly, the DVM assembly can be programmed to

take a number of readings per trigger with a programmable

delay between readings. This feature, combined with

internal storage of sixty 5 digit readings, permits easy

stand-alone data logging.

Installed in the 3497A, there is a 20 channel analog

signal reed relay multiplexer assembly. This assembly is

used to multiplex signals to the 3497A DVM. Each channel



















































Figure 3.8 Computer and Data Acquisition/Control System








43

consists of three, low thermal offset dry reed relays, one

relay each for Hi, Lo and Guard. The low thermal offset

voltage characteristics of this multiplexer makes it ideal

for precise low level measurements of transducers. The

relays may be closed in a random sequence or increment

between programmable limits.

The other component of the data acquisition/control

system, the HP-6940B Multiprogrammer, provides flexible and

convenient Input/Output expansion and conversion capability

for computers. This versatility has made the Multiprogram-

mer an important part of many different types of automatic

systems, including production testing, monitoring and

control (e.g. Litton, 1986). In the current application,

however, the 6940B, interfaced to the computer through the

HP-59500A Multiprogrammer Interface, is used exclusively to

control the stepping motor.

A stepping motor control card, model 69335A, was

installed in the Multiprogrammer. The card is programmed by

a 16-bit word originating at the computer to generate from 1

to 2047 square wave pulses at either of two output terminals

of the card. When these outputs are connected to the

clockwise and counterclockwise input terminals of the

stepping motor translator, the output pulses are converted

to clockwise or counterclockwise steps of the associated

motor. As the card is supplied from the factory, the output

is a waveform of positive symmetrical square-wave pulses

with a nominal frequency of 100 Hz. If this frequency is








44

not suitable, it can be changed to any value between 10 Hz

and 2 kHz by changing the value of one resistor and one

capacitor in the card. The output frequency can also be

made programmable by connecting to the card an external

programmable resistor.

During early stages of the research, the Multiprogram-

mer was also used to monitor all the devices by means of

Relay Output/Readback and High Speed A/D Voltage Converter

cards, as used by Litton (1986). Electrical noise rejection

in the low level outputs of the pressure transducers and

load cell was attempted by means of analog low pass filters

(Malmstadt et al., 1981). Several preliminary tests were

performed using this hardware configuration, whereby each

transducer output was obtained as the average of 10-20

individual readings, to further reduce any noise. It was

found, however, that the level of noise in the response was

still unacceptable. Therefore, it was decided to undertake

a detailed investigation of the transducers response using

different size capacitors. In addition, the use of digital

filters (Kassab, 1984) was incorporated, and the HP-3497A

was tried for the first time, as an alternative to the

Multiprogrammer. Appendix C describes the study undertaken.

It was concluded, as a result of the study, that the HP-

3497A would be used to monitor all transducers. In the case

of the LVDT, the output is not affected so much by noise.

However, it was decided to change it to the HP-3497A also







45

and to leave the HP-6940B exclusively to control the

stepping motor.



The Controlling Program

The program that controls the test, called SLURRY1, was

written in BASIC for the HP-86B. It is a user-friendly

program and presently allows two types of test: a Constant

Rate of Deformation test (CRD) and a Controlled Hydraulic

Gradient test (CHG). However, other types of loading

conditions can be very easily incorporated in the program,

such as constant rate of loading, step loading, etc.

In the CRD test, the program sends a signal to the

stepper motor every half-second to turn forward a given

number of steps, corresponding to the desired rate of

deformation. A calibration between number of steps and

vertical displacement of the piston was made for the gear

box speed set at its maximum value; the value obtained was

30,000 steps/mm. Based on this value, the two deformation

rates used in the testing program correspond to the motor

speeds given in Table 3-2.



Table 3-2. Deformation Rates in CRD Tests

Deformation Rate (mm/min) Steps/min

0.008 240

0.02 600







46

In the CHG test, the excess pore pressures at the

bottom and top of the specimen, as well as the specimen

deformation, are continuously monitored. The average

hydraulic gradient across the specimen is computed from this

information. If the gradient differs from the desired value

by more than a defined percentage, the motor is activated

forward or backward accordingly to keep the gradient within

the desired range. The required number of steps at any

moment is estimated from the previous value of number of

steps per unit change in gradient. The experience with the

tests performed in this study shows the effectiveness of

this approach.

SLURRY1 is organized in a main program and several

subroutines. The main program reads the input information

and contains the two routines that control the CRD and CHG

tests, as described previously. Eight subroutines interact

with the main program to perform the operations described

below.

Subroutine CALIBRATIONS reads the calibration factors

for all the devices from a file on disk; it allows changing

or adding new devices to the file, after displaying the

current configuration on the monitor. Subroutine INITIALI-

ZATION takes the initial readings of the transducers and

LVDT; it also prints the general test information and

headings of the results table.

Subroutine STEPPING activates the motor as requested

by either the CRD or CHG routines. Subroutine RUNTIME







47

evaluates the elapsed time of the test at any moment.

Subroutines READLOWVOLT and READHIGHVOLT read consecutively

all the devices.

Subroutine CONVERTDATA uses the readings of the

transducers and LVDT, and their calibrations, to compute all

the pressures, load, and specimen deformation; these

parameters are stored on disk for future data reduction.

Subroutine TESTEND decides whether any of the conditions to

finish the test has been reached. Appendix D presents a

flowchart of the main routine of SLURRY1, and a listing of

the full program.



Test Procedure

The test, being controlled by the computer, runs by

itself without any human assistance. However, setting up

the apparatus requires 2 to 3 hours and is somewhat compli-

cated. This section describes details of the test proce-

dure.

In broad terms, the test procedure consists of the

following steps: (a) specimen preparation, (b) deairing and

calibration of the pressure transducers, (c) filling the

chamber with slurry and adjusting the load cell and LVDT,

(d) initiating computer control, (e) reading devices

periodically, (f) coring specimen at the end of the test,

and (g) reducing data.

The specimen is prepared in a 5 gallon plastic bucket

just before the beginning of the test. The slurry is







48

strongly stirred with an egg beater attached to an electri-

cal drill, to provide a uniform solids content. To reach

the desired value of solids content, quick determinations of

this value were made using an Ohaus Moisture Determination

Balance. This turned out to be a very handy tool. If

needed, water or thicker slurry was added to the mix to

achieve the desired solids content. Due to the lack of

available supernatant water in sufficient amount, tap water

was used in most of the tests. Two samples were always used

to perform a regular water content determination, from which

the initial solids content was determined. It was found

that the solids contents obtained with the Moisture

Determination Balance were always within 0.5% of the oven-

determined values.

An important part of the test preparation procedure is

the vacuum system shown schematically in Figure 3.9. This

is used to fill the test chamber with deaired water to

produce full saturation of the porous stones and to take the

zero readings of the pore pressure transducers (under

hydrostatic conditions). The operation of the vacuum system

is controlled by a series of four 3-way valves, used as

described in the following paragraph.

Water is sucked into the chamber by turning the vacuum

pump on with all four valves in the 'a' position. The water

can be drained out of the chamber by gravity. However, the

process is accelerated by pulling the water with vacuum with

valves 1 and 3 in the position 'b', and valves 2 and 4 in











6 VENT
VALVE 3


a





SL URTER

_ SLURRY


TO VACUUM
PUMP


6 a
VALVE E


Figure 3.9 Vacuum System


Table 3-3.

Operation

Fill with water

Drain water

Fill with slurry


Valve Positions in Vacuum System

Valve 1 Valve 2 Valve 3 Valve 4

a a a a

b a b a

a b a a,b


VALVE 1


~6b VENT


VALVE 4



WATER


SLURRY


190


C-4


I


VRLVE E


|







50

the position 'a'; toward the end of this process, however,

care must be exercised to prevent the entrance of air into

the water container. To avoid this, the vacuum pump is

turned off and valve 4 is vented (position 'b') when most of

the water has been drained; the remaining will drain by

gravity. The vacuum system is also used to fill the chamber

with slurry prepared in a container at the desired solids

content. To do this, valves 1 and 3 must be set to the

position 'a', while valve 2 is on the 'b' position. Table

3-3 summarizes the valve positions required for each

operation.

The following is a list of the steps followed in the

test procedure:

1. Assemble the vacuum system, set the piston to the sample

height, and pull deaired water into the chamber.

2. Turn on the transducers power supply and HP-3497A; check

the supply voltage of 10 Volts by reading it from the front

panel of the HP-3497A. Allow a warming up time of 10-15

minutes.

3. Apply full vacuum to the chamber to deair the porous

stones; check how fast the transducers respond by turning

the vacuum on and off several times.

4. Check the calibration of all five transducers by raising

(or lowering) the height of water by 10 cm and taking the

corresponding voltage readings using the front panel of the

HP-3497A; the computed change in height of water must be 10

1 cm.







51

5. Set the height of water to the height to be used in the

test.

6. Run the program SLURRY1 and enter the required data

(sample height, initial solids content, etc.); the program

will take the zero readings of the pore pressure transducers

at this point.

7. When prompted by the program, drain the water and pull

the slurry into the chamber using the vacuum system; check

that the piston is at the right height. The program has

paused at this moment.

8. Take the vacuum attachment off and set the motor control

switch to "manual".

9. Set up the load cell by operating it manually, the LVDT,

and the pivoting arm.

10. Add water over the piston to reach the desired height

(usually 11 cm. over the slurry height), as used for the

zero readings; this is done to guarantee that the piston is

always submerged.

11. Change the motor control to "computer" and check that

the LVDT power supply is on.

12. After everything has been verified press the "CONT" key

to resume the computer control of the test.

13. SLURRY1 prints heading of the output printout and the

test starts.

From this moment the control and monitoring of the test

is completely taken by the computer. Readings of the

different devices are taken periodically as specified by the







52

user. The time of reading, pressures, load, and specimen

deformation are stored on a disk file specified by the user,

for future data reduction. The test stops automatically

when the maximum time specified is reached. Termination of

the test also occurs when any of several abnormal conditions

occurs, such as exceeding a pressure transducer or the load

cell.

Once the test is completed and the chamber attachments

have been removed, the supernatant water is removed and the

specimen is cored using a device similar to that used by

Beriswill (1987) in his centrifuge bucket. The cored

material was sectioned into three pieces to determine the

solids content near the top, at the middle, and near the

bottom of the specimen. Due to the difficulties in obtain-

ing a good sample, no attempt was made to determine the

solids content-depth relationship. An average final solids

content was determined from these three values.

The allowed deviation in the transducers response,

recommended in step 4 of the test procedure, is the result

of observations about the transducers sensitivity during the

testing program. Table 3-4 shows the results of one pre-

test verification of the calibration/sensitivity of all five

pressure transducers.

With water in the test chamber, a set of readings, R1,

was taken using the front panel of the HP-3497A. The height

of water was then increased by exactly 10 cm, and new

readings were taken, R2. With these values and the factory







53

Table 3-4. Verification of Transducer Calibration

Transducer R1 R2 Calibration Ap Ah
No. (mV) (mV) (mV/psi) (psi) (cm)
T.S. -1.586 -2.115 3.568 0.1483 10.43
1 -17.610 -18.568 6.370 0.1504 10.58
2 -22.856 -24.002 7.418 0.1545 10.87
3 9.363 8.364 6.900 0.1448 10.18
4 8.698 6.970 12.800 0.1350 9.50



calibration factors, the change in hydrostatic pressure, Ap,

was computed. Assuming the unit weight of water as 62.4

pcf, the change in the height of water, Ah, was computed.

Four of the five transducers gave heights above 10 cm,

with a maximum deviation of 0.87 cm for transducer No. 2.

Surprisingly, in this test the total stress transducer (3-

bar range) did not produce the maximum deviation, and pore

pressure transducer No. 4 (5-psi range) did not produce the

minimum. In the case of the total stress transducer, where

similar results were observed in other tests, the low

deviation was attributed, at least partially, to the

beneficial effect of not having the porous disc. The

relatively large deviation of pore pressure transducer No. 4

is probably the result of the random nature of the varia-

tion. In another test, for example, the same transducer

gave a deviation of only 0.024 cm when the height of water

was increased by 10 cm.

These observations led to the conclusion of allowing a

deviation of 1 cm, when checking the calibration of the

transducers prior to the test. One centimeter of water







54

(0.014 psi) is taken as the approximate sensitivity of these

pressure transducers.















CHAPTER IV
AUTOMATED SLURRY CONSOLIDOMETER--
DATA REDUCTION



Introduction

A main objective during the development of this new

test was to make direct measurements of as many variables as

possible, in order to minimize the use of theoretical

principles or assumptions. The formulation of the two

constitutive relationships required in finite strain

consolidation theory involves three variables, namely, void

ratio, effective stress, and coefficient of permeability.

Direct measurement of these parameters is not feasible.

Instead, they will be evaluated from well accepted soil

mechanics principles, such as Darcy's law and the effective

stress principle, using the measured values of load, excess

pore pressures, specimen deformation, and others.

The following sections describe the proposed method of

data analysis to obtain the constitutive relationships of

the slurry. In the analysis, the specimen is treated as an

element of soil with uniform conditions, although it is

recognized that the void ratio and other parameters change

with depth mostly due to the boundary conditions. This

assumption was necessary due to the lack of a proper method

to measure this variation. Thus, the specimen will be

characterized by average values of void ratio, effective

55







56

stress, and coefficient of permeability. If certain condi-

tions of the test are controlled, the errors introduced by

this assumption can be minimized as will be discussed later

in this chapter.



Determination of Void Ratio

A direct evaluation of the void ratio in a sample of

soil is not usually possible since volumes are not easily

measured. Instead, the void ratio is most commonly obtained

from unit weights and the use of phase diagram relation-

ships. In the slurry consolidometer, however, an average

value of void ratio can be readily obtained from the

specimen height and the initial conditions.

Figure 4.1 shows the phase diagrams of the specimen

initially and at any later time, t. Two assumptions are

made at this point, namely, that the slurry is fully

saturated and that the volume of solids in the specimen, Vs,

does not change throughout the test. Both of these assump-

tions can be made with confidence.

From Figure 4.1a, the total volume of specimen at the

beginning of the test can be expressed as

A.hi (1 + ei)-Vs (4.1)

where A is the cross section of the specimen, hi is the

initial height, and ei is the initial void ratio.

At time t (Figure 4.1b), the height of the specimen has

been reduced to h, due to the compression of volume of voids

AV. The volume of the specimen is now

















Cu
U)
*i-.





C

0
*I-I




.C-
r-
0





0







Cu
0







U)




0)
i-i





'-4
*r-

.C

i-(
D


o 0
Cl


i^_ ^ ^ ^^ ^ ^ ^ ^


/ "
o ..J





g-- --

_______ ^ / /







58

A.h (1 + e)-Vs (4.2)

where e is the new void ratio.

Dividing equation 4.2 by equation 4.1 and solving for

the void ratio leads to

e (h/hi).(l+ei) 1 (4.3)

considering that both A and Vs are constant.

The phosphate industry uses the term solids content, S,

to describe the consistency of the slurry. This is defined

as

S(%) (Ws/Wt).100 (4.4)

where Ws is the weight of solids, and Wt is the total

weight. It can be easily shown that this is related to the

water content by the relation

S(%) 100/(1 + w) (4.5)

where w is the water content in decimal form.

From phase diagrams, it is easily proved that

Sre Gs.w (4.6)

where Sr is the degree of saturation, and Gs is the specific

gravity of the solids.

Combining equations 4.5 and 4.6, for a degree of

saturation of 100%, leads to a useful relationship between

the void ratio and the corresponding solids content of the

slurry. This is


S(%) 100.Gs/(Gs + e)


(4.7)







59

Determination of Effective Stress

The evaluation of an average value of effective stress

involves a large number of variables, including the applied

load, specimen weight, four excess pore pressures, and

sample and piston friction. First, the effective stress at

the location of each transducer is expressed as

a' = am + aw uh ue (4.8)

where

-a' is the effective stress

-am is the total stress component due to the applied load

-aw is the total stress component due to the specimen weight

-uh is the hydrostatic pore pressure and

-ue is the excess pore pressure recorded in the transducer.

The buoyant stress is defined as

ab aw uh = 7b.Z (4.9)

where z is the depth of the transducer and 7b is the buoyant

unit weight, to be computed from the average void ratio as

7b 7w'(Gs )/( + e) (4.10)

Substituting equation (4.9) into equation (4.8) we obtain

a' am + ab ue (4.11)

The total stress am is to be computed from the load

cell reading, but it must include two important effects,

namely, piston and sample friction. In order to account for

the first one of these effects in the CRD test, dummy tests

were run with the piston in water, while recording the load

cell readings. The values obtained for two different

deformation rates are reported in next chapter. The







60

estimated piston friction is subtracted from the load cell

readings in the actual test to obtain a corrected load

value, P. In the case of the CHG test, due to the nature of

the test, the behavior of piston friction is expected to be

more erratic and unpredictable, and no attempt was made to

estimate its value.

The reading of the 3-bar PDCR 81 pressure transducer

installed at the bottom of the chamber, atb, is used to

estimate the side friction along the specimen. The zero

reading of this total stress transducer is taken after the

specimen is placed in the chamber. Therefore, if there

were no friction, this transducer would record the stress

induced by the piston load. However, this is not the case.

In a very simplistic approach, the difference between atb

and the piston pressure, att, obtained from the corrected

load cell reading is distributed linearly with depth to

evaluate the total stress induced by the motor load am.

This is

am att (att atb).(z/h) (4.12)

where z is the depth of the transducer under consideration.

Once the effective stress has been computed at the

depth of every transducer, the average effective stress is

obtained from the area of the a'-z curve as

a' (Area under a'-z)/h (4.13)

Figure 4.2 shows schematically the variation of a' with

depth, indicating the distances between transducers in the

test chamber. The effective stress exactly at the bottom of







61

the specimen is assumed equal to aj. For this case the

average effective stress simplifies to
a' [1.235Ca+2.5(a'i+2au2+a)+(h-11.235)(a'3+a ) ]/h (4.14)

where aj represents the effective stress at the jth trans-

ducer, and h must be in centimeters.





-T 1\-------- ) 4
z



5 cm

h



5 cm




1.235 cm


Figure 4.2 Variation of Effective Stress with Depth



Obviously, if the specimen has deformed such that the

piston passes beyond the location of transducer No. 3, or

even No. 2, equation 4.14 must be modified accordingly not

to include those transducers readings. The corresponding

equations are given below.

For transducers 1 and 2 in the specimen (h < 11.235 cm.),

a' [1.235a' + 2.5(a'+'2) + h(h-6.235)(a'2+oa )]/h (4.15)







62

For only transducer 1 in the specimen (h < 6.235 cm),

a' [1.235a'1 + (h 1.235)(a' + a4)]/h (4.16)

It must be emphasized that these equations are valid only

for the dimensions of this particular chamber, as given in

Chapter III.

In this approach it is important that the distribution

of effective stress with depth be close to uniform, to

conform to the assumption of specimen uniformity. This can

be obtained by having a relatively small hydraulic gradient

across the specimen. In the CHG test this can be easily

achieved since the gradient is controlled. In the CRD test,

however, the hydraulic gradient is not controlled. Thus, to

overcome this limitation the rate of deformation can be

slowed sufficiently to produce acceptable pore pressure

ratios.



Determination of Permeability

The coefficient of permeability, k, is obtained from

Darcy-Gersevanov's law (McVay et al., 1986):

n(Vf Vs) -ki (4.17)

where n is the soil porosity,

Vf is the fluid velocity,

VS is the solids velocity, and

i is the hydraulic gradient.

A second equation, however, is needed in order to solve for

the coefficient of permeability. McVay et al. (1986)

expressed the mass conservation of the fluid phase as









6- + 0 (4.18)


and the volume conservation of the solids as

6[l-nl + 6[(l-n)V ] 0 (4.19)
6t 6E

where q = n.Vf is the exit fluid velocity, and

e is the spatial coordinate.

Replacing equation 4.18 into equation 4.19 leads to

6q + 6[(l-n)V ] 0 (4.20)
66 6e

Being a function of only one independent variable, equation

4.20 can be directly integrated to give

q + (l-n)Vs = constant (4.21)

and replacing the expression for q, we obtain

nVf + (l-n)Vs = constant (4.22)

Since at the bottom boundary Vf Vs 0, equation 4.22

further reduces to

nVf + (l-n)Vs = 0 (4.23)

This equation represents the condition of continuity of the

two-phase system at any given time t, and was first proposed

by Been and Sills (1981). Combining equations 4.17 and 4.23

to eliminate the fluid velocity leads to

Vs k.i (4.24)

the relationship from which the coefficient of permeability

will be evaluated. By substituting equation 4.24 into

either equation 4.17 or 4.23, an expression for the fluid

velocity is obtained. This is

Vf lnki (4.25)
n e







64

which can be expressed in terms of the solids velocity by

using equation 4.24 as

Vf -Vs/e (4.26)

Equations 4.24 through 4.26 allow an interesting

comparison between small and large deformation consolidation

processes. First, equation 4.24 shows that, for a given

hydraulic gradient, the higher the coefficient of permeabil-

ity, the higher the velocity of solids. Let us consider,

for example, a slurry consolidation under its own weight

from an initial void ratio of 15 (S = 15%). At the end of

the consolidation process, the slurry will probably have

deformed about half of its initial height, reaching a void

ratio around 6 or 7. Experimental data to be presented in

Chapter V will reveal that such a slurry has an initial

permeability in the order of 10-4 cm/sec.

If the same clay existed in a natural state with a void

ratio of only 1 or 2, it would probably have a permeability

in the order of 10-8 cm/sec; this is 10,000 times smaller

than that of the slurry with initial void ratio of 15. The

consolidation of such a material would be considered a small

strain process. Thus, assuming the same hydraulic gradient,

the solids velocity of the second material (small strain)

would be 10,000 times smaller than that of the former (large

strain). This simple example may help to justify the

assumption of a rigid skeleton, i.e. zero solids velocity,

made in small strain consolidation theory.







65

Additionally, the fluid velocity expressions also pro-

vide some information that may help to understand the

difference between small and large strain consolidation

theories. It can be observed from equation 4.26 that the

fluid velocity is e times smaller than the solids velocity.

This means that Vf is relatively smaller in the case of a

slurry with a very large void ratio. In a natural clay

stratum, where the void ratio is commonly less than 1, the

fluid velocity would actually be larger than the solids

velocity.

Returning to the determination of the coefficient of

permeability, to obtain its average value, one must use the

average hydraulic gradient across the specimen and the

average solids velocity. The average hydraulic gradient is

obtained from the weighted average slope of excess pore

pressure distribution. The distance between transducers is

used as the weighing factor. The resulting average

hydraulic gradient is
i (ul u4)/h/7y (4.27)

which only depends on the excess pore pressure at the

boundaries. The evaluation of the average solids velocity,

on the other hand, presents a problem. Specifically,

between any two readings, taken at times t and t+At, the

mean velocity of the piston represents the solids velocity

at the top of the specimen. This is

Vpiston &h/At (4.28)

It is also known that the solids velocity at the bottom

of the specimen is zero. However, the actual distribution







66

of Vs along the specimen is not known. Since it is not

believed that the error introduced will be significant, the

average solids velocity is taken as the average of the

solids velocity at the two boundaries, i.e.

Vs Vpiston/2 (4.29)

Using equations 4.24 and 4.27 through 4.29, the average

coefficient of permeability is easily obtained from

k Vs/i Vpiston/(2i) (4.30)

To carry out the data reduction using the approach des-

cribed above, a BASIC program, SLURRY2, was developed to run

in the HP-86B. The program, that reads directly the data

stored by SLURRY1, computes the average values of void

ratio, effective stress, and coefficient of permeability at

every time that a set of readings was taken. These values,

together with the corresponding time, specimen height,

gradient, and other parameters, are printed out as they are

computed.

For the case of the phosphatic clays of Florida, it has

been suggested that the two constitutive relationships can

be described as power curves of the form (e.g. Ardaman and

Assoc., 1984):

e A(a')B (4.31)

k CeD (4.32)

Using a log-log linear regression, SLURRY2 computes the

parameters A, B, C, and D and the corresponding coefficients

of correlation. The program can also plot the two curves

(experimental data) using different units and arithmetic or







67

log axes, according to the user's choice. A listing of

SLURRY2 is included in Appendix E.















CHAPTER V
AUTOMATED SLURRY CONSOLIDOMETER--
TEST RESULTS



Testing Program

The material selected for this study was Kingsford

clay, a waste product of the mining operations by IMC

Corporation in Polk County, Florida. This slurry has been

studied extensively (Ardaman and Assoc., 1984; Bloomquist,

1982; McClimans, 1984), and it is typical of the very

plastic clays found in Florida's phosphate mines (Wissa et

al., 1982). Kingsford clay consists mostly of montmorillo-

nite and has the following index properties (Ardaman and

Assoc., 1984; McClimans, 1984):

LL 230% PI = 156% Gs = 2.71 Activity = 2.2

The testing program developed during this part of the study

consisted of four Constant Rate of Deformation tests and

four Controlled Hydraulic Gradient tests. The former were

intended to investigate the effect of the initial solids

content and the deformation rate upon the compressibility

and permeability relationships. In the CHG tests the

influence of the hydraulic gradient on the results was to be

studied. The effect of the initial specimen height, about

15 cm. for all the tests, was not investigated. Table 5-1

presents the testing conditions of both groups of tests.







69

Table 5-1. Conditions of Eight Tests Conducted

Test hi (cm) Si (%) Rate (mm/min) Gradient
CRD
CRD-1 14.7 15.3 0.02
CRD-2 14.9 10.2 0.02
CRD-3 15.0 16.2 0.008
CRD-4 15.0 10.7 0.008
CHG
CHG-l 15.0 15.6 2.0
CHG-2 15.0 16.4 4.0
CHG-3 15.0 16.3 10.0
CHG-4 15.0 16.0 20.0



CRD Tests Results

Of the four CRD tests, two of them were conducted on

dilute slurries with solids content between 10% and 11%

(CRD-2 and CRD-4), while the other two tests were conducted

on denser specimens with solids contents in the order of 15%

to 16% (CRD-1 and CRD-3). In each group, one test was run

at a slow rate of deformation of 0.008 mm/min (CRD-3 and

CRD-4), while the other was run at a faster rate of 0.02

mm/min (CRD-1 and CRD-2).

Tests CRD-l and CRD-2 were performed with an early

version of the test chamber whose differences from the

present design are worth mentioning. Originally the

pressure transducers were mounted in a pipe-threaded brass

fitting, which had to be tighten in order to seal properly.

This fitting soon began to crack the acrylic and therefore

it was replaced with the 0-ring sealed fitting currently

used. In the original chamber, transducer No. 1 was located

at 0.6 cm from the bottom of the chamber, and not 1.235 cm

as in the present chamber.







70

During the development of the equipment several pistons

were tried in the chamber to produce a snug fitting with the

minimum possible friction. In the case of test CRD-l the

piston used was fairly loose and a filter cloth was wrapped

around the bottom plate to prevent the escape of slurry, but

allowing free drainage. This arrangement allowed the piston

to fall freely in water. Therefore, no piston friction was

included in the analysis of test CRD-1. Instead, the

submerged weight of the piston was added to the applied

motor load. The resulting additional pressure of 0.0109 psi

is not significant for most of the test, but it does affect

the initial portion of the compressibility curve.

The specimen of test CRD-l started at a solids content

of 15.3% (e 14.97) and a height of 14.7 cm. The test was

conducted at a rate of deformation of 0.02 mm/min for 62

hours (= 2.5 days). Readings were taken every 30 minutes

(124 data points). The final specimen height was 7.19 cm

and the computed average solids content was 28.5% (e -

6.81). Direct measurement of the solids content led to an

average value of 28.7% with a variation of 4.7% across the

specimen, which indicates a very good agreement. Figure 5.1

shows the compressibility and permeability plots for test

CRD-l as produced by the data reduction program. Both

curves show a very well defined behavior.

For test CRD-2, the old chamber was still used but a

much tighter piston was tried. At this point in time no

attempt was made to estimate the magnitude of the piston

















































































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73

friction, but it was suspected to be large enough to affect

the compressibility curve. The specimen in this test began

at a solids content of 10.2% (e = 23.96) with a height of

14.9. The test was run at a deformation rate of 0.02 mm/min

for 72 hours (3 days), with 30 minutes between readings. At

the end of the test, the LVDT-based height of the specimen

was 6.02 cm, but visual observation of the specimen indi-

cated a value of around 5.7 cm. A similar discrepancy was

also found in the solids content. The computed value was

22.97% (e 9.09), while the measured average was 24.37%

with a gradient of 6.98% across the specimen. If the

observed specimen height of 5.7 cm were accepted as correct,

then the computed solids content would be about 24%, which

agrees very well with the measured value. This discrepancy

is attributed to possible disadjustment of the pivoting arm-

LVDT arrangement.

When the data of test CRD-2, with a dilute specimen,

was first reduced, the average effective stress showed

negative values up to a solids content of about 13.5%. The

data reduction program was later modified to make zero any

negative effective stress computed at the location of the

pore pressure transducers. This result seems to indicate

that below this solids content the slurry has no effective

stresses, or these are two low to be detected with the

equipment used. Once the program was modified to eliminate

negative values, it was observed that the average effective

stress increased above 0.01 psi (the estimated sensitivity







74

of the transducers) when the solids content was again about

13.4%. Figure 5.2 shows the compressibility and permeabi-

lity curves of test CRD-2 as plotted by SLURRY2. The

initial portion of the compressibility plot (Figure 5.2a)

shows clear evidence of pseudo-static piston friction.

Another interesting aspect of the plot is the step-like

shape. This effect may be attributed to a discontinuity in

the computed effective stress when the piston passes by

transducer No. 3 (at h 11.235 cm.), as a result of the

analytical approach used. However, this irregular effect is

not observed with the same magnitude in all the tests. The

permeability plot, on the other hand, exhibits a well

defined trend with almost no scatter.

The new chamber described in Chapter III was used for

the rest of the tests. It was found that the O-Ring sealed

piston did not fall freely in the chamber; a study was

conducted to estimate the magnitude of the piston friction.

With water in the chamber, dummy tests were conducted and

the load cell readings recorded with time. Since transducer

No. 4 did not record any build-up of pressure, it was

assumed that the load cell reading was only reflecting the

piston friction. For the deformation rate of 0.02 mm/min,

the average friction obtained was 6.5 lbs, while for the

rate of 0.008 mm/min the average value was 8.6 lbs; in both

cases the variation of the recorded load was very small.

The testing program carried out in this part of the

research never attempted to study the statistical validity




















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77

of any particular observation. Nevertheless, it was inter-

esting to investigate the duplicability of the tests

results. With this in mind, an additional test was con-

ducted with similar conditions to those of test CRD-l. This

test, the first one with the new chamber, was originally

intended to be a different test, conducted for 7 days at the

slower rate of deformation of 0.008 mm/min. After the test

had been running for 6 hours, it was sadly discovered that

somebody had turned the main breaker off and that the test

had been aborted. To avoid wasting the specimen, it was

decided to run a quicker test (3 days) which would approxi-

mately duplicate test CRD-l. The initial height of the

aborted test was 14.7 cm and the initial solids content was

15.7%. Although the specimen had deformed about 3 mm when

the test stopped, no corrections were made on the initial

values once the test was restarted. The results of both

tests, CRD-l and its duplicate, are shown in Figure 5.3.

Considering the conditions under which the duplicate test

was conducted and expected variations in the material

itself, it can be said that the results are reproduced quite

well.

The compressibility plot of the duplicate test shows an

abrupt discontinuity in the effective stress. This could be

explained with the same arguments given for test CRD-2.

The other two CRD tests were run at the slower rate of

deformation (0.008 mm/min). Test CRD-3 was initiated at a

solids content of 16.2% (e 14.01) with a specimen height


















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80

of 15 cm. After running for 168 hrs (7 days), with 2 hours

between readings, the final height was 7.32 cm (computed),

while the observed value was 7.1 cm, indicating a very good

agreement. As for the final solids content, the computed

value was 29.99% (e 6.33), while the measured average was

29.94 with a variation of only 2.66% across the specimen,

again an excellent agreement. Figure 5.4 shows the compres-

sibility and permeability curves obtained from test CRD-3.

The fact that the time interval between readings was

relatively large may have resulted in the loss of valuable

information during early parts of the test.

Finally, test CRD-4 began at a solids content of 10.66%

(e = 22.70) with the specimen height at 15 cm. This test

was the longest one, running for 216 hr (9 days), and

proving that the apparatus is capable of working for long

periods of time without any problem. For approximately 1

day, the results of this test indicated inconsistent

results, such as negative values of permeability. These

results were attributed to the extremely low pore pressures

being read; these points were discarded. At the end of the

test the computed specimen height was 5.1 cm, while the

observed value was 4.5, a quite significant difference. The

computed final solids content was 27.75% (e = 7.06) and the

measured value was 29.68%, with a variation across the

specimen of only 1.56%. Figure 5.5 shows the compressi-

bility and permeability plots obtained from test CRD-4. The

compressibility plot shows significant scatter with initial










81








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85

evidence of piston friction and some irregular behavior

around an effective stress of 1 psf, in a way similar to

test CRD-2. Both of these tests started at the low solids

content level, and this may be partially responsible for

these results.

Table 5-2 summarizes the conditions of the specimens at

the end of the four CRD tests, and shows the duration of

each test.


Table 5-2. Summary of CRD Tests Results

Test Duration Final Height (cm) Final Solids Cont.(%)
(hrs) Computed Observed Computed Measured Gradient

CRD-l 62 7.19 7.1 28.5 28.7 4.7

CRD-2 72 6.02 5.7 23.0 24.4 7.0

CRD-3 168 7.32 7.1 30.0 29.9 2.7

CRD-4 216 5.10 4.5 27.8 29.7 1.6



The results of these tests clearly show that the

variation in solids content with depth is significantly

smaller in those tests performed at the slower rate of

deformation. This result is important considering the

assumption of specimen uniformity made during the analysis

of the data. This condition, however, can never be com-

pletely satisfied since the excess pore pressure dissipates

faster at the top boundary. Thus, although the total stress

in the specimen is close to uniform (assuming self-weight is

smaller than the motor load), the excess pore pressure

distribution is not. Figure 5.6 shows the distribution of





















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Full Text
CONSOLIDATION PROPERTIES OF PHOSPHATIC CLAYS
FROM AUTOMATED SLURRY CONSOLIDOMETER
AND CENTRIFUGAL MODEL TESTS
By
RAMON E. MARTINEZ
A DISSERTATION PRESENTED TO THE GRADUATE
SCHOOL OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1987

DEDICATED
VIRGINIA,
FOR THEIR
AND TO MY
FOR THEIR
PRAYERS.
GOD BLESS
WITH ALL MY LOVE TO MY WIFE,
AND MY SON, JUAN RAMON,
DEVOTED LOVE AND PATIENCE.
PARENTS, DAMASO AND CATALINA,
SUPPORT, ENCOURAGEMENT, AND
THEM ALL.

ACKNOWLEDGMENTS
I would like to express my deepest gratitude to the
members of my supervisory committee. Foremost, I am
grateful to Dr. Frank C. Townsend for serving as chairman of
the committee. However, Dr. Townsend's support included far
more than his experience and knowledge on the subject of
phosphatic clay consolidation. His personal interest,
friendship, and love for Panama will outlast in my memory
the technical aspects of my career.
I am also very thankful to Dr. Michael C. McVay for
serving on the committee and for his valuable assistance and
always appropriate comments throughout the development of my
doctoral research. My gratitude is extended to Dr. John L.
Davidson, not only for being on the committee, but also for
giving me the opportunity to observe what an excellent
teacher should be; I will definitely try to imitate him.
Special thanks are expressed to Dr. Gustavo Antonini, of the
Latin American Center, for taking the time and interest of
serving as the external member of the committee.
I have intentionally left Dr. David Bloomquist to the
end of the list of committee members. I can not emphasize
enough my gratitude to "Dave," as he prefers to be called.
Dave was a key element in the development of all the
equipment reported in this research. Most of what I now
know about laboratory equipment and instrumentation I
i i i

learned from him. But Dave's most valuable qualification is
his attitude toward work. He enjoys so much his work around
the lab that, while working with him, you also enjoy yours.
I extend my gratitude to Dr. J. Schaub, chairman of the
Civil Engineering Department. It is because of all these
faculty members that I will remember my stay at UF not only
as a profitable experience, but also as an enjoyable one.
I also must express my gratitude to the Universidad
Tecnológica de Panamá for supporting me during the pursuit
of this degree. I want to specially thank Ings. Héctor
Montemayor and Jorge L. Rodriguez, dean and vicedean of the
Civil Engineering College, and Dr. Victor Levi S., the
university president.
The friendship and support of many colleague graduate
students is also recognized. I want to make a special
recognition to Pedro Zuloaga, whose friendship I am sure
will continue after my return to Panama. The list of other
good friends who were part of my long career at UF includes,
but is not limited to, Sarah Zalzman, Charles Moore, Jeff
Beriswill, Hwee-Yen Kheng, Kwasi Badu-Tweneboah, Nick
Papadopoulos, Charlie Manzione, John Gill, and my Panamanian
colleague, Javier Navarro.
The financial support of the Florida Institute for
Phosphate Research was instrumental in the development of
the research and is acknowledged here. I also want to
recognized Randy Bushey of the Florida Department of Natural
Resources for providing financial support for this research.
i v

TABLE OF CONTENTS
Pa.&e.
ACKNOWLEDGMENTS iii
LIST OF TABLES viii
LIST OF FIGURES ix
ABSTRACT xiii
CHAPTERS
I INTRODUCTION 1
Problem Statement 1
Purpose and Scope of the Study 4
II BACKGROUND AND LITERATURE REVIEW 6
Introduction 6
Slurry Consolidation Laboratory Tests 7
Settling Column Tests 11
CRD Slurry Consolidation Tests 12
Centrifugal Modelling 20
Constitutive Properties 22
IIIAUTOMATED SLURRY CONSOLIDOMETER--EQUIPMENT AND
TEST PROCEDURE 27
Introduction 27
The Test Chamber 27
The Stepping Motor 36
The Computer and Data Acquisition/Control System.. 39
The Controlling Program 45
Test Procedure 47
IV AUTOMATED SLURRY CONSOLIDOMETER--DATA REDUCTION... 55
Introduction 55
Determination of Void Ratio 56
Determination of Effective Stress 59
Determination of Permeability 62
VAUTOMATED SLURRY CONSOLIDOMETER--TEST RESULTS 68
v

Testing Program 68
CRD Tests Results 69
CHG Tests Results 93
Testing Influence 109
VI CENTRIFUGE TESTING--EQUIPMENT, PROCEDURE, AND
DATA REDUCTION 120
Introduction 120
Test Equipment and Procedure 122
Method of Data Reduction 131
VII CENTRIFUGE TESTING RESULTS 142
Testing Program 142
Determination of Constitutive Relationships 143
Comparison of CRD and Centrifuge Test Results 178
Effect of Surcharge on Pore Pressure Response 182
Some Comments on the Time Scaling Exponent 191
VIII COMPARISON OF CENTRIFUGAL AND
NUMERICAL PREDICTIONS 202
Introduction 202
The Constitutive Relationships 204
Predictions of Ponds KC80-6/0 and KC80-10.5/0 206
Predictions of Ponds CT -1 , CT-2/3, and CT-5 211
IX CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH... 231
Summary and Conclusions 231
Suggestions for Future Research 237
APPENDICES
A TIME SCALING RELATIONSHIP 240
Introduction 240
Permeability Scaling Factor 241
Governing Equation in the Centrifuge 242
B LVDT-PIVOTING ARM CALIBRATION 244
C ANALYSIS OF NOISE EFFECT IN THE TRANSDUCERS
RESPONSE 247
D AUTOMATED SLURRY CONSOLIDOMETER CONTROLLING
AND MONITORING PROGRAM (SLURRYl) 254
SLURRY1 Flowchart 254
Listing of SLURRYl 260
E AUTOMATED SLURRY CONSOLIDOMETER
DATA REDUCTION PROGRAM (SLURRY2) 270
v i

F TRANSDUCER CALIBRATION IN THE CENTRIFUGE 281
G CENTRIFUGE MONITORING PROGRAM 286
H CENTRIFUGE DATA REDUCTION PROGRAM
AND OUTPUT LISTINGS 289
Data Reduction Program 289
Data Reduction Output of Test CT-1 295
Data Reduction Output of Test CT-2 299
I NUMERICAL PREDICTION PROGRAM AND
EXAMPLE OUTPUT LISTINGS 304
Listing of Program YONG-TP 304
Prediction of Pond KC80-6/0 315
BIBLIOGRAPHY 320
BIOGRAPHICAL SKETCH 326
vi i

LIST OF TABLES
Table Page
2-1. Kingsford Clay Parameters 23
3-1. Slurry Cons o 1idometer Transducer Information 35
3-2. Deformation Rates in CRD Tests 45
3-3. Valve Positions for Vacuum System 49
3-4. Verification of Transducer Calibration 53
5-1. Conditions of Eight Tests Conducted 69
5-2. Summary of CRD Tests Results 85
5-3. Summary of CHG Tests Results 99
6-1. Centrifuge Test Transducer Information 126
7-1. Centrifuge Testing Program 142
7-2. Partial Output of the Analysis of Test CT -1 158
7-3. Partial Output of the Analysis of Test CT-2 172
7-4. Modelling of Model Results (Bloomquist and
Townsend, 1984) 196
7-5. Time Scaling Exponent Obtained from Data
in Table 7-4 196
7-6. Modelling of Models on Tests CT-2 and CT - 3 201
C-l. Summary of Transducers Response Using
Various Filtering Techniques 251
F-l. Calibration Data for Transducer No. 1 283
F-2. Calibration Data for Transducer No. 2 284
F-3. Calibration Data for Transducer No. 3 285
v i i i

LIST OF FIGURES
Figure Pape
3.1 - Schematic of Automated Slurry Cons o 1idometer 28
3.2 - Schematic of Slurry Cons o1idometer Chamber 29
3.3 - Pore Pressure Transducer PDCR 81 32
3.4 - Photograph of Slurry Cons o 1idometer Chamber 34
3.5 - Motor Translator, Gear Box, and Stepper Motor.... 37
3.6 - Schematic of Motor Translator Connections 38
3.7 - Entire Slurry C ons o 1 i dome t e r Assembly 40
3.8 - Computer and Data Acquisition/Control System 42
3.9 - Vacuum System 49
4.1 - Phase Diagrams 57
4.2 - Variation of Effective Stress with Depth 61
5.1 - Results of Test CRD-1 71
5.2 - Results of Test CRD-2 75
5.3 - Duplication of Test CRD-1 78
5.4 - Results of Test CRD-3 81
5.5 - Results of Test CRD-4 83
5.6 - Pore Pressure and Effective Stress Distributions
with Depth for Test CRD-1 86
5.7 - Summary of CRD Tests 88
5.8 - Results of Test CHG-1 94
5.9 - Results of Test CHG-2 97
5.10 - Results of Test CHG-3 100
5.11 - Results of Test CHG-4 102
i x

5.12 - Pore Pressure and Effective Stress Distributions
with Depth for Test CHG-2 105
5.13 - Summary of CHG Tests 106
5.14 - Deformation Rate and Hydraulic Gradient with
Time for Tests CRD-2 and CHG-3 110
5.15 - Comparison of CRD and CHG Tests Results 112
5.16 - Constitutive Relationships Proposed for
Kingsford Clay 117
6.1 - Schematic of Centrifuge and Camera Set-up 123
6.2 - Centrifuge Bucket 125
6.3 - Sampler for Solids Content Distribution 128
6.4 - Effect of Stopping and Re-starting Centrifuge.... 130
6.5 - Variation of Void Ratio with Depth 134
6.6 - Location of Material Node i 137
6.7 - Excess Pore Pressure Distribution 139
7.1 - Height-Time Relationship for Test CT -1 145
7.2 - Solids Content Profiles for Test CT-1 146
7.3 - Evaporation Effect on Excess Pore Pressure 148
7.4 - Evaporation Correction for Test CT-1 150
7.5 - Pore Pressure with Time for Test CT-1 151
7.6 - Pore Pressure Profiles for Test CT-1 153
7.7 - Parabolic Distribution Excess Pore Pressure
at t = 2 hours for Test CT-1 156
7.8 - Constitutive Relationships from Centrifuge
Test CT-1 161
7.9 - Height-Time Relationship for Test CT-2 165
7.10 - Solids Content Profiles for Test CT-2 166
7.11 - Evaporation Correction for Test CT-2 168
7-12 - Pore Pressure with Time for Test CT-2 169
7.13 - Pore Pressure Profiles for Test CT-2 170
x

7.14 - Constitutive Relationships from Centrifuge
Test CT-2 173
7.15 - Comparison of CT-1 and CT-2 Results 176
7.16 - Comparison of CRD and Centrifuge Test Results. . . . 179
7.17 - Pore Pressure Profiles for Test CT-4 184
7.18 - Bucket Used in Centrifuge Surcharge Tests 186
7.19 - Height-Time Relationship for Test CT-5 188
7.20 - Pore Pressure Profiles for Test CT-5 189
7.21 - Pore Pressure with Time for Test CT-5 190
7.22 - Modelling of Models using Bloomquist and
Townsend (1984) Data 198
7.23 - Modelling of Models using Tests CT-2 and CT-3. . . . 200
8.1 - Prediction of Pond KC80-6/0 using Constitutive
Relationships obtained from Test CRD-1 207
8.2 - Comparison of YONG-TP, UF-McGS, and
QSUS Outputs 209
8.3 - Prediction of Pond KC80-10.5/0 using Constitutive
Relationships obtained from Test CRD-1 210
8.4 - Prediction of Pond CT-1 using Constitutive
Relationships obtained from Test CRD-1 212
8.5 - Prediction of Pond CT-2/3 using Constitutive
Relationships obtained from Test CRD-1 213
8.6 - Comparison of Centrifuge Tests KC80-10.5/0
and CT-6 215
8.7 - Prediction of Pond CT-1 using Centrifuge
Test Parameters 216
8.8 - Measured and Predicted Void Ratio Profiles
for Pond CT-1 218
8.9 - Predicted Excess Pore Pressure Profiles
for Pond CT-1 219
8.10 - Measured and Predicted Excess Pore Pressure
Profiles at a Model Time of 2 hours for
Pond CT-1 221

8.11 - Prediction of Pond CT-2/3 using Centrifuge
Test Parameters 222
8.12 - Measured and Predicted Void Ratio Profiles
for Pond CT-2/3 224
8.13 - Prediction of Pond CT-6 using Centrifuge
Test Parameters 226
8.14 - Prediction of Pond CT-5 using Centrifuge
Test Parameters 227
8.15 - Measured and Predicted Excess Pore Pressure
Profiles for Test CT-5 228
8.16 - Measured and Predicted Void Ratio Profiles
for Pond CT-5 230
B.l - Two Positions of Pivoting Arm 244
B.2 - Initial Inclination of Pivoting Arm 245
C.l - Response of Pressure Transducer No. 1 252
C.2 - Response of Load Cell 253
F.l - Radii r^ and r2 for Transducer No. 1 283
F.2 - Calibration Plot for Transducer No. 1 283
F.3 - Radii r^ and r2 for Transducer No. 2 284
F.4 - Calibration Plot for Transducer No. 2 284
F.5 - Radii r^ and r2 for Transducer No. 3 285
F.6 - Calibration Plot for Transducer No. 3 285
x i i

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
CONSOLIDATION PROPERTIES OF PHOSPHATIC CLAYS
FROM AUTOMATED SLURRY CONSOLIDOMETER
AND CENTRIFUGAL MODEL TESTS
By
RAMON E. MARTINEZ
De c emb e r 19 8 7
Chairman: Dr. Frank C. Townsend
Major Department: Civil Engineering
As a by-product of phosphate mining and other indus¬
trial processes, a very dilute fine-grained slurry is pro¬
duced, which consolidates over long periods of time in large
retention ponds. Numerical prediction of the magnitude and
time rate of settlement of these slurries requires a knowl¬
edge of the effective stress-void ratio and the permeabil¬
ity-void relationships of the material. The purpose of this
research was to develop equipment and techniques for deter¬
mining these relationships by (1) performing automated
slurry consolidation experiments and (2) centrifugal model
tests.
An automated slurry cons o 1idometer, which is fully
controlled by a computer - data acquisition system that
x i i i

monitors load, pore pressure, total stress, and deformation,
was developed. The load is applied by a stepping motor.
Results from the tests conducted show the effectiveness of
the apparatus. The Constant Rate of Deformation test was
found to have several advantages over the Controlled
Hydraulic Gradient test and is recommended for future
applications; the results from both tests were consistent.
A "pseudo-preconsolidation" effect, attributed to the
initial remolded condition of the specimen, was observed in
both constitutive relationships. Thus, the curves are not
unique but depend upon the initial solids content. However,
different curves approach what seems to be a "virgin zone."
The compressibility relationship also was found to be
dependent upon the rate of deformation.
The technique using centrifugal modelling is based on
the measurement of pore pressure and void ratio profiles
with time, and the use of a material representation of the
specimen. The compressibility relationship obtained was in
good agreement with the results of CRD tests performed at a
slow rate of deformation. The permeability relationship
plotted parallel to the CRD curves, however, permeability
values were approximately a half order of magnitude higher.
Further research is required to explain this difference.
The constitutive relationships obtained in the study
were used to predict the behavior of hypothetical ponds
modelled in the centrifuge. A good agreement between
centrifugal and numerical models was found.
x IV

CHAPTER I
INTRODUCTION
Problem Statement
The production of phosphate fertilizers from Florida's
mines involves the excavation of approximately 300 million
cubic yards of material (overburden and matrix containing
the phosphate) annually. This is roughly equal to the
entire volume excavated during the construction of the
Panama Canal (Carrier, 1987). During the phosphate benefi-
ciation process, large amounts of water are used to wash the
matrix in order to separate the phosphate from the sand and
clay forming that layer. As a by-product of the process, a
very dilute fine-grained slurry is produced with very low
solids contents (weight of solids 4- total weight).
Florida's phosphate mines produce more than 50 million tons
of such waste clays annually (Carrier et al. , 1983) .
Disposal of these waste clays is accomplished by
storing them in large containment areas or ponds, and allow¬
ing them to settle/consolidate over long periods of time.
During the initial sedimentation phase, the slurry reaches a
solids content on the order of 10-15% within a few weeks or
months, depending on several physio-chemical properties of
the material (Bromwell, 1984; Bromwell and Carrier, 1979;
Scott et al. , 1985) . Subsequently, a very slow process of
1

2
self-weight consolidation begins, which can require several
decades to achieve a final average solids content of
approximately 20-25%. Because of this time delay, research
efforts have been concentrated on the consolidation behavior
rather than the sedimentation phase of these slurries.
The design of the disposal areas, as well as the
estimate of time required for reclamation thereof, presents
a challenging problem to geotechnical engineers, who must
estimate the magnitude and time rate of settlement of the
slurry, as well as the final pond conditions. It has been
well established that conventional linear consolidation
theory is inappropriate for these materials (Bromwell, 1984;
Cargill, 1983; Croce et al., 1984; McVay et al., 1986).
This is primarily the result of the significant changes in
permeability and compressibility that occur as these
slurries consolidate to very large strains (Bromwell and
Carrier, 1979). Accordingly, large-strain nonlinear
consolidation theory has been used to model the self-weight
consolidation process of these soft, very compressible soil
deposits (see e.g. McVay et al., 1986), and several computer
codes have been written to predict their behavior applying
this theory (Cargill, 1982; Somogyi, 1979, Yong et al.,
1983; Zuloaga, 1986).
The use of large-strain consolidation theory requires a
clear definition of two constitutive relationships of the
slurry, namely, the effective stress-void ratio relation and
the permeabi1ity-void ratio relation. Unfortunately, our

3
capability of measuring accurately these soil properties has
not advanced as fast as our ability to represent the physi¬
cal process by a mathematical model. The results of the
numerical predictions are very susceptible to these input
material properties, primarily the permeability relationship
(Hernandez, 1985; McVay et al., 1986). Comparison of
centrifugal and numerical predictions has found good agree¬
ment on the magnitude of settlement. However, good predic¬
tions of the rate of settlement require improvement in
laboratory input data, primarily the permeability relation¬
ship (Carrier et al. , 1983; Townsend et al . , 1987).
Traditional consolidation tests are not suitable for
the study of the consolidation properties of highly com¬
pressible clays, mainly because they rely on curve fitting
methods and small strain theory to characterize the consoli¬
dation process. Although several attempts to develop large
deformation consolidation tests are reported in the litera¬
ture, the Slurry Consolidation Test has emerged as one of
the most popular (Ardaman and Assoc., 1984; Bromwell and
Carrier, 1979; Carrier and Bromwell, 1980; Scott et al. ,
1985). Unfortunately, the test, which is essentially a
large-scale version of the standard oedometer, suffers from
some drawbacks, among them its extremely long duration of
several months.
Alternative tests are being developed. These include
settling column tests, constant rate of deformation consoli¬
dation tests, and others. Chapter II will discuss the

4
details of these tests. To date, however, there is no
standard approach that satisfactorily measures the compres¬
sibility and permeability of very soft soils and soil-like
materials .
Purpose and Scope of the Study
The purpose of this research is to develop a technique
to determine accurately the compressibility and permeability
relationships of phosphatic clays and other slurries. To
achieve this objective, two approaches are followed. The
first one involves testing in a newly developed automated
slurry consolidometer, while the second involves centrifuge
testing. The automated slurry consolidometer should be
capable of (1) accommodating a relatively large volume of
slurry, (2) producing large strains in the specimen, (3)
allowing different loading conditions, (4) monitoring and/or
controlling load, deformation, pore pressures, and other
parameters, and (5) testing a wide range of solids content.
A major concern in the development of this consoli¬
dometer was to avoid the use of any assumptions concerning
the theoretical behavior of the slurry in analyzing the
data. Instead, the adopted test method measures directly
many of the required parameters and computes others from
well accepted soil mechanics principles, such as the
effective stress principle and Darcy's law. This approach
to the problem is different from those attempted by others,
as will be discussed in Chapter II (literature review).

5
Chapter III describes in detail the test equipment and
procedure while Chapter IV presents the proposed method of
analysis of the test data. Chapter V presents the results
of several tests conducted on a Florida phosphatic clay.
The second approach used to obtain constitutive
relationships of the material is centrifugal testing. This
involves measuring pore pressure and solids content profiles
in a centrifuge model with time. The use of updated Lagran-
gian coordinates for a number of points along the specimen,
in conjunction with the previously described data, allows
the determination of the compressibility and permeability of
the slurry. Chapter VI describes the test procedure,
instrumentation, and method of data reduction. Chapter VII
presents the results of several centrifuge tests on the same
clay used in the slurry consolidation tests. A comparison
of the results of both approaches is also presented in this
chapter .
One of the main applications of centrifuge testing is
to validate the results of computer predictions (McVay et
al., 1986; Scully et al., 1984). In Chapter VIII the
constitutive relationships obtained in this research are
used to predict the behavior of a hypothetical pond. These
predictions are compared with the results of centrifugal
modelling. Finally, Chapter IX presents the conclusions and
suggestions for future research.

CHAPTER II
BACKGROUND AND LITERATURE REVIEW
Int ro due tion
The main reasons for performing a consolidation
analysis are (1) to determine the final height of the
deposit (theoretically at t = ®) and (2) to evaluate the
time rate of settlement. Other information, such as pore
pressure or void ratio distributions at any time, can also
be obtained from the analysis. Of course, such an analysis
requires the determination of several consolidation proper¬
ties of the soil. In traditional consolidation analysis,
the first of the two objectives is accomplished by knowing
the preconso 1idation pressure and the compression index.
The second objective requires the determination of the
coefficient of consolidation.
Along with the development of his classical one¬
dimensional consolidation theory, Terzaghi (1927) proposed
the first consolidation test, known today with minor
modifications as the step loading test and standardized as
ASTM D 2435-80. Since its first introduction, several
procedures have been proposed to analyze the data in order
to solve for the material properties; this is usually accom¬
plished by a curve fitting procedure. The test has several
drawbacks, among them that it is time consuming and the
6

7
results are highly influenced by the load increment ratio
(Znidarcic, 1982). To overcome some of the limitations of
the step loading test, other testing techniques have been
proposed. Among the most popular are the Constant Rate of
Deformation test (Crawford, 1964; Hamilton and Crawford,
1959) and the Controlled Hydraulic Gradient test (Lowe et
al . , 1969) . The analysis procedure for these tests relies
on small strain theory to obtain the material properties.
Znidarcic et al. (1984) present a very good description of
these and other consolidation tests, with emphasis on their
different methods of analysis. They conclude that these
tests are limited to problems where linear or constant
material properties are good approximations of the real soil
behavior.
Consequently, conventional consolidation tests are not
suitable for very soft soils or slurries, which will undergo
large strains and exhibit highly nonlinear behavior. In
large strain theory the soil is characterized by two
constitutive relationships, namely, the effective stress-
void ratio relation and the permeabi1ity-void ratio rela¬
tion, and not by single parameters such as the coefficient
of consolidation or the compression index.
Slurry Consolidation Laboratory Tests
Accordingly, there is a definite need to develop
testing techniques appropriate to study the consolidation
properties of soft soils and sediments. Lee (1979)

8
describes a number of early efforts (1964-1976) to develop
large deformation consolidation tests. He developed a
fairly complicated step loading oedometer, which monitored
the load, pore pressures, and deformation of a 4-inch
diameter and 6 - inch high specimen.
of his
test data was based on a linearized form of the finite
strain consolidation theory, using a curve fitting construc¬
tion analogous to the square root of time method in the
conventional oedometer. The test provided the stress-strain
relationship (compressibility) and a coefficient of consol¬
idation, which is assumed to be constant for a given load
increment. Permeability values could be obtained from this
coefficient of consolidation.
Lee introduced, in a special test, the use of a flow
in order to reduce the pore pressure gradient
across the specimen and approximate this to a uniform
condition. This allowed him to make direct computations of
the permeability. The test program conducted by Lee was on
specimens with initial void ratios in the order of 6.
Although some of the characteristics of Lee's apparatus are
valuable, the overall approach is probably not appropriate
for testing dilute slurries with initial void ratios of 15
or more.
A very popular test, most probably due to its relative
simplicity, developed specifically for testing very dilute
fine-grained sediments is the Slurry Consolidation Test
(Ardaman and Assoc., 1984; Bromwell and Carrier, 1979;

9
Carrier and Bromwell, 1980; Keshian et al., 1977; Roma,
1976; Scott et al., 1985; Wissa et al., 1983). The test is
essentially a large-scale version of the standard oedometer,
using a much larger volume of soil to allow the measurement
of large strains. The specimen diameter is usually in the
order of 10-20 cm and its initial height is 30 to 45 cm.
Slurry consolidation tests are usually conducted on speci¬
mens with initial solids content near the end of sedimenta¬
tion. The specimen is first allowed to consolidate under
its own weight, recording the height of the specimen
periodically. The average void ratio at any time is
computed from this height and the initial conditions.
Subsequent to self-weight consolidation, the specimen
is incrementally loaded and allowed to consolidate fully
under each load. Typical loading stresses begin as low as
0.001 kg/cm^ and increase, using a load increment ratio of
2, to values usually less than 1 kg/cm^ (Ardaman and Assoc.,
1984; Bromwell and Carrier, 1979). At the end of each load
increment, average values of void ratio and effective stress
are computed, leading to the compressibility relationship.
A typical test will last several months.
To determine the permeability relationship several
approaches can be used. First, a constant head permeability
test can be conducted at the end of each load increment.
However, in doing this, care must taken to minimize seepage-
induced consolidation, which is commonly accomplished by
applying very small gradients (Ardaman and Assoc. , 1984;

10
Wissa et al., 1983), or by reducing the applied load to
counterbalance the tendency of the effective stress to
increase (Scott et al . , 1985).
In a different approach, the coefficient of permeabil¬
ity, k, at the end of each load increment is computed from
the coefficient of consolidation at 90% consolidation,
obtained from a square root of time method similar to the
conventional oedometer; this is given by (Carrier and
Bromwe11, 1980)
k = cv av O'w
1 + ef
(2.1)
2
with CV - l hf â–  (2.2)
c 9 0
where ef = final void ratio
av = coefficient of compressibility = de/dÚ'
hf «= final height of specimen
tgo = elapsed time to 90% consolidation
T = factor similar to the standard time factor, which
depends on the void ratio; typically 0.85 to 1.2.
Such an approach is based on a modified form of
Terzaghi's theory, obtained from finite strain computer
simulations of the slurry consolidation test (Carrier et
al., 1983; Carrier and Keshian, 1979). In some instances
(e.g. Ardaman and Assoc., 1984; Keshian et al., 1977; Wissa
et al., 1983), Terzaghi's classical theory is used directly
to backcalculate the permeability.
In a third approach, used during the self-weight phase
of the test, the permeability is obtained from the

11
self-imposed hydraulic gradient (Bromwell and Carrier,
1979). Of course, this approach requires very accurate
measurements of pore pressure, which is not a standard part
of the test; for example, for a 45-cm height specimen of a
typical phosphatic clay, with initial solids content of 16%,
the initial maximum excess pore is only about 0.07 psi.
In summary, the slurry consolidation test is a rela¬
tively simple procedure to obtain the constitutive relation¬
ships of diluted soils. However, it suffers from two major
drawbacks, specifically, its extremely long duration of up
to 6 to 7 months (Carrier et al., 1983) and the shortcoming
of partially relying on small strain theory to interpret the
test results.
Settling Column Tests
Several variations of self-weight settling column tests
have been used to study the settlement behavior of slurries.
Relatively small specimens have been used to study the end
of sedimentation conditions of very dilute sediments
(Ardaman and Assoc., 1984), to define the compressibility
relation of the material at low effective stresses (Cargill,
1983; Scully et al., 1984; Wissa et al., 1983) and the
highest possible void ratio of the material as a soil, i.e.
the fluid limit, (Scully et al., 1984), and in some cases,
even the permeability relationship (Poindexter, 1987). In
these tests, the compressibility relationship is readily
obtained from water content measurements with depth at the

12
end of the consolidation process. Determination of the
permeability, on the other hand, requires curve fitting
methods using a linearized version of the finite strain
consolidation theory.
Larger settling tests with specimen heights of up to 10
meters (Been and Sills, 1981; Lin and Lo , 1984; Scott et
al. , 19 85 ) are perhaps the best approach to study the
sedimentation/consolidation behavior of sediments. If
properly monitored, such tests can provide all the needed
characteristics of the slurry. Proper monitoring of the
test includes measurements of pore pressure and density
profiles with time. The approach, however, has major
limitations. Specifically, those tests on small and very
dilute samples only cover a small range of effective stress,
while the tests with large specimens would take so long that
they become impractical for any purpose other than research.
CRD Slurry Consolidation Tests
Perhaps, one of the most promising tests to study the
consolidation properties of slurries and very soft soils is
the constant rate of deformation (CRD) consolidation test.
The test is applicable over a wide range of initial void
ratios (e^ = 10-20) (Scully et al., 1984). Very large
strains can be achieved (up to 80%) and, compared to other
tests, it can be performed in a relatively short period of
time (in the order of one week) (Schiffman and Ko, 1981).
The test allows automatic and continuous monitoring and with

13
the right approach it can provide both, the compressibility
and permeability relationships, over a wide range of void
ratios .
To interpret the results of CRD tests, two different
philosophies can be followed. In one case, one could choose
to measure experimentally only those variables needed to
solve the inversion problem, i.e. obtain the material
characteristics from the governing equation, usually after
some simplifications, knowing the solution observed experi¬
mentally; this would be the equivalent of the curve fitting
methods in conventional tests. For example, in the conven¬
tional approach only the specimen height is monitored in the
test. By curve fitting techniques and the solution of the
governing equation, the coefficient of consolidation and
other properties, including compressibility and permeabil¬
ity, are computed.
Alternatively, one could try to measure directly as
many parameters as possible and avoid the use of the
governing equation, reducing the number of assumptions
concerning the theoretical behavior of the material. For
example, measuring the pore pressure distribution in a
conventional oedometer could lead to the compressibility
curve by only using the effective stress principle. With
the rapid development in the areas of electronics and
instrumentation the use and acceptance of this last approach
will definitely grow.

14
The University of Colorado's CRD test (Schiffman and
Ko , 1981; Scully et al. , 1984; Znidarcic, 1982) can be
classified in the first one of these categories. The test
uses a single - drained 2 - inch specimen. The analysis
procedure neglects the self-weight of the material and
assumes the function g(e) to be piecewise linear in order to
simplify the governing equation (Znidarcic, 1982; Znidarcic
et al., 1986); this is given by
g(e) =
da'
(2.3)
7w(l+e) de
where yw is the unit weight of water, e is the void ratio,
and the other terms have been previously defined.
The test only measures the total stress and pore
pressure at both ends of the specimen, as well as its
deformation. An iterative procedure using the solution of
the linearized differential equation, in terms of the void
ratio, yields the void ratio - effective stress relationship.
The permeabi1ity-void ratio relation can then be computed
from the definition of g(e). However, Znidarcic (1982)
found that this approach produced a 15%-30% error in the
computed values of g(e), and therefore the permeability;
this was for a case where the compressibility relationship
was accurate within 2%.
In an alternative method suggested to overcome the
above problem, the solution of the linearized governing
equation is used as before to obtain the compressibility
relationship. From the theoretical distribution of excess
pore pressure, the hydraulic gradient, i, at the drained

15
boundary can be determined. With this value the coefficient
of permeability is readily obtained from
k (2.4)
where v is the apparent relative velocity at the boundary,
equal to the imposed test velocity; in this form, k is not
directly affected by errors in the calculated values of
g(e) .
Due to the limitations of using consolidation tests to
obtain the permeability, Znidarcic (1982) stressed the
importance of a direct measurement using the flow pump test.
In this technique a known rate of flow is forced, by the
movement of a piston, through the sample and the generated
gradient is measured. This induced gradient must be small
(less than 2) in order to minimize seepage - induced consoli¬
dation (Scully et al . , 1984).
The flow pump test is used in conjunction with a step
loading test to generate the permeabi1ity-void ratio
relationship. This technique, however, is more appropriate
in the case of very stiff and permeable samples (Znidarcic,
1982), where no significant excess pore pressures would be
developed. It has been used for slurries at relatively low
void ratios (e < 8) (Scully et al. , 1984) , and soft samples
of kaolinite (e < 2.8) (Croce et al., 1984).
Znidarcic (1982) has also proposed the use of a
simplified analysis procedure to obtain the permeability
from a CRD test. If the void ratio and therefore the
coefficient of permeability are assumed uniform within the

16
specimen, then the pore pressure distribution is found to be
parabolic. This is justified in those cases where the test
produces very small but measurable pore pressures at the
undrained boundary. From here, the hydraulic gradient and
permeability are easily computed.
An important parameter in any CRD consolidation test is
the rate of deformation. This will determine the amount of
excess pore pressure that builds up in the specimen. Most
analysis procedures assume that the void ratio within the
sample is uniform. However, even when the weight of the
material is negligible, the pore pressure and the effective
stress are not uniform, due to the boundary conditions.
Thus, the assumption of uniform void ratio could never be
met. Nevertheless, it is desirable to keep the hydraulic
gradient small in order to minimize the error introduced by
the assumption. This can be achieved by running the test at
the lowest possible velocity. In the case of the small
strain controlled rate of strain consolidation theory (ASTM
D 4186), an estimate strain rate of 0.0001 %/minute is sug¬
gested for soils with high liquid limits of 120%-140%; the
liquid limit of a typical phosphatic clay is even higher.
The test procedure specifies that the strain rate should be
selected such that the generated excess pore pressure be
between 3% and 20% of the applied vertical stress at any
time during the test. Unfortunately, there are no equi¬
valent recommendations for the case of large deformation
consolidation tests. It has been suggested that an

17
acceptable deformation rate should produce a maximum excess
pore pressure of up to 30%-50% of the applied stress
(Znidarcic, 1982).
A variation of the CRD consolidation test was developed
at the U.S. Army Engineer Waterways Experiment Station (WES)
for testing soft, fine-grained materials (Cargill, 1986) and
to replace the use of the standard oedometer as the tool to
obtain the compressibility and permeability relationship of
dredged materials (Cargill, 1983). In this test, denoted
large strain, controlled rate of strain (LSCRS) test, a 6-
inch in diameter specimen of slurry is loaded under a
controlled, but variable, strain rate; the specimen height
can be up to 12 inches. The main reason for selecting a
controlled and not a constant rate of strain was to minimize
testing time to, typically, 12-16 hours (Poindexter, 1987).
The WES test monitors the pore pressure at 12 ports
along the specimen using 3 pressure transducers and a system
of lines and valves, with the associated problems of system
compliance and dearing. The effective stress at each end of
the specimen as well as its deformation are also measured
with time.
Analysis of the LSCRS data requires the use of the
results obtained from the small self-weight consolidation
test (Poindexter, 1987) in order to generate the compres¬
sibility and permeability relationships. In the approach,
the first void ratio distribution in the specimen is
computed from the measured effective stress, using the

18
value of the compression index, Cc , obtained from the self¬
weight test; at point i the void ratio is given by
ei “ eref - Cc l°g(*i/*ref> (2.5)
where eref = reference void ratio on the previously
determined e-a' curve
crref = value of effective stress at eref
a' = effective stress for which e^ is being
calculated
Between any two points where the void ratio is being
computed, the volume of solids, 1^, is given by
li - hi/(l + ei) (2.6)
where h^ — actual thickness of the increment
e^ = average void ratio of the increment
Since the total volume of solids is constant throughout the
test, the calculated void ratio distribution is adjusted to
satisfy this condition. After this adjustment is done, the
compressibility curve is extended further by using the
average values of effective stress and void ratio of points
next to the moving end as the next reference point. The
process is repeated using the new measured data at increas¬
ing loads.
Determination of the coefficient of permeability at the
moving boundary of LSCRS test is obtained from Darcy's law
using an expression equivalent to equation 2.4. In addi¬
tion, the approach obtains the permeability at interior
points from an estimate of the apparent fluid velocity,

19
obtained from the equation of fluid continuity (Poindexter,
1987 ) .
Many deficiencies have been found in the LSCRS test.
Because of the rapid rate of deformation, consolidation does
not occur uniformly throughout the specimen and a filter
cake of material forms at the drained boundary. Additional¬
ly, the analysis of the test data requires a trial and error
procedure which depends on the results of a self-weight test
to provide a starting point. Last, but not least, the test
equipment is extremely complicated and requires frequent
manual adjustment and monitoring. WES is currently working
on the development of a new test device and procedure
(Poindexter, 1987) to replace the LSCRS test; it will be a
constant rate of strain apparatus and the test is expected
to last from 5 to 10 days. Automatic controlling and
monitoring, through a computer/data acquisition system, will
be incorporated in the test.
Conventional consolidation tests, such as the step
loading test or the CRSC test are very frequently used to
complement the results of large - deformation conso 1idometers
(Ardaman and Assoc., 1984; Cargill, 1983; Poindexter, 1987;
Wissa et al., 1983). In some cases, conventional testing
methods and analysis procedures have been used exclusively
(Cargill, 1983). These tests are usually conducted on
preconso 1idated specimens to facilitate handling and trim¬
ming. Such tests will provide information on the behavior

20
of the material at relatively low void ratios (e < 7)
(Ardaman and Assoc. , 1984) .
Centrifugal Modelling
Centrifugal modelling has been used quite extensively
to predict the consolidation behavior of slurries under
different disposal schemes (Beriswell, 1987; Bloomquist and
Townsend, 1984; McClimans, 1984; Mikasa and Takada, 1984;
Townsend et al., 1987). Several attempts have been made to
determined the soil's constitutive relationships from
centrifuge testing (Croce et al., 1984; McClimans, 1984;
Townsend and Bloomquist, 1983) with relatively good results
obtained in the case of effective stress-void ratio rela¬
tion. Perhaps, one of the most valuable applications of
centrifugal modelling is to validate computer predictions
(Hernandez, 1985; McVay et al., 1986; Scully et al., 1984).
The main advantages of centrifugal modelling in the
study of the consolidation behavior of slurries are (1) the
duplication in the model of the stress level existing in the
prototype and (2) the significant reduction in the time
required to achieve a given degree of consolidation in the
model. This is given by
tm = tp/nx (2.8)
where tm = elapsed time in the model
tp = elapsed time in the prototype
n = acceleration level in number of g's
x
time scaling exponent

21
A major problem with centrifugal modelling is the
determination of the time scaling exponent, x. Theoretical¬
ly, this exponent is 1.0 for sedimentation and 2.0 for
consolidation. In Appendix A a proof is presented where the
governing equation of the finite strain self-weight consoli¬
dation theory holds in the model if and only if x = 2. A
different proof of this result, based on mechanical simila¬
rity, is given by Croce et al. (1984).
However, experimental results based on modelling of
models and reported by several researchers indicate somewhat
contradictory conclusions. An exponent of 2.0 has been
confirmed for the centrifugal modelling of the consolidation
of soft kaolinite clay with a relatively low initial void
ratio of 2.86 (Croce et al., 1984). Scully et al. (1984)
found that the time scale exponent varied from 1.90 to 2.3
for a slurry with initial void ratio of 15; they concluded
that the exponent could be assumed to be 2.0 and that
sedimentation probably did not occur in the tests.
By contrast, the results of Bloomquist and Townsend
(1984) show that starting with an initial void ratio of 16,
the scaling factor progresses from 1.6 to 2.0. They
attributed these values to the existence of two zones in the
slurry, hindered settlement and consolidation. As these
zones approach, consolidation predominates and the theoreti¬
cal exponent of 2.0 is achieved; this occurred at an average
solids content of 20.9% (e = 10.3), practically at the end
of the test.

22
Constitutive Properties
One of the basic assumptions of any of the formulations
of large strain consolidation theory is that the soil's
constitutive relationships are of the general form (e.g.
Cargill, 1982)
a' = a'(e) (2.7a)
k - k(e) (2.7b)
and that they are unique for a given material. Equation
2.7a determines how much consolidation will take place,
while equation 2.7b describes how fast this will happen.
Roma (1976) reported that the best compressibility
relationship for phosphatic clays was a power curve of the
form
e - A-{o')B (2.8)
Likewise, the permeability relationship was expressed by the
function
k=C.(e)D (2.9)
Traditionally, it has been accepted that phosphatic clays
can be characterized by these relationships (Ardaman and
Assoc., 1984; Carrier and Bromwell, 1980; Somogyi, 1979),
and very little effort, if any, has been dedicated to
corroborate the validity of such relationships. This may be
attributed, in part, to the convenience presented by the
simplicity of the expressions and, just maybe, to the bad
habit or tradition of geotechnical engineers to stay with
the "status-quo.

23
The parameters A,B,C,D obtained by several studies for
Kingsford phosphatic clay are presented in Table 2-1.
Table 2-1. Kingsford Clay Parameters
S our c e
A
B
C
D
Ardaman and Assoc. (1984)
26.81
-0.269
7.74E-7
3.56
Somogyi et al.
(1984)
23.00
-0.237
1.03E- 6
4.19
Carrier et al.
(1983)
24.36
-0 . 290
1.34E- 6
3.41
McClimans (1984)
19.11
-0.187
7.59E-14
11.12
Townsend/B1oomquist (1983)
22.30
-0.230
2.03E-9
7.15
These parameters are for a' in psf and k in ft/day.
Ardaman and Assoc.'s parameters are based on slurry consoli¬
dation tests and conventional CRSC and incremental loading
tests. Somogyi et al. parameters were obtained from
laboratory slurry consolidation tests and CRSC tests, as
well as field data.
The parameters attributed to Carrier et al. (1983) were
obtained from the constitutive relationships proposed by
them in terms of the Atterberg limits of the clay, as
preliminary design properties. These relationships, for a
specific gravity of the solids of 2.7, are given by
e = (0.48PI) (a' ) "° ■ 29 (2.10a)
k = (2 . 57PI)*4•29(e)4•29/(l + e) (2.10b)
where PI is the plasticity index in percentage, a' is in
kPa, and k is in m/sec. Using a plasticity index of 156%
reported for this clay (Ardaman and Assoc., 1984; McClimans,

24
1984), a number of data points with void ratios between 5
and 15 were generated. A log-log linear regression, with
very high correlation coefficients, led to the parameters
given in Table 2-1 after the necessary units conversion.
Finally, McClimans' and Townsend and Bloomquist's parameters
were obtained by back-calculations from selected centrifugal
tests.
Table 2-1 shows a tremendous discrepancy in the parame¬
ters defining the constitutive relationships, mainly in
those corresponding to the permeabi1ity-void ratio relation.
This can be the result of improper testing techniques, the
relationships not being unique, or both.
The use of the power functions in computer predictions
introduces an important inconsistency. Under quiescent
conditions, for example, the slurry is deposited at a known
and usually constant solids content. According to equation
2.8, the material must have an initial effective stress
throughout its depth. This implies two things; first, the
initial excess pore pressure will be less than the buoyant
stress and, second, the points at the surface will have an
effective stress which does not exist. The computer
programs overcome this inconsistency by imposing on the pond
a dummy surcharge equal to the initial effective stress
(Somogyi, 1979; Zuloaga, 1986).
The results of several studies suggest that the
constitutive relationships of slurried soils not only are
not power curves, but also are not unique. Specifically,

25
variations in the compressibility relations have been
observed in different soils, especially at low effective
stresses (Been and Sills, 1981; Cargill, 1983; Imai, 1981;
Mikasa and Takada, 1984; Scully et al., 1984; Umehara and
Zen, 1982; Znidarcic et al., 1986). These variations have
been attributed by some to the effect of the initial void
ratio.
Scully et al. (1984) reported the existence of a
"preconsolidation" effect in the compressibility curves
obtained from CRD tests; they concluded that this effect was
most probably the result of the initial void ratio. Similar
results on the permeabi1ity-void ratio relation have not
been specifically reported. However, the curves presented
by several researchers suggest the existence of a zone
similar to the apparent preconsolidation effect observed in
compressibility curves (Scully et al., 1984; Znidarcic,
1986 ) .
Another important aspect that may be conclusive to
better understand the consolidation behavior of slurries is
their initial conditions when they are first deposited.
Scott et al . (1985 ) found in their large settling column
tests that, when the material was first placed in the
cylinders, the pore pressures were equal to the total
stresses over the full height. A similar response was
observed in samples with initial solids content of 10% and
31%. In the case of the denser specimen, a uniform decrease
in pore pressure was observed in 30 days, when no

26
significant consolidation had taken place; this was attri¬
buted to the appearance of an effective stress by
thixotropy. Thus, these results indicate that the slurry
has no effective stress when deposited, regardless of its
initial solids content. If this is the case, the compressi¬
bility relationship can not be unique, at least initially.

CHAPTER III
AUTOMATED SLURRY CONSOLIDOMETER--
EQUIPMENT AND TEST PROCEDURE
Int ro duetion
This chapter describes the test equipment and procedure
of a new automated slurry consolidation test, developed
specifically to obtain the compressibility and permeability
relationships of slurries and very soft soils. Figure 3.1
shows a schematic arrangement of the equipment, which con¬
sists of the following components:
1) test chamber,
2) stepping motor,
3) data acquisition/control system.
The following sections describe in detail each one of these
components. At the end of the chapter, the test procedure
is presented.
The Test Chamber
The specimen of slurry is contained in an acrylic
cylinder with a diameter of 0.2 meters (8 inches) and 0.35
meters (14 inches) height. Figure 3.2 is a schematic of the
test chamber. The initial height of the specimen can be
varied between 0.10 and 0.20 meters (4-8 inches).
A double-plate piston is used to apply the load on the
specimen; the two plates, 3.75 inches apart, help prevent
27

28
Motor
Power Supply
Motor
Manual Control
Load Cell1
Loading
Piston"
Power
Supply
Connection T
Box tE
nT
Gear Box
Stepping
iMotor
Pivoting Arm
' • N'''< • - ■
u
LVDT
T: Transducer
DATA ACQUISITION
SYSTEM
PLOTTER
DISK DRIVE
Figure 3.1
Schematic of Automated Slurry Cons o 1idometer

29
Figure 3.2
Schematic of Slurry Consolidometer Chamber

30
tilting of the piston. At the bottom of the piston, a
porous plastic plate allows top drainage of the specimen. A
filter cloth, wrapped around the bottom plate, closes the
small, nonuniform gap between the piston and the walls of
the cylinder, while allowing water to drain freely.
Originally, this gap was filled with a rubber 0-ring around
the bottom plate; however later, it was found that the
filter cloth served the function better and reduced the
piston friction.
Located directly on top of the piston rod, a load cell
measures the load acting on the specimen at any time. Two
load cells, 200-lb and 1000-lb range, both manufactured by
Transducers, Inc. have been used in this research.
Along the side of the acrylic cylinder, two 1-bar (1
bar = 100 kPa = 14.5 psi) and one 20-psi miniature pressure
transducers are used to monitor the excess pore pressure in
the specimen. Transducer No. 1 is located 1.235 centimeters
from the bottom of the chamber. Transducers No. 2 and No. 3
are placed 5 centimeters above the previous one. An add¬
itional 350-mbar (5 psi) transducer (No. 4), located on the
moving piston, is used to detect any excess pore pressure
building up at the supposedly free - drainage boundary. The
transducers were mounted inside an 0-ring sealed brass
fitting, which threads directly onto the wall of the
chamber. Locating the transducers directly in contact with
the specimen eliminates the problems of tubing, valves, and
system dearing.

31
All the pressure transducers used in the test are model
PDCR 81, manufactured by Druck Incorporated, of England.
They consist of a single crystal silicon diaphragm with a
fully active strain gauge bridge diffused into the surface.
These transducers are gage transducers, thus eliminating the
potential problem of variations in atmospheric pressure,
with a combined nonlinearity and hysteresis of ±0.2% of the
best straight line. To resist the effective stress of the
soil, i.e. only measure pore pressure, a porous filter plate
or stone is placed in front of the diaphragm. The standard
porous stone is made of ceramic with a filter size of 1-3
microns; a 9-12 microns sintered bronze stone is also
available. Figure 3.3 shows a photograph of the PDCR 81 and
a sketch indicating its dimensions.
At the bottom of the specimen another pressure trans¬
ducer (3-bar range), without the porous stone, is used to
measure the total vertical stress at this point. This
measurement, coupled with the load cell readings, makes it
possible to determine the magnitude of the side friction
along the specimen.
A major objective during the design phase of the
equipment was to make it fully automatic. This presented an
obstacle when trying to define the best way to measure the
specimen deformation, which was anticipated to be up to 4-6
inches. The problem was solved using a Direct Current
Linear Variable Differential Transformer (LVDT) and the
pivoting arm arrangement shown in Figure 3.2. The LVDT,

32
(a)
e Li
dimensions: mm
BLUE: SUPPLY NEGfiTIVE
YELLOU: OUTPUT POSITIVE
GREEN: OUTPUT NEGRTIVE
(b)
- Pore Pressure Transducer PDCR81. a) Photograph;
b) Sketch Showing Dimensions
Figure 3.3

33
model GCD-121-1000 and manufactured by Schaevitz, has a
nominal range of ±1 inch and linearity of ±0.25% at full
range.
The horizontal distances from the pivoting point of the
arm to the center of the specimen and to the LVDT tip were
accurately measured as 121.2 mm and 35.6 mm, respectively,
which resulted in an arm ratio of 1:3.40. This arrangement
allows measuring specimen deformations over 6 inches. The
factory calibration of the LVDT was converted using the arm
ratio to yield directly the deformation of the specimen.
Appendix B evaluates the converted calibration of the LVDT
and proves that computations of the deformation are indepen¬
dent of the initial inclination of the arm.
Figure 3.4 is a photograph of the test chamber showing
the pressure transducers, the loading piston, the LVDT, and
the pivoting arm. Table 3.1 summarizes the information on
the different devices. The recommended excitation for
these transducers is 5 VDC, but this was increased to 10
VDC, the maximum allowed, to improve the transducer sensi¬
tivity. Although the 200-lb load cell was used in most of
the tests, the information on the 1000-lb load cell is also
included since this was used in some tests where the load
was expected to be large.

34
Figure 3.4 - Photograph of Slurry Conso 1idometer Chamber

Table 3-1. Slurry Cons o 1idometer Transducer Information
DEVICE
MODEL
SERIAL No.
TOTAL
STRESS
PDCR 81
3021
PWP
#1
PDCR 81
2998
PWP
#2
PDCR 81
2955
PWP
#3
PDCR 81
3092
PWP
#4
PDCR 81
3241
LOAD
CELL
T182 - 200 - 10P1
73169
T1 8 2 - IK-10P1
49650
LVDT
CCD-121 - 1000
3220
RANGE
EXCITATION
CALIBRATION
3 bars
10 VDC
3.568
mV/psi
1 bar
10 VDC
6.370
mV/psi
1 bar
10 VDC
7.418
m V / p s i
2 0 p s i
10 VDC
6 . 900
mV/psi
5 p s i
10 VDC
12.80
mV/p s i
200 lb
10 VDC
0.099805 mV/lb
1000 lb
10 VDC
0.019943 mV/lb
2 in
+/- 15 VDC
0.117
V / m m

36
The Stepping Motor
The load applied to the specimen is produced by a
computer-controlled stepping motor and a variable speed
transmission arrangement, located as shown in Figure 3.1.
The stepping motor is a key element of the apparatus; its
versatility is crucial in allowing different types of
loading conditions.
The stepping motor is manufactured by Bodine Electric
Company, model 2105, type 34T3FEHD. It operates under 2.4
VDC and 5.5 amps/phase. The motor has a minimum holding
torque of 450 oz-in and a SLEW (dynamic) torque of 400 oz-
in, producing 200 steps per revolution or 1.8 degree per
step.
The motor is driven by a THD-1830E Modular Translator,
model No. 2902, also made by Bodine. The translator uses
and external 24 VDC power supply. The photograph of Figure
3.5 shows the front panel of the translator (left), and the
stepper motor (right), while Figure 3.6 presents a schematic
diagram of the back of the instrument with the cover
removed, showing the connections to the stepping motor. For
this configuration, the following resistances are required
Suppression Resistor: R^ = 13 ohms @ 18W
Series Resistors (2): R2 = 3.6 ohms @ 175W
Logic Resistor: R3 = 15 ohms @ 2W
All control line connections to the stepping motor control
card are made through a 15 pin "D" connector, located on the
side of the translator. For manual (front panel) control of

3 7
Figure 3.5
Motor Translator, Gear Box, and Stepper Motor

OVERALL SYSTEM SCHEMATIC
ir THD - 1830E
© @ ©
©
& i 2
1» CC *1
Cl
CS A
s
r |
T T 1
15 Pin
‘D’ Connector
Stepper
Motor
Resistors
Figure 3.6 - Schematic of Motor Translator Connections

39
the motor, pins 6 and 13 of the connecter are jumped. A
switch that allows this jumping was installed next to the
translator. In this way the control of the motor can be
easily switched between manual and computer. Manual
operation of the motor is very important during setting up
and dismantling of the test.
The variable speed transmission (gear box), made by
Graham, converts the motor rotation into vertical movement
of a threaded rod, which acts directly on the loading piston
(Figure 3.5). Even if the motor is running at full speed,
the gear box allows minute movement of the loading piston.
During the testing program, the speed control of the gear
box was set at its maximum, producing a vertical displace¬
ment in the order of 3E-05 mm/step. Figure 3.5 also shows
the load cell at the bottom of the threaded rod.
Figure 3.7 shows a photograph of the entire test
assembly. The equipment was mounted on a steel frame.
The Computer and Data Acquisition/Control System
Figure 3.8 shows a photograph of the computer system
used to control and monitor the test. The computer is a
Hewlett Packard, model 86B, with 512 KB of memory and a
build-in BASIC Interpreter.
The data acquisition/control system has two components:
an HP-3497A and an HP-6940B, both manufactured by Hewlett
Packard. The HP-3497A, a state-of-the-art data acquisition
and control unit, is used to monitor the pressure

40
Figure 3.7 - Entire Slurry Conso 1idometer Assembly

41
transducers, load cell, and LVDT outputs. The unit can be
remotely operated from the computer or through the front
panel display and keyboard.
The 3497A Digital Voltmeter (DVM) installed in the unit
is a 5H digit, 1 microvolt sensitive voltmeter. Its
assembly is fully guarded and uses an integrating A/D
conversion technique, which yields excellent noise rejec¬
tion. Its high sensitivity, together with autoranging and
noise rejection features, makes it ideal for measuring the
low level outputs of thermocouples, strain gauges and other
transducers. The DVM includes a programmable current source
for high accuracy resistance measurements when used simulta¬
neously with the voltmeter.
The 3497A DVM assembly is very flexible and can be
configured to meet almost any measurement configuration. It
may be programmed to obtain a maximum of 50 readings per
second in 5H digit mode or 300 readings per second in 3h
digit mode. The 3497A DVM may be programmed to delay before
taking a reading to eliminate any problem with settling
times. Similarly, the DVM assembly can be programmed to
take a number of readings per trigger with a programmable
delay between readings. This feature, combined with
internal storage of sixty 5h digit readings, permits easy
stand-alone data logging.
Installed in the 3497A, there is a 20 channel analog
signal reed relay multiplexer assembly. This assembly is
used to multiplex signals to the 3497A DVM. Each channel

42
Figure 3.8
Computer and Data Acquisition/Control System

consists of three, low thermal offset dry reed relays, one
relay each for Hi, Lo and Guard. The low thermal offset
voltage characteristics of this multiplexer makes it ideal
for precise low level measurements of transducers. The
relays may be closed in a random sequence or increment
between programmable limits.
The other component of the data acquisition/control
system, the HP-6940B Multiprogrammer, provides flexible and
convenient Input/Output expansion and conversion capability
for computers. This versatility has made the Multiprogram¬
mer an important part of many different types of automatic
systems, including production testing, monitoring and
control (e.g. Litton, 1986). In the current application,
however, the 6940B, interfaced to the computer through the
HP-59500A Multiprogrammer Interface, is used exclusively to
control the stepping motor.
A stepping motor control card, model 69335A, was
installed in the Multiprogrammer. The card is programmed by
a 16-bit word originating at the computer to generate from 1
to 2047 square wave pulses at either of two output terminals
of the card. When these outputs are connected to the
clockwise and counterclockwise input terminals of the
stepping motor translator, the output pulses are converted
to clockwise or counterclockwise steps of the associated
motor. As the card is supplied from the factory, the output
is a waveform of positive symmetrical square-wave pulses
with a nominal frequency of 100 Hz. If this frequency is

44
not suitable, it can be changed to any value between 10 Hz
and 2 kHz by changing the value of one resistor and one
capacitor in the card. The output frequency can also be
made programmable by connecting to the card an external
programmable resistor.
During early stages of the research, the Multiprogram¬
mer was also used to monitor all the devices by means of
Relay Output/Readback and High Speed A/D Voltage Converter
cards, as used by Litton (1986). Electrical noise rejection
in the low level outputs of the pressure transducers and
load cell was attempted by means of analog low pass filters
(Malmstadt et al., 1981). Several preliminary tests were
performed using this hardware configuration, whereby each
transducer output was obtained as the average of 10-20
individual readings, to further reduce any noise. It was
found, however, that the level of noise in the response was
still unacceptable. Therefore, it was decided to undertake
a detailed investigation of the transducers response using
different size capacitors. In addition, the use of digital
filters (Kassab, 1984) was incorporated, and the HP-3497A
was tried for the first time, as an alternative to the
Multiprogrammer. Appendix C describes the study undertaken.
It was concluded, as a result of the study, that the HP-
3497A would be used to monitor all transducers. In the case
of the LVDT, the output is not affected so much by noise.
However, it was decided to change it to the HP-3497A also

45
and to leave the HP-6940B exclusively to control the
stepping motor.
The Controlling Program
The program that controls the test, called SLURRY1, was
written in BASIC for the HP-86B. It is a user-friendly
program and presently allows two types of test: a Constant
Rate of Deformation test (CRD) and a Controlled Hydraulic
Gradient test (CHG). However, other types of loading
conditions can be very easily incorporated in the program,
such as constant rate of loading, step loading, etc.
In the CRD test, the program sends a signal to the
stepper motor every half-second to turn forward a given
number of steps, corresponding to the desired rate of
deformation. A calibration between number of steps and
vertical displacement of the piston was made for the gear
box speed set at its maximum value; the value obtained was
30,000 steps/mm. Based on this value, the two deformation
rates used in the testing program correspond to the motor
speeds given in Table 3-2.
Table 3-2. Deformation Rates in CRD Tests
Deformation Rate (mm/min) Steps/min
0.008 240
0.02
600

46
In the CHG test, the excess pore pressures at the
bottom and top of the specimen, as well as the specimen
deformation, are continuously monitored. The average
hydraulic gradient across the specimen is computed from this
information. If the gradient differs from the desired value
by more than a defined percentage, the motor is activated
forward or backward accordingly to keep the gradient within
the desired range. The required number of steps at any
moment is estimated from the previous value of number of
steps per unit change in gradient. The experience with the
tests performed in this study shows the effectiveness of
this approach.
SLURRY1 is organized in a main program and several
subroutines. The main program reads the input information
and contains the two routines that control the CRD and CHG
tests, as described previously. Eight subroutines interact
with the main program to perform the operations described
b elow.
Subroutine CALIBRATIONS reads the calibration factors
for all the devices from a file on disk; it allows changing
or adding new devices to the file, after displaying the
current configuration on the monitor. Subroutine INITIALI¬
ZATION takes the initial readings of the transducers and
LVDT; it also prints the general test information and
headings of the results table.
Subroutine STEPPING activates the motor as requested
by either the CRD or CHG routines. Subroutine RUNTIME

evaluates the elapsed time of the test at any moment.
Subroutines READLOWVOLT and READHIGHVOLT read consecutively
all the devices.
Subroutine CONVERTDATA uses the readings of the
transducers and LVDT, and their calibrations, to compute all
the pressures, load, and specimen deformation; these
parameters are stored on disk for future data reduction.
Subroutine TESTEND decides whether any of the conditions to
finish the test has been reached. Appendix D presents a
flowchart of the main routine of SLURRY1, and a listing of
the full program.
Test Procedure
The test, being controlled by the computer, runs by
itself without any human assistance. However, setting up
the apparatus requires 2 to 3 hours and is somewhat compli¬
cated. This section describes details of the test proce¬
dure .
In broad terms, the test procedure consists of the
following steps: (a) specimen preparation, (b) deairing and
calibration of the pressure transducers, (c) filling the
chamber with slurry and adjusting the load cell and LVDT,
(d) initiating computer control, (e) reading devices
periodically, (f) coring specimen at the end of the test,
and (g) reducing data.
The specimen is prepared in a 5 gallon plastic bucket
just before the beginning of the test. The slurry is

48
strongly stirred with an egg beater attached to an electri¬
cal drill, to provide a uniform solids content. To reach
the desired value of solids content, quick determinations of
this value were made using an Ohaus Moisture Determination
Balance. This turned out to be a very handy tool. If
needed, water or thicker slurry was added to the mix to
achieve the desired solids content. Due to the lack of
available supernatant water in sufficient amount, tap water
was used in most of the tests. Two samples were always used
to perform a regular water content determination, from which
the initial solids content was determined. It was found
that the solids contents obtained with the Moisture
Determination Balance were always within ± 0.5% of the oven-
determined values.
An important part of the test preparation procedure is
the vacuum system shown schematically in Figure 3.9. This
is used to fill the test chamber with deaired water to
produce full saturation of the porous stones and to take the
zero readings of the pore pressure transducers (under
hydrostatic conditions). The operation of the vacuum system
is controlled by a series of four 3-way valves, used as
described in the following paragraph.
Water is sucked into the chamber by turning the vacuum
pump on with all four valves in the 'a' position. The water
can be drained out of the chamber by gravity. However, the
process is accelerated by pulling the water with vacuum with
valves 1 and 3 in the position 'b', and valves 2 and 4 in

49
Figure 3.9 - Vacuum System
Table 3-3.
Operation
Fill with water
Drain water
Valve Positions in Vacuum System
Valve 1 Valve 2 Valve 3 Valve 4
a a a a
b aba
a , b
Fill with slurry
a
b
a

50
the position 'a'; toward the end of this process, however,
care must be exercised to prevent the entrance of air into
the water container. To avoid this, the vacuum pump is
turned off and valve 4 is vented (position 'b') when most of
the water has been drained; the remaining will drain by
gravity. The vacuum system is also used to fill the chamber
with slurry prepared in a container at the desired solids
content. To do this, valves 1 and 3 must be set to the
position 'a', while valve 2 is on the 'b' position. Table
3-3 summarizes the valve positions required for each
operation.
The following is a list of the steps followed in the
test procedure:
1. Assemble the vacuum system, set the piston to the sample
height, and pull deaired water into the chamber.
2. Turn on the transducers power supply and HP-3497A; check
the supply voltage of 10 Volts by reading it from the front
panel of the HP-3497A. Allow a warming up time of 10-15
minutes.
3. Apply full vacuum to the chamber to deair the porous
stones; check how fast the transducers respond by turning
the vacuum on and off several times.
4. Check the calibration of all five transducers by raising
(or lowering) the height of water by 10 cm and taking the
corresponding voltage readings using the front panel of the
HP-3497A; the computed change in height of water must be 10 ±
1 cm .

51
5. Set the height of water to the height to be used in the
test.
6. Run the program SLURRYl and enter the required data
(sample height, initial solids content, etc.); the program
will take the zero readings of the pore pressure transducers
at this point.
7. When prompted by the program, drain the water and pull
the slurry into the chamber using the vacuum system; check
that the piston is at the right height. The program has
paused at this moment.
8. Take the vacuum attachment off and set the motor control
switch to "manual".
9. Set up the load cell by operating it manually, the LVDT,
and the pivoting arm.
10. Add water over the piston to reach the desired height
(usually 11 cm. over the slurry height), as used for the
zero readings; this is done to guarantee that the piston is
always submerged.
11. Change the motor control to "computer" and check that
the LVDT power supply is on.
12. After everything has been verified press the "CONT" key
to resume the computer control of the test.
13. SLURRYl prints heading of the output printout and the
test starts.
From this moment the control and monitoring of the test
is completely taken by the computer. Readings of the
different devices are taken periodically as specified by the

52
user. The time of reading, pressures, load, and specimen
deformation are stored on a disk file specified by the user,
for future data reduction. The test stops automatically
when the maximum time specified is reached. Termination of
the test also occurs when any of several abnormal conditions
occurs, such as exceeding a pressure transducer or the load
cell .
Once the test is completed and the chamber attachments
have been removed, the supernatant water is removed and the
specimen is cored using a device similar to that used by
Beriswill (1987) in his centrifuge bucket. The cored
material was sectioned into three pieces to determine the
solids content near the top, at the middle, and near the
bottom of the specimen. Due to the difficulties in obtain¬
ing a good sample, no attempt was made to determine the
solids content - depth relationship. An average final solids
content was determined from these three values.
The allowed deviation in the transducers response,
recommended in step 4 of the test procedure, is the result
of observations about the transducers sensitivity during the
testing program. Table 3-4 shows the results of one pre¬
test verification of the ca1ibration/sensitivity of all five
pressure transducers.
With water in the test chamber, a set of readings, R]^ ,
was taken using the front panel of the HP-3497A. The height
of water was then increased by exactly 10 cm, and new
readings were taken, R2. With these values and the factory

5 3
Table 3-4. Verification of Transducer Calibration
T r ans due e r
No .
R1
(mV)
r2
(mV)
Calibration
(mV/p si)
Ap
(psi)
Ah
(cm)
T . S .
-1.586
-2.115
3.568
0.1483
10.43
1
-17.610
-18.568
6 . 370
0.1504
10.58
2
-22.856
- 24.002
7.418
0.1545
10.87
3
9.363
8 . 364
6 . 900
0.1448
10.18
4
8.698
6.970
12.800
0.1350
9.50
calibration factors, the change in hydrostatic pressure, Ap,
was computed. Assuming the unit weight of water as 62.4
pcf, the change in the height of water, Ah, was computed.
Four of the five transducers gave heights above 10 cm,
with a maximum deviation of 0.87 cm for transducer No. 2.
Surprisingly, in this test the total stress transducer (3-
bar range) did not produce the maximum deviation, and pore
pressure transducer No. 4 (5-psi range) did not produce the
minimum. In the case of the total stress transducer, where
similar results were observed in other tests, the low
deviation was attributed, at least partially, to the
beneficial effect of not having the porous disc. The
relatively large deviation of pore pressure transducer No. 4
is probably the result of the random nature of the varia¬
tion. In another test, for example, the same transducer
gave a deviation of only 0.024 cm when the height of water
was increased by 10 cm.
These observations led to the conclusion of allowing a
deviation of ±1 cm, when checking the calibration of the
transducers prior to the test. One centimeter of water

54
(0.014 psi) is taken as the approximate sensitivity of these
pressure transducers.

CHAPTER IV
AUTOMATED SLURRY CONSOLIDOMETER--
DATA REDUCTION
Intro due tion
A main objective during the development of this new
test was to make direct measurements of as many variables as
possible, in order to minimize the use of theoretical
principles or assumptions. The formulation of the two
constitutive relationships required in finite strain
consolidation theory involves three variables, namely, void
ratio, effective stress, and coefficient of permeability.
Direct measurement of these parameters is not feasible.
Instead, they will be evaluated from well accepted soil
mechanics principles, such as Darcy's law and the effective
stress principle, using the measured values of load, excess
pore pressures, specimen deformation, and others.
The following sections describe the proposed method of
data analysis to obtain the constitutive relationships of
the slurry. In the analysis, the specimen is treated as an
element of soil with uniform conditions, although it is
recognized that the void ratio and other parameters change
with depth mostly due to the boundary conditions. This
assumption was necessary due to the lack of a proper method
to measure this variation. Thus, the specimen will be
characterized by average values of void ratio, effective
55

56
stress, and coefficient of permeability. If certain condi¬
tions of the test are controlled, the errors introduced by
this assumption can be minimized as will be discussed later
in this chapter.
Determination of Void Ratio
A direct evaluation of the void ratio in a sample of
soil is not usually possible since volumes are not easily
measured. Instead, the void ratio is most commonly obtained
from unit weights and the use of phase diagram relation¬
ships. In the slurry conso 1idometer, however, an average
value of void ratio can be readily obtained from the
specimen height and the initial conditions.
Figure 4.1 shows the phase diagrams of the specimen
initially and at any later time, t. Two assumptions are
made at this point, namely, that the slurry is fully
saturated and that the volume of solids in the specimen, Vg,
does not change throughout the test. Both of these assump¬
tions can be made with confidence.
From Figure 4.1a, the total volume of specimen at the
beginning of the test can be expressed as
A • h - (1 + ei)-Vs (4.1)
where A is the cross section of the specimen, h^ is the
initial height, and e^ is the initial void ratio.
At time t (Figure 4.1b), the height of the specimen has
been reduced to h, due to the compression of volume of voids
AV .
The volume of the specimen is now

~1
? «V
1
\
ts
!
VOIDS
}
V
{
s
L
^ SOLIDS x
(a)
A V
VOIDS
~t
\
e
!
xWWWWW
I
V
A
\
S
I
^ SOLIDS ^
WWWWVx
(b)
Ln
Figure 4.1 - Phase Diagrams, a.) Initial Conditions; b) Conditions at tine t

58
A•h - (1 + e)*VS (4.2)
where e is the new void ratio.
Dividing equation 4.2 by equation 4.1 and solving for
the void ratio leads to
e = (h/hi).(l+ei) - 1 (4.3)
considering that both A and Vs are constant.
The phosphate industry uses the term solids content, S,
to describe the consistency of the slurry. This is defined
as
S(%) - (Ws/Wt)•100 (4.4)
where Ws is the weight of solids, and Wt is the total
weight. It can be easily shown that this is related to the
water content by the relation
S(%) - 100/(1 + w) (4.5)
where w is the water content in decimal form.
From phase diagrams, it is easily proved that
Sr*e=Gs»w (4.6)
where Sr is the degree of saturation, and Gs is the specific
gravity of the solids.
Combining equations 4.5 and 4.6, for a degree of
saturation of 100%, leads to a useful relationship between
the void ratio and the corresponding solids content of the
slurry. This is
S(%) = 100•Gs/(Gs + e)
(4.7)

59
Determination of Effective Stress
The evaluation of an average value of effective stress
involves a large number of variables, including the applied
load, specimen weight, four excess pore pressures, and
sample and piston friction. First, the effective stress at
the location of each transducer is expressed as
- °m + aw * uh - ue (4-8)
where
-o' is the effective stress
-om is the total stress component due to the applied load
-ctw is the total stress component due to the specimen weight
-u^ is the hydrostatic pore pressure and
-ue is the excess pore pressure recorded in the transducer.
The buoyant stress is defined as
ab = aw ‘ uh = Tb*z (4.9)
where z is the depth of the transducer and 7^ is the buoyant
unit weight, to be computed from the average void ratio as
7b " 7W* (4.10)
Substituting equation (4.9) into equation (4.8) we obtain
= CTm + CTb - ue (4.11)
The total stress om is to be computed from the load
cell reading, but it must include two important effects,
namely, piston and sample friction. In order to account for
the first one of these effects in the CRD test, dummy tests
were run with the piston in water, while recording the load
cell readings. The values obtained for two different
deformation rates are reported in next chapter. The

60
estimated piston friction is subtracted from the load cell
readings in the actual test to obtain a corrected load
value, P. In the case of the CHG test, due to the nature of
the test, the behavior of piston friction is expected to be
more erratic and unpredictable, and no attempt was made to
estimate its value.
The reading of the 3-bar PDCR 81 pressure transducer
installed at the bottom of the chamber, a tb ' use<^ to
estimate the side friction along the specimen. The zero
reading of this total stress transducer is taken after the
specimen is placed in the chamber. Therefore, if there
were no friction, this transducer would record the stress
induced by the piston load. However, this is not the case.
In a very simplistic approach, the difference between
and the piston pressure, att, obtained from the corrected
load cell reading is distributed linearly with depth to
evaluate the total stress induced by the motor load om.
This is
CTm = att * (att - CTtb)*(z/h) (4.12)
where z is the depth of the transducer under consideration.
Once the effective stress has been computed at the
depth of every transducer, the average effective stress is
obtained from the area of the o'-z curve as
o' « (Area under o' - z )/h (4.13)
Figure 4.2 shows schematically the variation of o' with
depth, indicating the distances between transducers in the
test chamber. The effective stress exactly at the bottom of

61
the specimen is assumed equal to aFor this case the
average effective stress simplifies to
o' = [1.235a'1 + 2.5(a,1 + 2CT^ + a¿)+h(h- 11.235 ) (a'3 + a4) ]/h (4.14)
where aj represents the effective stress at the jth trans¬
ducer, and h must be in centimeters.
Figure 4.2 - Variation of Effective Stress with Depth
Obviously, if the specimen has deformed such that the
piston passes beyond the location of transducer No. 3, or
even No. 2, equation 4.14 must be modified accordingly not
to include those transducers readings. The corresponding
equations are given below.
For transducers 1 and 2 in the specimen (h < 11.235 cm.),
o' = [1.235a'! + 2 . 5 ( o'i + o'2 ) + h (h - 6 . 2 3 5 ) ( a '2 + o^ ) ] /h (4.15)

62
For only transducer 1 in the specimen (h < 6.235 cm) ,
o’ = [1.235*1 + h(h - 1.2 3 5)(*1 + *4)]/h (4.16)
It must be emphasized that these equations are valid only
for the dimensions of this particular chamber, as given in
Chapter III.
In this approach it is important that the distribution
of effective stress with depth be close to uniform, to
conform to the assumption of specimen uniformity. This can
be obtained by having a relatively small hydraulic gradient
across the specimen. In the CHG test this can be easily
achieved since the gradient is controlled. In the CRD test,
however, the hydraulic gradient is not controlled. Thus, to
overcome this limitation the rate of deformation can be
slowed sufficiently to produce acceptable pore pressure
ratios.
Determination of Permeability
The coefficient of permeability, k, is obtained from
Darcy-Gersevanov's law (McVay et al., 1986):
n(V f - Vs) - -ki (4.17)
where n is the soil porosity,
Vf is the fluid velocity,
Vs is the solids velocity, and
i is the hydraulic gradient.
A second equation, however, is needed in order to solve for
the coefficient of permeability. McVay et al. (1986)
expressed the mass conservation of the fluid phase as

63
la. + in
fie fit
O
(4.18)
and the volume conservation of the solids as
itl-n] , S[(l-n)Vs]
fit fie
where q = n*Vf is the exit fluid velocity, and
e is the spatial coordinate.
Replacing equation 4.18 into equation 4.19 leads to
JcL fi[(l-n)Vs] _
fie fie
Being a function of only one independent variable,
4.20 can be directly integrated to give
q + (l-n)Vs = constant
and replacing the expression for q, we obtain
nVf + (l-n)Vs = constant
Since at the bottom boundary Vf = Vg = 0, equation
further reduces to
(4.19)
(4.20)
equation
(4.21)
(4.22)
4.22
nVf + (l-n)Vs = 0 (4.23)
This equation represents the condition of continuity of the
two-phase system at any given time t, and was first proposed
by Been and Sills (1981). Combining equations 4.17 and 4.23
to eliminate the fluid velocity leads to
(4.24)
the relationship from which the coefficient of permeability
will be evaluated. By substituting equation 4.24 into
either equation 4.17 or 4.23, an expression for the fluid
velocity is obtained. This is
V s - k • i
VH
(1-n)
n
ki -
ki
(4.25)

64
which can be expressed in terms of the solids velocity by
using equation 4.24 as
vf “ 'vs/e (4.26)
Equations 4.24 through 4.26 allow an interesting
comparison between small and large deformation consolidation
processes. First, equation 4.24 shows that, for a given
hydraulic gradient, the higher the coefficient of permeabil¬
ity, the higher the velocity of solids. Let us consider,
for example, a slurry consolidation under its own weight
from an initial void ratio of 15 (S = 15%). At the end of
the consolidation process, the slurry will probably have
deformed about half of its initial height, reaching a void
ratio around 6 or 7. Experimental data to be presented in
Chapter V will reveal that such a slurry has an initial
permeability in the order of 10'^ cm/sec.
If the same clay existed in a natural state with a void
ratio of only 1 or 2, it would probably have a permeability
in the order of 10'® cm/sec; this is 10,000 times smaller
than that of the slurry with initial void ratio of 15. The
consolidation of such a material would be considered a small
strain process. Thus, assuming the same hydraulic gradient,
the solids velocity of the second material (small strain)
would be 10,000 times smaller than that of the former (large
strain). This simple example may help to justify the
assumption of a rigid skeleton, i.e. zero solids velocity,
made in small strain consolidation theory.

65
Additionally, the fluid velocity expressions also pro¬
vide some information that may help to understand the
difference between small and large strain consolidation
theories. It can be observed from equation 4.26 that the
fluid velocity is e times smaller than the solids velocity.
This means that Vf is relatively smaller in the case of a
slurry with a very large void ratio. In a natural clay
stratum, where the void ratio is commonly less than 1, the
fluid velocity would actually be larger than the solids
ve1o city.
Returning to the determination of the coefficient of
permeability, to obtain its average value, one must use the
average hydraulic gradient across the specimen and the
average solids velocity. The average hydraulic gradient is
obtained from the weighted average slope of excess pore
pressure distribution. The distance between transducers is
used as the weighing factor. The resulting average
hydraulic gradient is
i = (ux - u4)/h/7w (4.27)
which only depends on the excess pore pressure at the
boundaries. The evaluation of the average solids velocity,
on the other hand, presents a problem. Specifically,
between any two readings, taken at times t and t+At, the
mean velocity of the piston represents the solids velocity
at the top of the specimen. This is
Vpiston - Ah/At (4.28)
It is also known that the solids velocity at the bottom
of the specimen is zero. However, the actual distribution

66
of Vs along the specimen is not known. Since it is not
believed that the error introduced will be significant, the
average solids velocity is taken as the average of the
solids velocity at the two boundaries, i.e.
Vs “ ^piston/^ (4.29)
Using equations 4.24 and 4.27 through 4.29, the average
coefficient of permeability is easily obtained from
k = Vs/i = Vpiston/(2i) (4.30)
To carry out the data reduction using the approach des¬
cribed above, a BASIC program, SLURRY2, was developed to run
in the HP-86B. The program, that reads directly the data
stored by SLURRY1, computes the average values of void
ratio, effective stress, and coefficient of permeability at
every time that a set of readings was taken. These values,
together with the corresponding time, specimen height,
gradient, and other parameters, are printed out as they are
computed.
For the case of the phosphatic clays of Florida, it has
been suggested that the two constitutive relationships can
be described as power curves of the form (e.g. Ardaman and
Assoc., 1984):
e = A(cj' )B (4.31)
k = CeD (4.32)
Using a log-log linear regression, SLURRY2 computes the
parameters A, B, C, and D and the corresponding coefficients
of correlation. The program can also plot the two curves
(experimental data) using different units and arithmetic or

A lis ting o f
67
log axes, according to the user'
SLURRY2 is included in Appendix
choice .

CHAPTER V
AUTOMATED SLURRY CONSOLIDOMETER--
TEST RESULTS
Testing Program
The material selected for this study was Kingsford
clay, a waste product of the mining operations by IMC
Corporation in Polk County, Florida. This slurry has been
studied extensively (Ardaman and Assoc., 1984; Bloomquist,
1982; McClimans, 1984), and it is typical of the very
plastic clays found in Florida's phosphate mines (Wissa et
al . , 1982 ). Kingsford clay consists mostly of montmorillo-
nite and has the following index properties (Ardaman and
Assoc., 1984; McClimans, 1984):
LL = 230% PI = 156% Gs - 2.71 Activity = 2.2
The testing program developed during this part of the study
consisted of four Constant Rate of Deformation tests and
four Controlled Hydraulic Gradient tests. The former were
intended to investigate the effect of the initial solids
content and the deformation rate upon the compressibility
and permeability relationships. In the CHG tests the
influence of the hydraulic gradient on the results was to be
studied. The effect of the initial specimen height, about
15 cm. for all the tests, was not investigated. Table 5-1
presents the testing conditions of both groups of tests.
68

69
Table 5-1. Conditions of Eight Tests Conducted
Test
hi (cm)
Si .(%)
CRD
CRD-1
14.7
15.3
CRD-2
14.9
10.2
CRD-3
15.0
16 . 2
CRD-4
15.0
10.7
CHG
CHG -1
15.0
15 . 6
CHG- 2
15.0
16.4
CHG- 3
15.0
16.3
CHG - 4
15.0
16.0
Rate fmm/min) Gradient
0.02
0.02
0.008
0.008
2.0
4.0
10.0
20.0
CRD Tests Results
Of the four CRD tests, two of them were conducted on
dilute slurries with solids content between 10% and 11%
(CRD-2 and CRD-4), while the other two tests were conducted
on denser specimens with solids contents in the order of 15%
to 16% (CRD-1 and CRD-3). In each group, one test was run
at a slow rate of deformation of 0.008 mm/min (CRD-3 and
CRD-4), while the other was run at a faster rate of 0.02
mm/min (CRD-1 and CRD-2).
Tests CRD-1 and CRD-2 were performed with an early
version of the test chamber whose differences from the
present design are worth mentioning. Originally the
pressure transducers were mounted in a pipe-threaded brass
fitting, which had to be tighten in order to seal properly.
This fitting soon began to crack the acrylic and therefore
it was replaced with the 0-ring sealed fitting currently
used. In the original chamber, transducer No. 1 was located
at 0.6 cm from the bottom of the chamber, and not 1.235 cm
as in the present chamber.

70
During the development of the equipment several pistons
were tried in the chamber to produce a snug fitting with the
minimum possible friction. In the case of test CRD-1 the
piston used was fairly loose and a filter cloth was wrapped
around the bottom plate to prevent the escape of slurry, but
allowing free drainage. This arrangement allowed the piston
to fall freely in water. Therefore, no piston friction was
included in the analysis of test CRD-1. Instead, the
submerged weight of the piston was added to the applied
motor load. The resulting additional pressure of 0.0109 psi
is not significant for most of the test, but it does affect
the initial portion of the compressibility curve.
The specimen of test CRD-1 started at a solids content
of 15.3% (e -= 14.97) and a height of 14.7 cm. The test was
conducted at a rate of deformation of 0.02 mm/min for 62
hours (=: 2.5 days). Readings were taken every 30 minutes
(124 data points). The final specimen height was 7.19 cm
and the computed average solids content was 28.5% (e =
6.81). Direct measurement of the solids content led to an
average value of 28.7% with a variation of 4.7% across the
specimen, which indicates a very good agreement. Figure 5.1
shows the compressibility and permeability plots for test
CRD-1 as produced by the data reduction program. Both
curves show a very well defined behavior.
For test CRD-2, the old chamber was still used but a
much tighter piston was tried. At this point in time no
attempt was made to estimate the magnitude of the piston

16
15
14
13
12
11
10
9
8
7
6
TEST CRD-1
RATE = 0.02 mm/min
hi = 14. 7 cm
Si = 15.33 % ei = 14.97
F
* + +
s
L
V
s
v
y
y
y,
\
1 10 100 1000
Effective Stress (psf)
(a)
.1 - Results of Test CRD-1. a) Compressibility Relationship; b) Permeability
Relationship

16
15
14
13
12
11
10
9
8
7
6
TEST CRD-1
RATE = 0.02 mm/min
hi = 14.7 cm
Si = 15.33 %
ei = 14.97
±H
—■
+
+f
++
+
+
+
|H
â– +-
A
F
3t
$
f-
-
V
1-
K
, Tj
t + +
. +
*•-
%
lo"2 10"1 10°
Coefficient of Permeability, k (ft/day)
(b)
Figure 5.1—Continued

73
friction, but it was suspected to be large enough to affect
the compressibility curve. The specimen in this test began
at a solids content of 10.2% (e = 23.96) with a height of
14.9. The test was run at a deformation rate of 0.02 mm/min
for 72 hours (3 days), with 30 minutes between readings. At
the end of the test, the LVDT-based height of the specimen
was 6.02 cm, but visual observation of the specimen indi¬
cated a value of around 5.7 cm. A similar discrepancy was
also found in the solids content. The computed value was
22.97% (e = 9.09), while the measured average was 24.37%
with a gradient of 6.98% across the specimen. If the
observed specimen height of 5.7 cm were accepted as correct,
then the computed solids content would be about 24%, which
agrees very well with the measured value. This discrepancy
is attributed to possible disadjustment of the pivoting arm-
LVDT arrangement.
When the data of test CRD-2, with a dilute specimen,
was first reduced, the average effective stress showed
negative values up to a solids content of about 13.5%. The
data reduction program was later modified to make zero any
negative effective stress computed at the location of the
pore pressure transducers. This result seems to indicate
that below this solids content the slurry has no effective
stresses, or these are two low to be detected with the
equipment used. Once the program was modified to eliminate
negative values, it was observed that the average effective
stress increased above 0.01 psi (the estimated sensitivity

of the transducers) when the solids content was again about
13.4%. Figure 5.2 shows the compressibility and permeabi¬
lity curves of test CRD-2 as plotted by SLURRY2. The
initial portion of the compressibility plot (Figure 5.2a)
shows clear evidence of pseudo-static piston friction.
Another interesting aspect of the plot is the step-like
shape. This effect may be attributed to a discontinuity in
the computed effective stress when the piston passes by
transducer No. 3 (at h = 11.235 cm.), as a result of the
analytical approach used. However, this irregular effect is
not observed with the same magnitude in all the tests. The
permeability plot, on the other hand, exhibits a well
defined trend with almost no scatter.
The new chamber described in Chapter III was used for
the rest of the tests. It was found that the 0-Ring sealed
piston did not fall freely in the chamber; a study was
conducted to estimate the magnitude of the piston friction.
With water in the chamber, dummy tests were conducted and
the load cell readings recorded with time. Since transducer
No. 4 did not record any build-up of pressure, it was
assumed that the load cell reading was only reflecting the
piston friction. For the deformation rate of 0.02 mm/min,
the average friction obtained was 6.5 lbs, while for the
rate of 0.008 mm/min the average value was 8.6 lbs; in both
cases the variation of the recorded load was very small.
The testing program carried out in this part of the
research never attempted to study the statistical validity

25
24
23
22
21
20
19
18
17
15
15
14
13
12
11
10
9
•
TEST CRD-2
RATE = 0.02 mm/min
hi = 14. 9 cm
Si = 10. 16 % ei = 23. 96
â– T
+ '
+
*».
«
+
' *
Í
:
â– 
.
h
+
VJ
â– J
It
f
\
s
»
*
*
•
a
L
. 1 1 10 100
Effective Stress (psf)
(a)
5.2 - Results of Test CRD-2. a) Compressibility Relationship; b) Permeability
Relationship

25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
TEST CRD-2
RATE = 0.02 mm/min
hi = 14. 9 cm
Si = 10. 16 %
ei = 23.96
.if-
*
H
.4
-
h 4-
—1
*
j
hit
*
é
&
+
/
r
if
.
â–  fe?
P
10-2 10"1 10° 101
Coefficient of Permeability, k (ft/day)
(b)
Figure 5.2—continued

77
of any particular observation. Nevertheless, it was inter¬
esting to investigate the dup1icabi1ity of the tests
results. With this in mind, an additional test was con¬
ducted with similar conditions to those of test CRD-1. This
test, the first one with the new chamber, was originally
intended to be a different test, conducted for 7 days at the
slower rate of deformation of 0.008 mm/min. After the test
had been running for 6 hours, it was sadly discovered that
somebody had turned the main breaker off and that the test
had been aborted. To avoid wasting the specimen, it was
decided to run a quicker test (3 days) which would approxi¬
mately duplicate test CRD-1. The initial height of the
aborted test was 14.7 cm and the initial solids content was
15.7%. Although the specimen had deformed about 3 mm when
the test stopped, no corrections were made on the initial
values once the test was restarted. The results of both
tests, CRD-1 and its duplicate, are shown in Figure 5.3.
Considering the conditions under which the duplicate test
was conducted and expected variations in the material
itself, it can be said that the results are reproduced quite
we 11 .
The compressibility plot of the duplicate test shows an
abrupt discontinuity in the effective stress. This could be
explained with the same arguments given for test CRD-2.
The other two CRD tests were run at the slower rate of
deformation (0.008 mm/min). Test CRD-3 was initiated at a
solids content of 16.2% (e = 14.01) with a specimen height

co
(a)
Figure 5.3 - Duplication of Test CRD-1. a) Compressibility Relationship;
b) Permeability Relationship

(b)
Figure 5.3—continued

80
of 15 cm. After running for 168 hrs (7 days), with 2 hours
between readings, the final height was 7.32 cm (computed),
while the observed value was 7.1 cm, indicating a very good
agreement. As for the final solids content, the computed
value was 29.99% (e = 6.33), while the measured average was
29.94 with a variation of only 2.66% across the specimen,
again an excellent agreement. Figure 5.4 shows the compres¬
sibility and permeability curves obtained from test CRD-3.
The fact that the time interval between readings was
relatively large may have resulted in the loss of valuable
information during early parts of the test.
Finally, test CRD-4 began at a solids content of 10.66%
(e = 22.70) with the specimen height at 15 cm. This test
was the longest one, running for 216 hr (9 days), and
proving that the apparatus is capable of working for long
periods of time without any problem. For approximately 1
day, the results of this test indicated inconsistent
results, such as negative values of permeability. These
results were attributed to the extremely low pore pressures
being read; these points were discarded. At the end of the
test the computed specimen height was 5.1 cm, while the
observed value was 4.5, a quite significant difference. The
computed final solids content was 27.75% (e = 7.06) and the
measured value was 29.68%, with a variation across the
specimen of only 1.56%. Figure 5.5 shows the compressi¬
bility and permeability plots obtained from test CRD-4. The
compressibility plot shows significant scatter with initial

15
14
13
12
11
10
9
8
7
6
TEST CRD-3
RATE = 0.008 mm/min
hi = 15 cm
Si = 16.21 % ei = 14.01
>
4
4
>
+
4-
X
H
Í1
•
'r
*
:»
+ *4
V
r.
N
S
r
4
'
-
1 10 100 1000
Effective Stress (psf)
(a)
Figure 5.4 - Results of Test CRD-3. a) Compressibility Relationship;
b) Permeability Relationship

15
14
13
12
11
10
9
0
7
6
TEST CRD-3 RATE - 0.008 mm/min
hi = 15 cm
Si = 16.21 %
ei = 14.01
..
V*
+
+ +
â–¼
s4
A
('*
J
J
/
*
•
±*
r~
.++ ♦
+
+
10'2 10-1 10°
Coefficient of Permeability, h (ft/day)
CO
N>
(b)
Figure 5.4—continued

24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
•
TEST CRD-4
RATE = 0.008 mm/min
hi = 15 cm
Si = 10.66 % el = 22.71
â– 1-
+
+
+
+ ' â– 
*
t
«
*t\
A
u
Si
A
â– 
i
b
fl L-
4
1 r
It
N
â– 
^ -Hi
♦a*.
. 1 1 10 100
Effective Stress (psf)
(a)
Figure 5.5 - Results of Test CRD-4. a) Compressibility Relationship;
b) Permeability Relationship

24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
10"3 10-2 10_1 10° 101
Coefficient of Permeability, k (ft/day)
(b)
Figure 5.5—continued
CO

85
evidence of piston friction and some irregular behavior
around an effective stress of 1 psf, in a way similar to
test CRD-2. Both of these tests started at the low solids
content level, and this may be partially responsible for
these results.
Table 5-2 summarizes the conditions of the specimens at
the end of the four CRD tests, and shows the duration of
each test.
Table 5-2. Summary of CRD Tests Results
Test
Duration
(hr s )
Final Height (cm)
Computed Observed
Final
Computed
Solids Cont.(%)
Measured Gradient
CRD-1
62
7 . 19
7 . 1
28.5
28.7
4.7
CRD-2
72
6.02
5 . 7
23.0
24.4
7.0
CRD- 3
168
7 . 32
7 . 1
30.0
29.9
2 . 7
CRD - 4
216
5 . 10
4.5
27.8
29.7
1 . 6
The results of these tests clearly show that the
variation in solids content with depth is significantly
smaller in those tests performed at the slower rate of
deformation. This result is important considering the
assumption of specimen uniformity made during the analysis
of the data. This condition, however, can never be com¬
pletely satisfied since the excess pore pressure dissipates
faster at the top boundary. Thus, although the total stress
in the specimen is close to uniform (assuming self-weight is
smaller than the motor load), the excess pore pressure
distribution is not. Figure 5.6 shows the distribution of

P.P.(t=1170)
E.S.(t=1170)
P.P.(t=3720)
E.S.(t=3720)
P.P.(psi) E.S.(psi)
Figure 5.6 - Pore Pressure and Effective Stress Distributions
with Depth for Test CRD-1

87
excess pore pressure and effective stress with depth at two
different times in test CRD-1. The first one, for t = 19.5
hr, corresponds to an average solids content of 18.3% (e =
12.13), and an average effective stress of only 0.11 psi.
The second time plotted is at the end of the test (t = 62
hr), corresponding to an average solids content of 28.5%
(e = 6.81) and an average effective stress of 1.27 psi.
It is clear from Figure 5.6 that the effective stress
and therefore the void ratio are far from being uniform with
depth, especially toward the end of the test when the
hydraulic gradient increases significantly. The pore
pressure ratio, defined in this test as the ratio of the
excess pore pressure in transducer No. 1 to the total stress
at the bottom of the specimen, is commonly used in CRD tests
to limit the magnitude of the excess pore pressure. For
test CRD-1, for example, performed at the rate of 0.02
mm/min, the pore pressure ratio increased up to about 88% at
the end of the test. Contrarily, for test CRD-4, performed
at the slow deformation rate, the maximum pore pressure
ratio was about 54%. Pore pressure ratios between 30% and
50% have been recommended by Znidarcic (1982).
The results of the four CRD tests are plotted together
in Figure 5.7. The compressibility curves shown in Figure
5.7a demonstrate the effects of initial solids content and
rate of deformation. First, all four tests show a "precon¬
solidation" effect, which depends on the initial solids
content. Such an effect has been reported without any

26
24
22
20
IB
16
14
12
10
8
6
4
1
Fi
^ CR0-1 Sia15.3Z 0.02 â– â– /â– in
a CRD-2 Sia10.2Z 0.02 «/«in
â–¡ CRD-3 Sia16.2Z 0.008 m/nin
â–  CRD-4 Sia10. 7Z 0.008 im/nin
* • 1 • # * *»"»| ■ ■ ■ ■ * * *»
4 IE-3 IE-2 IE-1 1E 0 IE 1
Effective Stress (psi)
(a)
iré 5.7 - Summary of CRD Tests, a) Compressibility Relationship;
b) Permeability Relationship

26
24
22
20
18
16
14
12
10
8
6
4
^ CRD-1 Sia15.3Z 0.02 ma/min
^ CR0-2 SM0.2Z 0.02 mm/min
â–¡ CRO-3 Si=16.2Z 0.008 iw/iin
â–  CRD-4 Si=10.7Z 0.008 m/nin
af* □ °
4 IE-3 IE-2
Permeability (ft/day)
IE-1
IE 0
IE 1
(b)
Figure 5.7—continued
CO
vO

90
explanation by Scully et al. (1984), and can also be
observed in tests reported by Mikasa and Takada (1984).
It is believed that the preconsolidation effect is the
result of testing a specimen that begins in a highly
remolded state, due to specimen mixing and preparation.
Under such conditions the effective stresses are practically
zero at the beginning of the test, regardless of the initial
solids content. As the specimen is initially stressed, the
soil particles start interacting and regaining the struc¬
tural arrangement that was lost during remolding, in some
kind of thixotropic effect. Thus, the effective stresses
increase relatively quickly early in the test, without
significant reduction in void ratio, until the compression
curve reaches a point where it breaks down to enter the
virgin zone. It is believed that this behavior also occurs
in the field since mining slurries are deposited in a very
remolded condition. Poindexter (1987) justifies the use of
remolded specimens of dredged material on the basis of the
destruction of any insitu internal structure by the dredging
process.
It is clearly noticeable in Figure 5.7a that the two
lower solids content curves, CRD-2 and CRD-4, approach
almost perfectly the virgin zone of the corresponding higher
solids content curves, CRD-1 and CRD-3. Thus, the initial
solids content affects the preconso 1idation zone, but the
virgin zone slopes are independent of initial conditions.
The rate of deformation appears to have a similar effect on

91
both the dilute and the dense specimens. In the virgin
portion of the curves, the faster tests (CRD-1 and CRD-2)
plot parallel and to the right of the slower tests (CRD-3
and CRD-4). Thus, the slope of the virgin curve is inde¬
pendent of deformation rate for the range of these test
conditions.
It is conceivable that a minor part of the disagreement
on the compressibility curves between the fast and slow
tests may be attributed to equipment problems. For example,
test CRD-1 was analyzed assuming no piston friction; on the
contrary, the submerged weight of the piston (0.0109 psi)
was added to the effective stress, based on observations
that indicated that the piston moved freely inside the
chamber. However, for subsequent tests this approach was
changed when a new chamber and piston were introduced, and
piston friction was incorporated. However, the magnitude of
these effects has been analyzed and found to be small.
Their influence will be more significant early in the test,
when the effective stress are relatively small. For
example, at the end of test CRD-1, if piston friction is
considered, the effective stress would only decrease by
about 5%. However, the comparison shows that the effective
stress in test CRD-3 at the same void ratio is almost 60%
smaller than that of test CRD-1.
Thus, the effect of deformation rate on the compressi¬
bility relationship is believed to be a true soil response.
In the case of small strain CRD tests, it is a well accepted

92
fact that decreasing the rate produces a decrease in the
measured effective stress (Mesri and Choi, 1987). A
comprehensive study by Leroueil et al. (1985) on five
different natural Canadian clays clearly showed that, at a
given strain, the higher the strain rate, the higher the
effective stress. They proposed a rheological model in
which the effective stress-void ratio relationship is not
unique but incorporates the strain rate. Although similar
results have not been reported for large deformation
consolidation tests, there is no reason to eliminate the
possibility of the same behavior on remolded slurries.
The permeability curves of the four CRD tests,
presented in Figure 5.7b, show less scatter than those
corresponding to the compressibility relationship. In this
case the rate of deformation does not have any significant
effect on either the dilute (S¿ = 10-11%) or dense (S^ = 15-
16%) specimen. Similar to the compressibility relation¬
ships, the permeability curves show an initial preconsolida¬
tion portion, changing at a point which is a function of the
initial solids content. All curves clearly approach a well
defined virgin zone. A possible explanation for this
behavior could be found under the same arguments previously
given to explain the preconsolidation effects observed in
Figure 5.7a. Thus, the virgin slope of the e-k relationship
is independent of initial solids content and deformation
rate for this range of test conditions.

93
CHG Tests Results
The controlled gradient tests were performed under
different hydraulic gradients, but with initial solids
contents of 15% to 16%, similar to those of the constant
rate of deformation tests CRD-1 and CRD-3 (see Table 5-1).
In all the tests the specimen height was 15 cm. The
magnitude of the piston friction is undetermined in the CHG
tests .
The first test, CHG-1, was set for a low gradient of 2,
allowing a variation of ±5%. The initial solids content was
15.6% (e = 14.64). The test lasted for 192 hours (8 days),
taking readings every 2 hours for a total of 97 data points,
including the first time the desired gradient was reached at
about 15 minutes. The final height of the specimen was
computed from the LVDT reading as 9.23 cm, matching almost
exactly the observed value. The final solids content
computed was 23.9%, while the measured average value was
24.4% with a variation across the specimen of only 2%. With
the low gradient used in this test, the recorded values of
pressures and load were extremely small, producing signifi¬
cant scatter in the results. The maximum average effective
stress in this test was less than 0.2 psi. Figure 5.8 shows
the compressibility and permeability plots of test CHG-1.
The existence of an unpredictable piston friction was a
major disadvantage of the CHG tests. In trying to reduce
its magnitude, the 0-Ring around the bottom plate was
replaced by a filter cloth, and the friction estimated for

Void Ratio,
16
TEST CHG-1
GRADIENT “ 2
hi = 15 cm
Si = 15.62 X
ei - 14.64
4
4
4
4
+ l
«
4
4
H
TT
•4
\
ix
to
i
m
15
14
a 13
12
11
10
8
10 100
Effective Stress (psf)
(a)
Figure 5.8 - Results of Test CHG-1. a) Compressibility Relationship;
b) Permeability Relationship

16
15
14
13
12
11
10
9
0
TEST CHG-1
GRADIENT =2 hi = 15 cm
Si - 15.62 %
ei = 14.64
•
h
4
4-
4-
f
A
4
*
<
J?
r
*
+•
*â– *%
?
f
4 “
4
4
+ 4-
i *
A
i .
*
*â– 
jjt
4-
++
f
*4 '
10"2 10"1 10°
Coefficient of Permeabi1ity, k (ft/day)
(b)
Figure 5.8—continued

96
constant rates of deformation. It was found that for a rate
of 0.02 mm/min the average friction was 1.25 lb compared to
6.5 lb with the 0-Ring. For a deformation rate of 0.008
mm/min the friction was 2.06 lb versus 8.6 lb when the
0-Ring was used. These results led to the decision of using
the filter cloth for the rest of the CHG tests, and simply
neglecting the effect of the piston friction.
In the case of test CHG-2, the gradient was 4 ± 5%,
with an initial solids content of 16.4% (e = 13.77). The
test duration was 168 hours (7 days). Readings were taken
every hour for a total of 169 data points. At the end of
the test the computed specimen height was 8.33 cm, while the
observed value was 8.3 cm. The final solids content was
computed as 27.3% (e = 7.20), and the average measured value
was 28.1% with a variation of 2.2% across the specimen.
Figure 5.9 shows the compressibility and permeability curves
of test CHG-2. The higher gradient used produces values of
pressures and load which are read more accurately by the
devices, which in turn produces better defined curves.
The specimen of test CHG-3 had an initial solids
content of 16.3% (e = 13.86) and ended at a height of 6.55
cm with an average solids content of 33.0% (e « 5.49)
(computed values), after 168 hours (7 days) of testing.
Direct measurements of solids content at the end of the test
produced an average value of 35% with a variation of only
0.44% across the specimen, with an observed final height of
6.2 cm. The gradient set for this test was of 10 ± 5%.

Void Ratio
CO
Effective Stress (psf)
(a)
Figure 5.9 - Results of Test CHG-2. a) Compressibility Relationship;
b) Permeability Relationship
10
100

Void Ratio,
15
TEST CHG-2
¡ GRADIENT -4 hi *» 15 cm
Si - 16.44 % ei - 13.77
+
+
h
*
*
F
*
$
r
+j
f
H
+jP
10~3 10~2 10"1 10°
Coefficient of Permeability, k (ft/day)
(b)
Figure 5.9—continued

99
Readings for test CHG-3 were taken every hour, produc¬
ing a total of 169 data points. Figure 5.10 shows the plots
produced by SLURRY2 as the data is reduced. Again, the
higher gradient produces less scatter in the results.
The last test, CHG-4, was run at the highest hydraulic
gradient, 20 ± 2.5%, for 120 hours (5 days). The initial
solids content was 16%. Readings were taken again every
hour, producing 121 data points. At the end of the test the
computed height was 6.22 cm, corresponding to a solids
content of 33.8%. The observed final height was 6.0 cm and
the measured average solids content was 35.9% with a varia¬
tion of 1.18% across the specimen. Figure 5.11 shows the
plots obtained from test CHG-4. The final conditions for
the specimens of the four CHG tests are summarized in Table
5 - 3 .
Table 5-3. Summary of CHG Tests Results
Test Duration Final Height (cm) Final Solids Cont.(%)
(hr s )
Comnuted
Ob s e rve d
Computed
Measured
Gradient
CHG-1
192
7 .23
7 . 2
23.9
24.4
2.0
CHG - 2
168
8.33
8 . 3
27.4
28.1
2 . 2
CHG-3
168
6.55
6 . 2
33.0
35.0
0.4
CHG-4
120
6.22
6.0
33.8
35.9
1 . 2

Void Ratio
10 100 1000
Effective Stress (psf)
(a)
Figure 5.10 - Results of Test CHG-3. a) Compressibility Relationship;
b) Permeability Relationship
100

15
14
13
12
11
10
9
8
7
6
5
TEST CHG-3
GRADIENT - 10 hi - 15 cm
Si = 16.35 X ei - 13.86
•
a.
-
+
+
+
+
<-
.
f
i
d
i
¿
+
P
í
i
L-
+
*
â–  â– 
10“3 10“2 10"1
Coefficient of Permeability, k (ft/day)
(b)
Figure 5.10—continued
101

Void Ratio
Effective Stress (psf)
(a)
Figure 5.11 - Results of Test CHG-4. a) Compressibility Relationship;
b) Permeability Relationship
102

Void Ratio,
15
a
14
13
12
11
10
9
0
7
6
5
TEST CHG-4
GRADIENT » 20
hi = 15 cm
Si - 16 X
ei “ 14.23
+
.
â– t
+
+
+
H-H
â– 
4
»
..r
1
i*A.
i
■tfí.
â–º
v
i-
**
1Í
â– 1 +
+
10"4 10"3 IQ"2 10
Coefficient of Permeability, k (ft/day)
(b)
Figure 5.11—continued

104
Figure 5.12 shows the pore pressure and effective
stress distributions at two different times for one of the
CHG tests. The first time is when the desired gradient of 4 ±
5% is first reached at about 23 minutes. At this time the
solids content is 16.8% (e = 13.45) and the average effec¬
tive stress, occurring mostly on the top fourth of the
specimen, is only about 0.12 psi. The second set of curves
is practically at the end of the test (167 hours), when the
average solids content is 27.3% (e = 7.21) and the average
effective stress is 0.33 psi, which is still relatively low.
These plots show that even at relatively low gradients, the
variation of effective stress with depth is significant.
The results of the four CHG tests are presented
together in Figure 5.13. The compressibility curves of
Figure 5.13a show a very interesting behavior. First, the
preconsolidation effect is not observed in these curves, due
in part to the fact that the specimen is loaded very fast
initially, without any reading taken until the desired
gradient is reached. In all the cases, the effective stress
initially jumped to a relatively high value, and immediately
started decreasing, contrary to all expectations. After
some time the effective stress began to increase again, as
the specimen continued to deform. It is interesting to
observe how parallel these initial portions of curves 2, 3
and 4 are. In the case of test CHG-1, with the lower
gradient, the curve shows a lot more scatter but a similar
trend is observed. Although not clearly understood, this

Test CHG-2
P.P.(t=23) E.S.(t=23) P.P.(t=10020) E.S.(t=10020)
P.P.(psi) E.S.(psi)
Figure 5.12 - Pore Pressure and Effective Stress Distributions
with Depth for Test CHG-2
105

o
•ri
â– P
o
cu
16
14-
12-
10-
8-
6-
^ CHG-1 Si°15,
a CHG-2 Si=*16,
â–¡ CHG-3 Si=16,
â–  CHG-4 Si=16,
T
1E-1
Effective Stress (psl)
II
(a)
Figure 5.13 - Summary of CHG Tests, a) Compressibility
b) Permeability Relationship
6Z i - 2
4Z i - 4
3Z i - 10
0Z i - 20
T~
: o
Relationship;
106

16
14-
12-
10-
8-
6-
4
IE-4 IE-3 IE-2 IE-1 IE 0
Permeab111ty (ft/day)
(b)
Figure 5.13—continued
^ CHG-1 Si=15.6Z i ° 2
* CHG-2 Si=16.4Z i B 4
□ CHG-3 Si=16.3Z i « 10
■ CHG-4 Si=16.0Z i « 20
’—•—■■■»■ ■ »"i —■ ■ i •—'— i —
107

108
strange behavior of the initial portion of the compressibil¬
ity curves is attributed to the drastic decrease in rate of
deformation in the controlled gradient tests; for example,
the mean deformation rate in test CHG - 3 dropped from a very
high initial value of 0.15 mm/min to about 0.02 mm/min in
just six hours. This result seems to corroborate the
conclusion obtained in the previous section concerning the
effect of deformation rate upon the compressibility.
Figure 5.13a also shows how all four compressibility
plots converge to a unique curve. This virgin zone of the
plot is independent of the hydraulic gradient or the
irregular behavior observed in the early portion of the
curves.
The permeability results of the four CHG tests are pre¬
sented in Figure 5.13b. The data points fall in a rela¬
tively small band. Thus the permeability relationship
obtained from these tests can be said to be independent of
the hydraulic gradient for the range of values considered in
the tests.

109
Testing Influences
In a CRD test, maintaining the deformation rate
constant forces the hydraulic gradient to increase with
time. Conversely, in a CHG test, keeping the hydraulic
gradient constant makes the deformation rate decrease from
very high values initially to extremely low values near the
end of the test. This effect is shown in Figure 5.14, where
plots of the rate of deformation and hydraulic gradient with
time are shown for one test of each type. First, it is
clearly observed that neither the rate of deformation in a
CRD test, nor the hydraulic gradient in a CHG, is completely
constant, due to equipment characteristics in the first case
and allowed variation in the second.
For the CRD test, the hydraulic gradient remains very
small (less than 2) for the first 2000 minutes of testing.
After this point, it increases very rapidly. In the case of
CHG test, the deformation rate is initially very high but
decreases very quickly to a value around 0.02 mm/min in 300-
400 minutes. This deacceleration effect is reduced from
that point on.
A comparison of the various constitutive curves clearly
shows that there is a more irregular behavior in the com¬
pressibility plots obtained from CHG tests (Figure 5.7a vs.
Figure 5.13a). This is attributed, at least partially, to
piston friction which probably behaves in a more erratic and
unpredictable way in the controlled gradient tests, due to
the way the specimen is loaded; its real magnitude is

CRD-2(Rate)
CRD-2(Grad.)
CHG-3(Rate)
CHG-3(Grad.)
Rate (mm/min) Gradient
Time (min)
Figure 5.14 - Deformation Rate and Hydraulic Gradient with Time
for Tests CRD-2 and CHG-3
110

Ill
completely unknown. For the CRD tests, on the other hand,
the piston friction was estimated from tests using only
water, indicating an almost constant value for a given rate
of deformation.
A comparison of the results of two CRD tests (1 and 3)
with two CHG tests (2 and 3) is shown in Figure 5.15. All
four tests had an initial solids content around 15% to 16%.
The permeability results of the CRD and CHG tests are
in good agreement, regardless of hydraulic gradient or
deformation rate. Conversely, in the case of the compressi
bility, at effective stresses of 0.2-0.4 psi (S = 23-25%)
the CHG curves approach the virgin portion of the curve
obtained from the test with low rate of deformation (CRD-3)
In all the tests performed to this date, it has been
observed that the permeability plot always shows a better
defined trend with less scatter. This is reasonable, con¬
sidering that the average values of void ratio and coeffi¬
cient of permeability are calculated from few parameters,
namely the specimen height and the pore pressures at the
bottom and top of the specimen (which are measured with the
two most accurate transducers). The calculated average
effective stress, on the other hand, not only depends upon
four pore pressure measurements plus that from the load
cell, but also depends on specimen friction estimated from
the total stress transducer reading (not very accurate) and
piston friction, which is completely unknown for the GHG
tests and only approximated for the CRD tests. With more

16
o
•H
-»->
o
aa
14-
12-
10-
8-
6-
^ CRD-1 Sia15.3Z 0.02 nn/min
CRD-3 Si=16.2Z 0.008 aua/uin
â–  CHG-2 Si=16.4Z i - 4
â–¡ CHG-3 Si=16.3Z i - 10
4 — •—»—•—»»»»»| » » ■ »■■»■■»■» 11
IE-3 IE-2 1E-1
Effective Stress (psi)
(a)
■ • • • « • • 11
1E 0
■» r
Figure 5.15 - Comparison of CRD and CHG Test Results, a) Compressibility
Relationship; b) Permeability Relationship
112

16
o
•#-*
+â– >
o
cu
14-
12-
10-
8-
6-
^ CRD-1 Si=15.3Z 0.02 nua/nin
^ CRO-3 Si=16.2Z 0.008 mn/min
â–  CHG-2 Si=16.4Z i ** 4
o CHG-3 Si=16.3Z i = 10
i"rirni
IE-4 1E-3
Perraeabi1ity (ft/day)
IE-2 1E-1
(b)
Figure 5.15—continued
■ 1 1 1 ■ » ■
1E 0

114
variables containing more measurement error, it could be
anticipated that the compressibility plots would show more
scatter. In addition, the compressibility relationship
depends more on the assumption of specimen uniformity since
the approach computes an average value of effective stress
from a distribution that may be highly variable due to the
boundary conditions.
A key element in the computation of the coefficient of
permeability is Darcy's law. Therefore, it is very impor¬
tant to evaluate its validity in the slurry cons o 1idometer.
Darcy's law is accepted as valid when the fluid flow is
laminar. The criterion to evaluate this condition is based
on Reynolds number. For the case of flow through porous
media, a Reynolds number has been defined as (Bear, 1979)
Re = q-d/v (5.1)
where q, the specific discharge, is defined as the volume of
fluid passing through a unit area of soil in a unit time; d,
a representative length of the porous matrix, is taken as
the diameter such that 10% of the soil by weight is smaller
(D^q); and v is the kinematic viscosity of the fluid.
Goforth (1986) found that, for sands, Darcy's law was
valid for Reynolds numbers below 0.2. A critical value of
Reynolds number in the slurry conso 1idometer tests is
probably obtained in a fast CRD test, near the end of the
test when the void ratio is minimum. The specific dis¬
charge, q, will be assumed to the average relative velocity
of the fluid with respect to the solids particles, since

115
both phases are moving. For example, for test CRD-1 with a
rate of deformation of 0.02 mm/min, the average solids
velocity is 0.01 mm/min (1.67E-04 mm/sec). Near the end of
the test, when the void ratio reaches a value of 7, the
absolute value of the average fluid velocity is computed
from equation 4.16 as
Vf = (1.67E-04)/7 - 2.38E-05 mm/sec (5.2)
Thus, the specific discharge is simply
q = 2 . 3 8 E- 0 5 + 1.67E-04 - 1.91E-04 mm/sec (5.3)
Using a value of D^q °f 0.002 mm and a kinematic viscosity
for water at 75° of 1 mm^/sec (Streeter and Wylie, 1975),
the Reynolds number is computed by substituting Equation 5.3
into Equation 5.1 as
Re = (1.91E-04 mm/sec)(0.002 mm)/(l mm^/sec)
= 3.8 E- 0 7 (5.4)
This very low value of Reynolds number indicates that
Darcy's law is valid in the tests, even for the fast
deformation rate. This result may very well explain the
agreement obtained in the permeability among the different
tests, regardless of the rate of deformation or hydraulic
gradient.
The results of the tests reported here suggest that
power functions like equations 4.31 and 4.32 may not be the
best mathematical representation of either the compressi¬
bility or permeability relationship. Although the virgin
zone of the experimental curves could be represented fairly
well by this type of function, the introduction of the

116
initial preconso1idation zone changes the entire picture.
The immediate result of this is that the permeability and
compressibility relationships would not be unique but would
depend on the initial solids content, as demonstrated by the
plots of Figure 5.7. In addition, computer codes that allow
the input of data points instead of the traditional A, B, C
and D power curve parameters to characterize the soil would
be more appropriate.
Finally, because of the abnormal behavior of the CHG
compressibility curves and other disadvantages of the test,
this testing method is not recommended for practical
applications or even for future study. The CRD test, on the
other hand, offers a number of advantages, such as the
possibility of anticipating the testing time required to
achieve a desired final condition. The results of the CRD
tests reported in this research are more reasonable. For
the sake of comparison, the constitutive curves obtained
from test CRD-1 are plotted in Figure 5.16, together with
the power curves fit to the experimental data and other
functions proposed for Kingsford clay (Table 2-1). The
power curve parameters obtained for test CRD-1, which
include the points in the preconsolidation zone, are
A - 18.03 B = -0.165
C = 3.619E-09 D = 6.27
with a correlation coefficient around 0.95 for both curves.
Although the power curves do not show the preconsolidation
effect observed in the CRD test, Figure 5.16 shows that

Data points
A.B.C.D
Ardaman
Somogy
Carrier
Void Ratio
117

Data Points
A,B|C|D
Ar daman
Somogy
Carrier
Void Ratio
Figure 5.16—continued
118

119
the overall behavior of the results of the CRD tests falls
within the range of the other curves.

CHAPTER VI
CENTRIFUGE TESTING--EQUIPMENT,
PROCEDURE, AND DATA REDUCTION
Introduction
Centrifuge testing has been used quite extensively to
model the sedimentation/consolidation process of slurries,
including the analysis of different disposal techniques
(Beriswill, 1987; Bloomquist, 1982; McClimans, 1984;
Townsend and Bloomquist, 1983), and to a lesser extend to
validate the results of numerical predictions (Hernandez,
1985; McVay et al. 1986; Scully et al., 1984).
Few attempts have been made, however, to obtain the
constitutive relationships of the slurry from centrifuge
testing. The compressibility relationships obtained by
McClimans (1984) and Townsend and Bloomquist (1983) agree
relatively well with the results of other tests (see Table
2-1). Their approach is based on the measurement of solids
content with depth after selfweight consolidation, when all
excess pore pressure has been dissipated. This measurement
allows determining the void ratio and the effective stress
with depth in the specimen. However, the number and quality
of the points obtained with this approach are largely
dependent upon the quality of the coring process. On the
other hand, the backcalculations and curve fitting methods
120

121
suggested in these studies to obtain the permeability
relationships yielded parameters which disagree signifi¬
cantly with the results of other tests.
Takada and Mikasa (1985) have also used centrifuge
tests for the determination of consolidation parameters.
Similar to the studies previously cited, the compressibility
curve is obtained from the water content profile at the end
of the test. The coefficient of permeability is obtained
from the initial settlement rate of selfweight consolida¬
tion. They derived the following expression for k, valid
only at the surface of the layer and for the early stage of
selfweight consolidation under single drainage.
where s is the initial settlement rate,
n is the acceleration level in g's
7W is the unit weight of water, and
is the initial buoyant unit weight.
In this approach, one test at a given initial void
ratio will represent one point of the permeability plot;
thus, a large number of tests with different initial
conditions are needed. Another disadvantage of the approach
is the difficulty in estimating the initial settlement rate.
This chapter describes a new technique developed
specifically to obtain the compressibility and permeability
relationships of soils from centrifuge testing. The
approach is based on measurements of excess pore pressure
and solids content with depth and time during the test.

122
These allow computing the void ratio, effective stress, and
coefficient of permeability using a material representation
of the sample. Perhaps, the main advantage of the approach
is that the curves are obtained from a model with stress
conditions similar to those existing in the slurry pond.
The following sections of this chapter describe the test
equipment, procedure and method of data reduction.
Test Equipment and Procedure
The geotechnical centrifuge at the University of
Florida was used for the testing program carried out in this
study. The 1-m radius centrifuge can accelerate 25 Kg to 85
g's (2125 g-Kg) (Bloomquist and Townsend, 1984). In the
standard test procedure, the waste clay is contained in a 14
cm diameter by 15.25 cm high cast-acrylic container. This
container is housed in a swinging aluminum bucket, with a
vertical window that allows visual observation of the model.
A Polaroid camera in combination with a photo-electric pick-
off and flash delay are used to monitor the model height
during the test. Figure 6.1 shows a schematic drawing of
the centrifuge and photographic equipment. More detailed
descriptions of this equipment have been reported elsewhere
(Beriswill, 1987; Beriswill et al., 1987; McClimans, 1984).
A specimen height of 12 centimeters was selected for
this testing program. The distance from the center of
rotation to the bottom of one of the four buckets (bucket A)

Figure 6.1 - Schematic of Centrifuge and Camera Set-up
123

124
was measured as 43.125 inches (109.54 cm), and the distances
to the other buckets were adjusted to the same value. For
a 12-cm specimen, the radius to the center of gravity is
then 103.54 cm. Average acceleration levels of 60g and 80g
are achieved in this specimen with angular velocities of 228
and 263 r.p.m., respectively. The radial acceleration
gradient in each case is about ±5.6%, representing about
±3.5g in a 60g test and ±4.6g in 80g test.
Two new elements were added to the test in order to
accomplish the objectives established. They are the
measurements of excess pore pressure and solids content with
depth and time.
To measure the excess pore pressure distribution, the
acrylic bucket was modified by attaching three of the
pressure transducers used in the automated slurry consoli-
dometer described in Chapter III. Figure 6.2 shows a photo¬
graph of the modified bucket. Information on the three
transducers selected is shown in Table 6-1. The transducers
were located at 1, 5, and 9 centimeters from the bottom of
the specimen. For the model height used in the tests, this
arrangement was expected to produce a good pore pressure
curve. The excitation of the transducers was 10 VDC, as
used in the slurry cons o 1idometer tests. Monitoring of the
pressure transducers was done with the HP-3497A also
described in Chapter III.

125
Figure 6.2
Centrifuge Bucket

126
Table 6-1. Centrifuge Test Transducer Information
Transd .
Distance
Serial
Factory
Zero-Reading in
No .
from bottom
Numb e r
Calibration
12 - cm
Water (mV)
(cm)
(mV/psi)
6 0 g
8 0 g
1
1.0
2998
6 . 370
41.913
61.729
2
5.0
2955
7.418
19.145
33.329
3
9.0
3241
12 . 800
35.308
44.253
An evaluation of the transducer calibration in the high
acceleration level of the centrifuge was necessary. The
results of this study are presented in Appendix F. It was
found that the transducers performed well and that the
factory calibration factors were valid in the centrifuge.
These values were used in the analyses and are also included
in Table 6 -1.
The second requirement of the approach was the solids
content distribution. Two unsuccessful attempts were made
to measure it indirectly. One attempt tried to correlate
electrical resistivity with solids content, while the other
depended on measuring the total vertical stress at different
points in the specimen and from there computing the density
distribution; the density would readily lead to the void
ratio distribution. After failure of these approaches, it
was decided to measure the solids content directly. This
approach required the design of a system of small sub¬
samples that could be removed from the centrifuge periodi¬
cally. Each individual sub-sample is contained in a
perforated 2 - in PVC tube, as shown in Figure 6.3. The small
holes 2-cm apart along the side of the tube are designed to

127
allow insertion of the modified 3-cc syringe shown also in
Figure 6.3, and obtain a sample large enough to measure the
solids content by the standard procedure. These holes are
sealed with rubber plugs during the test. Depending on the
current height of the model, four to six solids content
points can be obtained from each sub-sample.
Three of these samples can be accommodated in a 14-cm
acrylic bucket. Three of the four buckets in the centrifuge
are used for this purpose, for a total of nine sub-samples.
Each bucket is filled with water around the PVC samplers to
reduce the possibility of slurry leakage. The fourth bucket
is reserved for the master specimen used to monitor the
specimen height and pore pressure distribution. Sub-samples
can be obtained at any chosen time interval; a good sequence
might be 1, 2, 4, 6, 8, 12, 24, 36, and 48 hours. Depending
on the initial solids content, the obtaining of a reasonably
good solids content profile before 1 hour is very difficult,
due to the diluteness of the material.
An obvious disadvantage of the direct measurement of
the solids content distribution is that the centrifuge must
be stopped to take the samples out. Of course, the time
that the centrifuge is not spinning must be excluded from
the total elapsed time of consolidation, with the starting
and stopping time accounted for as explained below.
A BASIC program written for the HP-86B monitors the
elapsed time of consolidation and reads the pressure
transducers. A listing of the program is included in

128
Figure 6.3 - Sampler for Solids Content Distribution

129
Appendix G. When the program is run, the user enters the
general test information. Depending on the acceleration
level entered, the program selects the appropriate zero
readings for each one of the three transducers. These
values were previously obtained from several runs using only
water at the exact model height, and are give in Table 6-1.
The corresponding calibration factors of the transducers are
incorporated into the program. After printing the general
test data and the headings for the excess pore pressure
table, the program pauses to allow synchronization with the
centrifuge.
When the centrifuge is started there is a start-up time
before reaching the desired acceleration. Bloomquist et al.
(1984) have shown that for consolidation, the elapsed time
should begin to be measured at two-thirds of the start-up
time. Considering that the start-up time is about two
minutes, for simplicity the elapsed time of consolidation is
recorded beginning one minute after starting the centrifuge.
With the program paused, the centrifuge is started at
the same time the CONT key is pressed in the HP-86B. The
program will then wait exactly one minute before setting the
time counter equal to zero. To account for the stopping and
re-starting time during the retrieval of each sample, it is
further assumed that both stopping and start-up times are
equal (Figure 6.4).
After the computer has taken the corresponding pore
pressure readings, the user pauses the program and

9' S
Figure 6.4 - Effect of Stopping and Re-starting Centrifuge
130

131
immediately stops the centrifuge. When spinning has fully
ceased, the sample is removed and replaced with a dummy
sampler with water to maintain proper balance of the
centrifuge. Just before re-starting the centrifuge, the
CONT key is pressed to continue the program. This approach
assumes that not including the stopping time in the elapsed
time is compensated by continuing the time count when the
centrifuge is re-started, as shown in Figure 6.4.
The computer takes the first readings of the transdu¬
cers at 2, 4, 8, 15, 30, and 60 minutes, time when the first
solids content sample is obtained. After that, a set of
readings is taken every hour. These readings and the
corresponding time are printed out in a table form. A disk
file of these data is not kept since the data reduction is
not done with the HP computer, but using a FORTRAN program
written for a DOS-based PC, as described in the next
section.
Method of Data Reduction
Analysis of the centrifuge data in order to obtain the
constitutive relationships of the slurry is based on updated
Lagrangian coordinates. The use of this coordinate system
is necessary since the computations of permeability are
based on the displacement of material points in the speci¬
men. In general terms, the approach can be explained as
follows. The model is divided into a number of equal thick¬
ness elements (10-20), and the reduced coordinates of their

132
boundaries, refered to here as material nodes, are calcu¬
lated. When a new distribution of void ratio is obtained
from each sample, the updated Lagrangian coordinate of each
material node can be computed from its known (constant)
reduced coordinate. By keeping track of the location of
each material node in this way, and using the measured pore
pressure distribution, it is possible to compute the effec¬
tive stress and the coefficient of permeability at each
point. This involves the use of the effective stress
principle, the generalized Darcy's law, and the principle of
continuity.
A key element in the approach to be followed is the
relationship between convective and reduced or material
coordinates (Cargill, 1982). The convective coordinate is
the "real" distance from a reference point, say the bottom
of the specimen, to the point under consideration. The
material coordinate, on the other hand, is a measure of the
volume of solids that exists up to that point. If x denotes
the convective coordinate of a point in the sample, and z is
the corresponding material coordinate, then they must be
related by the following relation.
dx
dz
= 1 + e
(6.1)
The material height of the specimen is readily obtained by
integrating equation 6.1, considering that the initial void
ratio is constant. This is,
hi
z *. = -i 3
c 1 + e ¿
(6.2)

133
where is the initial height, and e^ is the initial void
ratio. If the model is to be divided in N elements, then
the material thickness of each element is simply
Az = z t/N (6.3)
and the reduced coordinate of each one of the material nodes
or boundaries between these elements is
z ¿ = (i - 1) Az (6.4)
for i = 1 to (N+l). Of course, the material coordinate of
the first node (i = 1) is zero, and that of the node at the
surface (i = N+l) is zt. It is important to bear in mind
that these material coordinates are time - independent, i.e.
the material position of each node does not change through¬
out the consolidation process.
The buoyant stress at each material node is also time-
independent. At node i this can be easily computed,
assuming a constant acceleration field, as
abi ~ n(Gs-1)(zt'zi)Tw (6.5)
where n is the acceleration of the centrifuge in g's, Gs is
specific gravity of the solids, and yw is the unit weight of
water.
At time t, a discrete distribution of void ratio with
depth is obtained from a sample taken out of the centrifuge,
as shown in Figure 6.5a. It is assumed that a straight line
connects the points where the void ratio is known. In the
diagram, the distance Xj represents the convective coordi¬
nate of the jth point and h is the current model height.
The number of points where the solids content is known is

134
(a)
(b)
Figure 6.5 - Variation of Void Ratio with Depth.
a) Void Ratio Distribution; b) (1+e)'^
Distribution

135
denoted by M, and the distance between two consecutive
points is lj (equal to 2 cm., except for the top segment).
The material or reduced coordinate of point j can be
obtained integration Equation 6.1 as,
dx
(6.6)
+ e (x)
where e(x) indicates that the void ratio is a known function
of the convective coordinate x.
The integral of Equation 6.6 is nothing more than the
area under the curve of the inverse of (1 + e) versus x,
schematized in Figure 6.5b. Assuming straight lines between
points, the area up to point j is easily obtained from
simple geometry as
Aj = Aj.! + Md + ej)-1 + (1 + ej ,x)'11 ‘ij-1
(6.7)
for j = 2 to M, with Ap = 0. In particular, the total area,
A^, represents the material height of that particular
sample, which must be equal to the value obtained with
Equation 6.2 assuming that the samples are exactly equal and
that no errors exist in the sampling process or integration
scheme. The value of A^ computed for each sample will be an
indication of the accuracy of the approach.
A second objective for computing this areas is to
locate the current position (updated Lagrangian coordinate)
of each one of the material nodes, and whose material
coordinate was computed with Equation 6.4. The first step
is to identify in which region the node under consideration
falls, by comparing its reduced coordinate to the areas

136
Aj 's
For
ins tance,
if
a2 < zi
A
>
OJ
then
node i
falls in
the
s e c ond
region, i.
e .
b e tween
nodes
2 and
3 . In
general
let
us say
that Aj <
zi
< Aj+1-
as shown in
Figure
6.6.
The updated Lagrangian coordinate of node i is
j ’I
hi = v + E lk (6.8)
k-1
Thus, the problem reduces to evaluating the distance v
in the region where the node under consideration falls. To
achieve this goal, its reduce coordinate is expressed as
= Aj + 4[(l+ej)'l + ee]*v (6.9)
The distance ee is a function of v, and is obtained by
interpolating between points j and j+1; this is
ee = (1 + e-j)-1 - v [ (1 + e j ) ' 1 - (1 + e j +1) ‘1 ]/I j (6.10)
After substituting Equation 6.10 into Equation 6.9, and
simplifying, the following quadratic equation in v is
obtained.
[(1 + ej)-1-(l+ej+1)-X]v2 - 2(1 + ej)*1(v) + 2(Zi-Aj) - 0 (6.11)
Of the two real roots of this equation, one will not satisfy
the condition that 0 < v < lj, and it is discarded. The
other root is used in Equation 6.8 to obtain the new
convective coordinate of node i. Although physically the
coordinate should fall between two areas Aj and Aj+^, the
possibility of not finding the right root, or even obtaining
imaginary roots, still exists if the void ratio distribution
is not correct.

137
Figure 6.6
Location of Material Node i

138
Once the distance v is determined, the void ratio at
the node is obtained using Equation 6.10 and
ei - 1/ee - 1 (6.12)
The procedure is repeated for each material node. Thus, at
time t the new location of each node and its new void ratio
would be known.
Next, the excess pore pressure and the hydraulic
gradient at each node are obtained from the pore pressure
distribution recorded at the time under consideration. An
example of such a distribution is shown in Figure 6.7. For
simplicity, a linear behavior is assumed between measured
values of u.
Once the excess pore pressure at node i is determined,
the corresponding effective stress is easily obtained using
the effective stress principle. This is,
°i = abi ‘ ui (6.13)
with computed from Equation 6.5. Thus, the void ratio
and effective stress at each material node represent one
point in the compressibility curve. With nine samples
obtained at different times, the approach should yield a
considerable number of points, including a wide range of
effective stress. This apparent advantage may also lead to
a problem, namely, the existence of a large scatter in the
curve. Finally, it is worth mentioning that during the
consolidation process several material nodes will reach the
same void ratio levels in different times and, hopefully, at
the same effective stresses.

139
Figure 6.7
Excess Pore Pressure Distribution

140
The next objective of the test is to determine the
permeability relationship. For a sample taken from the
centrifuge at time t, the void ratio at each material node
has already been determined as previously explained. The
determination of the coefficient of permeability is then
based on equation 4.24, repeated here for convenience.
Vs = k*i (6.14)
The hydraulic gradient at time t has been already obtained
for each node from the recorded pore pressure distribution.
However, the instant solids velocity at that precise moment
is not known. Nevertheless, an estimate of this can be
obtained from the change in convective position of the
nodes. For node i this is
V
s i
hj(t-At) - hjCt)
At
(6.15)
where At is the time interval between samples taken, h^(t)
is the convective coordinate of node at time t, and h^(t-At)
is the value at time t-At. This mean solids velocity will
approach the instant value if the time interval is small
enough.
Thus the coefficient of permeability for node i, at
time t, is obtained from Equations 6.14 and 6.15 as
ki(t) - â– Ysi(t) (6.16)
1 i
A new set of pore pressure and void ratio readings
obtained at time t+At will allow determination of new values
of the coefficient of permeability for each material node.
As for the compressibility relationship, this approach would

141
yield a large number of data points, but considerable
scatter may exist in the results.
The determination of the constitutive relationships by
the numerical analysis described above requires a consider¬
able number of repetitive calculations in time and space.
Therefore, it was necessary to write a FORTRAN program to
handle this data reduction. Appendix H presents a listing
of this program.

CHAPTER VII
CENTRIFUGE TESTING RESULTS
Testing Program
A total of five centrifuge tests were performed to
implement the numerical analysis presented in Chapter VI for
determining the effective stress-void ratio - permeabi1ity
relationships, or for other complementary analyses. The
material used in the tests was the same as used in the
slurry conso 1idometer testing program, namely Kingsford
waste clay. The index properties of this material were
given in Chapter V.
Table 7-1 summarizes the conditions of the tests
conducted. The specific purpose of each test is included in
the table for ease of future reference, as well as a listing
of the necessary data obtained in the test.
Table 7-1. Centrifuge Testing Program
Test
No .
Ac c deration
(g's)
hi
(cm)
Si
(%)
Data
Obtained
Purp ose
o f the Test
CT-1
80
12.0
15.72
h , u , S
cr ' - e - k
CT- 2
60
12.0
16.05
h , u , S
Ú' -e-k, M/M
CT- 3
80
9.0
16.02
h
M/M
CT - 4
60
11.0
16.04
h , u
Surcharge
CT- 5
80
11.0
15.95
h , u
Surcharge
142

143
The first two tests, CT-1 and CT-2, were the only two
tests where the specimen height, pore pressure, and solids
content were monitored, in order to obtain the constitutive
relationships of the slurry according to the approach
presented in Chapter VI. Tests CT-2 (60g) and CT-3 (80g)
were used for a modelling of models (M/M); only the specimen
height was monitored in test CT-3.
After observing an unexpected behavior in the pore
pressure profiles of tests CT-1 and CT-2, and suspecting the
possibility of radial drainage in the specimens, tests CT-4
and CT-5 were designed to apply a surcharge load. The main
objective of these tests was to observe the behavior of the
pore pressure distribution for comparison with the profiles
observed in tests CT-1 and CT-2.
Determination of Constitutive Relationships
Two tests were conducted with measurements of pore
pressure and solids content, thus making it possible to
obtain the constitutive relationships of the material. The
first test, CT-1, was performed at 80 g's, with a specimen
initial height of 12 cm and initial solids content of
15.72%. Photographic monitoring of the specimen height was
done following the standard UF procedure. The test duration
was 38 hours, and the final model height was 5.95 cm.
To obtain the void ratio profiles, the sampling opera¬
tion described in Chapter VI was performed at times of 1, 2,
4, 8, 12, 22, and 38 hours, for a total of 7 sub-samples.

144
These sub-samples provide a second measurement of the
specimen height at the corresponding time. Figure 7.1
presents the height-log time relationship for test CT-1
obtained from both the photographs and the sub-samples. The
agreement between the two methods is very good.
However, the main objective of the sampling operation
is the determination of the solids content with depth. Six
solids content points were obtained at times 1 and 2 hours,
five points at times 4, 8 and 12 hours, and only four points
at times 22 and 38 hours. These samples, obtained with the
mini-piston sampler, weigh in the order of 5 grams including
the tare. Once oven-dried, the specimens weigh only around
2 grams. Thus an accurate weight determination is critical.
A 0.01 gram sensitivity electronic balance was used for this
purp ose.
Figure 7.2 presents the solids content profiles for
test CT-1 obtained at various times. It is important to
notice that for the first two or three profiles, the solids
content is larger near the surface, then decreases substan¬
tially with depth, and finally increases at the bottom of
the specimen. This behavior is not expected in a self¬
weight one - dimensional consolidation process, and leads to
the first suspicions that something different is occurring.
Toward the end of the test the solids content distribution
behaved in a more expected way, specifically the solids
content increases with depth.

13
12-
11-
10-
9-
0-
6-
Photogragh
SutrSanples
5 H ■ ■— i
IE 0 IE 1
Figure 7.1
I—*
4>
Ln
IE 2
Model Time (min)
i—»--i i ii| ■ v r
IE 3
Height-Time Relationship for Test CT-1

12
11
10
9
8
7
6
5
4
3
2
1
0
Figure 7.2 - Solids Content Profiles for Test CT-1
1A 6

147
Monitoring of the excess pore pressure is accomplished
through the computer/data acquisition system. For the first
hour of the test, the monitoring program takes transducer
readings at 2, 4, 8, 15, 30, and 60 minutes; afterwards, a
set of readings is taken every hour.
An aspect of the test which affects the excess pore
pressure evaluation is the evaporation of supernatant water.
The zero readings of the pressure transducers were obtained
with water in the container at the exact specimen height,
thus representing hydrostatic pore pressure. As supernatant
water evaporates during the test, the hydrostatic pore
pressure decreases (however, the buoyant stress does not
change). Since the excess pore pressures are computed every
time from the same pre-recorded zero readings, there will be
an error in them equal to the variation in hydrostatic pore
pressure. This effect is depicted in Figure 7.3. An
estimate of the correction for evaporation can be obtained
from the readings of the top transducer (No. 3), once this
is above the slurry - supernatant interface.
In the case of test CT-1, the time at which the
specimen height reaches the top transducer (h = 9 cm.) is
readily obtained from Figure 7.1 as 163 minutes. After this
moment, transducer No. 3 should theoretically read zero
(hydrostatic) pressure. Instead, it reads increasingly
higher negative values. At the end of the test, transducer
No. 3 recorded a pressure of -1.875 psi. Examination of the
specimen indicated that 1.6 cm of supernatant water had

INITIAL ELEVATION
148

149
evaporated during the test. At 80 g's, this loss of water
represents a decrease in hydrostatic pressure of about 1.8
psi, which is in good agreement with the value recorded by
the transducer.
The absolute value of the pressures recorded at
transducer No. 3 from t = 180 minutes to the end of the test
are plotted versus time in Figure 7.4. A linear correla¬
tion, indicating a constant rate of water evaporation, is
clearly observed in the figure. A linear regression
analysis led to the following expression for the correction
for evaporation in test CT-1,
Aue = -0.0254 + (8.453E-04)•t (7.1)
where t is the elapsed time of test in minutes. The zero-
intercept of this equation is not zero as expected, but the
error is considered minor. The correlation coefficient
found in the analysis was 0.999.
Because of the very high correlation coefficient, i.e.
good agreement between experimental readings and best fit
line, it was decided to simply use the negative of the
pressure recorded at transducer No. 3 as the correction for
evaporation after t = 163 min. The correction was added to
the excess pore pressures computed by the monitoring program
to obtain the correct values. The corrected excess pore
pressures at the location of the three transducers are
plotted versus time in Figure 7.5. The curves show the
expected pressure dissipation. Only the readings at 8 and
15 minutes seem to be off, with readings that are abnormally

Pressure Change (psi)
Figure 7.4
Evaporation Correction for Test CT-1

Excess Pore Pressure (psi)
Figure 7.5 - Pore Pressure with Time for Test CT-1

152
high in all three transducers. An explanation for this
result has not been found.
The excess pore pressure profiles at several times are
plotted in Figure 7.6. The initial buoyant stress distribu¬
tion is also shown in the figure. The excellent overlapping
between this and the excess pore pressure curve for t = 2
minutes leads to a very definite and important conclusion,
namely that the effective stresses are initially zero
throughout the specimen. This result immediately implies
that the power curve of equation 4.31 can not represent
properly the compressibility of the slurry.
As time progresses, the excess pore pressure profiles
exhibit a very peculiar and interesting behavior. The
pressure at transducer No. 2 (elevation 5 cm.) dissipates at
a rate so fast that the pore pressure profile soon shows a
curvature oppose to that expected. An extreme example of
this trend is observed at t = 12 hours, when the specimen
height is about 7 cm. Nevertheless, transducer No. 2
registers zero pressure, thus implying that the top 2
centimeters of the specimen are under hydrostatic condi¬
tions .
At first instance, this pore pressure response seemed
impossible to explain. To eliminate the possibility of
erroneous transducer readings, other complementary tests
were conducted, even switching transducer positions. These
tests confirmed that the response of the transducers was
reflecting a real process taking place in the specimen.

12
11
10
9
8
7
6
5
4
3
2
1
0
Jz .4 .6 .8 1
Excess Pore Pressure (psi)
Figure 7.6 - Pore Pressure Profiles for Test CT-1
153

154
To explain this strange pore pressure behavior it is
necessary to start by realizing that the transducers are
recording the excess pore pressure along the walls of the
acrylic container. As a result of the specimen deformation,
the relative movement of the slurry with respect to the
bucket walls apparently produces a shearing zone where the
confining horizontal stress is small and the permeability is
relatively higher; this effect, of course, diminishes with
depth. Thus, it is believed that the initial excess pore
pressures, generated by the buoyant weight of the slurry,
dissipate faster along the bucket-slurry boundary than at
the center of the specimen.
As a consequence of the above statement, radial
drainage will be taking place, at least in the upper part of
the specimen, speeding up the process of consolidation.
This conclusion is consistent with the results shown in
Figure 7.2, where the solids content increased faster near
the surface. Additionally, there is clear visual evidence
that at the end of the test a gap exists between the bucket
walls and the upper part of the specimen.
If the above reasoning is correct, then a major problem
arises, namely that the process taking place in the centrif¬
uge is not one-dimensional consolidation. Later in this
chapter, additional evidence of the possibility of radial
drainage will be presented, as well as the implications on
modelling of models and the time scaling exponent.

155
Nevertheless, the data collected in the test will be used in
the numerical approach to obtain the constitutive relations.
If the hypothesis of radial gradient is correct, it
becomes imperative to determine the excess pore pressure
distribution at the center of the specimen. Unfortunately,
placing transducers at the axis of the model is not an easy
task. Consequently, an approximation was made. It was
assumed that the excess pore pressure profile along the axis
of the specimen was parabolic, and that the value recorded
at transducer No. 1 (elevation 1 cm) represents also the
value at the center of the specimen. This last assumption
is justifiable by realizing that the conditions that may
produce radial drainage near the surface of the specimen
disappear near the bottom.
Knowing the values of the excess pore pressure at the
elevation of 1 cm and at the top of the specimen, and the
gradient at the bottom, an expression for the excess pore
pressure at any elevation, y, is readily obtained as
_Jil_y2 + —— ux
(h2-l) (h2-1)
(7.2)
where u^ is the excess pore pressure at transducer No. 1,
and h is the current height of the specimen in centimeters.
Figure 7.7 shows, as an example, the assumed parabolic
distribution for t = 2 hours, along with the excess pore
pressures recorded at the transducers at the same time. In
order to idealize a pseudo-one-dimensional situation and
have the opportunity of using the method proposed in Chapter

12
11
10
9
8
7
6
5
4
3
2
1
0
Parabolic Distribution
â–¡ Transducer Readings
Excess Pore Pressure (psi)
Figure 7.7 - Parabolic Excess Pore Pressure Distribution
at t = 2 hours for Test CT-1
156

157
VI, a rather crude but quite logical approach was followed.
The excess pore pressure and hydraulic gradient required in
the analysis were obtained as the average of the values
obtained with the recorded distribution at the boundary and
the assumed distribution at the center of the specimen. The
data reduction program listed in Appendix H was modified
accordingly to incorporate this approach. It was expected
that the approximation would, at least, provide a range
wherein the actual constitutive relationships exist.
Following this approach, the computer program was run
with the data collected in the test. In the analysis the
specimen was divided into 10 layers. A printout of the
output is included in Appendix H. The general test informa¬
tion, initial conditions, and the results of the analysis
for the first time increment analyzed (1 hour) are repro¬
duced in Table 7-2. Several points of the program output
are worth highlighting.
The reduced height of the specimen computed from the
initial height and void ratio is 0.772 cm. The solids
content profiles obtained from the sub-samples allow
computing a new value of this height, as explained in
Chapter VI. Comparison of these values with the initial
value provides an evaluation of the quality of the sampling
process. For the first sub-sample, for instance, the
reduced height of the specimen is computed as 0.768 cm, an
agreement with the initial value of 0.772 cm that is
excellent considering the difficulties associated with

158
Table 7-2. Partial Output of the Analysis of Test CT-1
*** Centrifuge Test CT-1 ***
Acceleration level = 80. g
Initial Height = 12.0 cm
Solids Content = 15.72% Void Ratio = 14.535
Number of Layers = 10
Reduced Height of the Specimen = 0.772 cm
Initial Conditions
Theoretical Gradient = 0.110
NODE
H ( I )
Z ( I )
BUOY.ST
EXC.P.P.
EFF
. STR
. GRADIENT
1 1
12
.0 0 0 0
0
.7 725
0 .
.0 0 0 0
0
.0 0 0 0
0 .
0 0 0 0
0 .
1119
1 0
1 0
.8 0 0 0
0
.6952
0 ,
.15 0 2
0
.1527
- 0 .
0 0 2 4
0 .
1119
9
9
.6 0 0 0
0
.6180
0 ,
,3 0 0 5
0
.3 0 5 4
- 0 .
0 0 4 9
0 .
1119
8
8
.4 0 0 0
0
.54 07
0 .
,4 5 0 7
0
.4 5 0 1
0 .
0 0 0 6
0 .
10 0 2
7
7
.20 0 0
0
.4 63 5
0 .
.60 0 9
0
.58 69
0 .
0 14 0
0 .
10 0 2
6
6
.0 0 0 0
0
.3 8 62
0
.7512
0
.7 23 7
0 .
0 2 7 5
0 .
1002
5
4
.80 0 0
0
.3 0 90
0
.9014
0
.866 4
0 .
0 3 50
0 .
1262
4
3
.60 0 0
0
.2317
1
.0516
1
.0 3 86
0 .
0 13 0
0 .
.1262
3
2
.4 0 0 0
0
.1545
1
.2019
1
.2109
- 0 .
0 0 9 0
0 .
.12 6 2
2
1
.20 0 0
0
.0 7 7 2
1
.3 52 1
1
.3 8 3 1
- 0 .
0 3 10
0 ,
,1262
1
0
.0 0 0 0
0
.0 0 00
1
.50 24
1
.5553
- 0 .
0 53 0
0 .
.12 6 2
N
e w T
i m e =
60
. 0 min
New
Height
= 10
. 20
c m
New Reduced Height of the Specimen = 0.768 cm
U ( I )
-
1.266 0 .
624
0 .
152
p s i
S ( J )
=
22 .
19 16
. 86
1 7
. 6 5
18.68
1 6 .
2 9
%
NODE
H
e
u
Eff.Str.
i
Vs
k (f t/d ay
1 1
10 .
263
13
.998
- 0 .
0 12
0 .
.012
0 .
.167
0 .
. 4824E-03
0
.1228E+00
1 0
9 .
152
12
.830
0 .
19 1
- 0 .
.041
0
.15 5
0 ,
. 4578E-03
0
.1218E+00
9
8 .
12 1
1 1
.898
0 .
362
- 0
.061
0 .
.14 0
0 .
. 4109E-03
0
.1158E+00
8
7 .
123
12
.050
0 .
514
- 0 .
.0 63
0 .
.129
0 .
. 3546E-03
0
.1097E+00
7
6 .
10 4
1 2
.356
0 .
6 5 7
- 0 .
,056
0 .
.118
0 .
, 3046E-03
0
. 9899E-01
6
5 .
065
12
.506
0 .
7 9 0
- 0 .
.038
0 .
.10 7
0 .
. 2596E-03
0
.8895E-01
5
4 .
0 17
12
.642
0 .
93 1
- 0 .
.029
0 ,
.114
0 .
. 2175E-03
0
.6419E-01
4
2 .
94 9
13
.013
1 .
062
- 0 .
.011
0 ,
,102
0 .
. 1 8 0 8E-03
0
.5605E-01
3
1 .
853
12
.987
1 .
183
0 .
.019
0 .
0 9 1
0 .
1518E-03
0
.4963E-01
2
0 .
8 6 1
1 0
.877
1 .
279
0 .
0 7 3
0 .
0 8 0
0 .
9413E-04
0
. 3 23 7E-01
1
0 .
0 0 0
9
.503
1 .
3 52
0 .
150
0 .
0 7 1
0 .
OOOOE+OO
0
.OOOOE+OO

159
obtaining the solids content profile. For the other sub-
samples, the reduced height of the specimen ranges between
0.776 and 0.792 cm.
Additionally, the measured solids content profile is
verified by comparing the computed model height and the
photographic value. For t = 60 minutes, for instance, the
photograph reveals a model height of 10.20 cm, while the
computed value is 10.26 cm, which represents an excellent
agreement. In other cases, however, the discrepancy is
somewhat larger.
Since the excess pore pressures are not known at t = 0,
the values used by the program as an approximation to obtain
the initial conditions correspond to those at t = 2 min. A
phenomenon already addressed is observed in the Table 7-2
column of initial effective stress; all the values (negative
or positive) are small enough to be considered zero for all
practical purposes. These results corroborate the conclu¬
sion of zero initial effective stresses. Additionally, the
theoretical initial gradient of 0.11, due to the buoyant
weight, compares well with the values computed from the pore
pressures recorded at 2 minutes.
For every time analyzed, the analysis provides a total
of eleven points, with information on location of the point,
its void ratio, excess pore pressure, effective stress,
hydraulic gradient, solids velocity, and coefficient of
permeability. At t = 60 minutes, the results shown in Table
7-2 indicate that the effective stresses in the specimen are

160
still negligible, except at the very bottom. As time
progresses, the effective stress front moves upward as can
be seen in the complete output printout of Appendix H.
Of the 11 points obtained for each time analyzed, the
one at the surface always has zero effective stress (very
small values are computed). However, its void ratio does
not remain constantly equal to the initial value, but
instead tends to decrease. It is admitted that this is the
location with the largest possibility of error in the solids
content measurement; however, its proximity to the super¬
natant water makes it very likely that the error would be an
underestimation of solids content (overestimating the void
ratio). This tendency of the void ratio at the surface to
decrease, regardless of the zero effective stress condition,
has been observed in other studies (Been and Sills, 1981;
Lin and Lohnes, 1984), but has not been explained.
Figure 7.8 presents the compressibility and permeabil¬
ity plots obtained from the analysis of test CT-1. Obvi¬
ously, the compressibility graph (Figure 7.8a) does not
include the surface point and those points where the
effective stress is either negative or less than 0.01 psi,
the minimum accurately measured value. The plot shows
considerable scatter at void ratios above 9. This is
largely the result of error in the determination of low
solids content values. It is clear from the figure how all
the points corresponding to different times converge to a
unique curve. Moreover, each set of points for a given time

14
13
12
11
10
9
8
7
6
5
4
a t
a t
â–¡ t
â–  t
O t
• t
1 & 2 hrs.
4 hrs.
8 hrs.
12 hrs.
22 hrs.
38 hrs.
-?â– 
• D ■
•Ph
A
-* ■—r—•—rm
IE—2
i ■—i—
IE—1
i ■ ■—■ »ii|
IE 0
-t 1 i
Effective Stress (psi)
(a)
igure 7.8 - Constitutive Relationships froir, Centrifuge Test CT-1,
a) Compressibility; b) Permeability
161

15
14
13
12
11
10
9
8
7
6
5
4
a t ° 1 hr.
a t â–  2 hrs.
â–¡ t â–  4 hrs.
■ t » 8 hrs.
o t â–  12 hrs.
• t ■ 22 hrs.
> *
°*.D
- rf3
■»
□ «
â–¡o
IE-3 IE-2 IE-1
Permeabi 1ity (ft/day)
(b)
Figure 7.8—continued
■ «I»»»'
IE 0
162

163
clearly extends the curve produced by points from previous
times .
Unfortunately, the plot of Figure 7.8a does not provide
information on the first portion of the compressibility
relationship (e > 12). In order to obtain this information,
it would be necessary to obtain sub-samples earlier in the
test and improve the sampling technique and accuracy of pore
pressure measurement. Consequently, the preconso 1i dation
effect observed in the results of CRD tests can not be
corroborated with these test results.
In the case of the permeability graph (Figure 7.8b),
the values calculated by the computer program correspond to
the prototype coefficient of permeability, which is n (the
centrifuge acceleration in g's) times smaller than the model
permeability, as demonstrated in Appendix A. In the
analysis, the bottom point of the specimen has zero solids
velocity at any time, and therefore does not provide any
permeability information. Similarly, all the points at the
end of the test (t = 38 hours) are excluded from the permea¬
bility plot because the hydraulic gradient has been reduced
to practically zero (0.001), and the computed coefficient of
permeability is meaningless.
As in the case of the compressibility plot, the
permeability graph of Figure 7.8b shows significant scatter.
Nevertheless, the points define a definite trend. Although
the preconso 1idation effect is not fully observed, the curve
seems to flatten at void ratios above 12.

164
The second centrifuge test, CT-2, was analyzed follow¬
ing the same procedure outlined for test CT-1. Test CT-2
was conducted under a normal centrifuge acceleration of 60
g's, versus 80 g's of test CT-1. The specimen initial
height was also 12 cm, and the initial solids content was
16.05%. The test duration was 48 hours and the final model
height was 6.0 cm.
Figure 7.9 shows the height-time curve obtained for
test CT-2 from the photographs and from direct observation
of the sub-samples obtained at times 1, 2, 4, 8, 12, 24, 35,
and 48 hours. The agreement is good, but the sub-sample
heights are slightly larger due to side effects.
The solids content profiles obtained from the sub¬
samples at various times are plotted in Figure 7.10. The
first three profiles show solids content at the surface
which are lower than the initial value; this absurd result
is easily explained by the high degree of wetness left on
the surface by the supernatant water. The initial solids
content was used for this point in the numerical analysis.
The same behavior observed in test CT-1, where the
solids content increases relatively faster near the surface,
is also clear in test CT-2. Later in the test, the solids
content profile behaves as expected, except that at the
surface the solids content increases above the initial
value. At the end of the test, two sub-samples were
obtained for verification. The agreement between the solids
content profiles of the two sub-samples was very good.

13
i — —'—i—• ■ • • • | '—'—■—• • • • • | ■—«—i—« • • • ■ | ■—>—«—■■■»»■
IE 0 IE 1 IE 2 IE 3 IE 4
Model Time (min)
ON
ui
Figure 7.9 - Height-Time Relationship for Test CT-2

12
11
10
9
B
7
6
5
4
3
2
1
0
20 22 24 26 28
Solids Content (Z)
34 36
Figure 7.10 - Solids Content Profiles for Test CT-2
166

167
For the measurement of the excess pore pressure
distribution, it was decided to re-evaluate the zero
readings of the transducers in the 12 cm of water. A test
conducted for this purpose prior to the actual test recorded
values of 41.913, 19.145, and 35.308 mV for transducers No.
1, 2, and 3, respectively. These values compare well with
those given in Table 6-1 for 60 g's, with a maximum differ¬
ence of about 1%. The new values were used to compute the
excess pore pressure.
The evaporation effect was analyzed as explained for
test CT-1, and the correction pressure is plotted versus
time in Figure 7.11. With a coefficient of correlation of
0.998, the equation of the best fit straight line is
Aue = - 0.04584 + (4.334E-04)•t (7.3)
In this case, it was decided to use the equation
obtained to compute the correction for evaporation at all
times. After the correction is applied, the excess pore
pressure at the transducers is plotted versus time in Figure
7.12. The curves show the expected pore pressure dissipa¬
tion. Figure 7.13 presents the profiles of excess pore
pressure at various times, along with the initial buoyant
stress distribution. Comparison of the latter with the
profile at t = 2 min. again demonstrates that the effective
stresses are initially zero throughout the specimen.
The sequence of excess pore pressure profiles of Figure
7.13 behaves much like that resulting from test CT-1. A
relatively faster dissipation of excess pore pressure takes

Pressure Change (psi)
Figure 7.11 - Evaporation Correction for Test CT-2

Excess Pore Pressure (psi)

12
n
10
g
8
7
6
5
4
3
2
1
0
i 1 r
.4 .6 .8
Excess Pore Pressure (psi)
Figure 7.13 - Pore Pressure Profiles for Test CT-2
170

171
place near the surface, an effect that is consistent with
the solids content profiles of Figure 7.10. Thus, again
radial drainage seems to be occurring in the test.
Following the same approximation of using the average
of the values at the boundary and at the center of the
specimen to estimate the one - dimensional excess pore
pressure and hydraulic gradient, the data reduction program
analyzed the data of test CT-2. Ten layers were also used
in the analysis. A complete printout of the results is
included in Appendix H. The general test information,
initial conditions, and the results of the analysis for t =
1 hour are reproduced in Table 7-3.
All the observations made about the results of test
CT-1 are found to be valid for test CT-2 as well. The
agreement between the initial reduced height of the specimen
and those computed from the sub-samples is good. The effec¬
tive stresses are initially zero and begin to increase at
the bottom of the specimen; as time progresses, an effective
stress front moves upward.
Figure 7.14 shows the compressibility and permeability
plots obtained from the analysis of test CT-2. Figure 7.14a
does not include those points with effective stress less
than 0.01 psi or negative. In the case of the permeability
plot, when the point at the surface results with an abnor¬
mally high void ratio (as a result of an erroneous solids
content), the point was discarded. Also, the permeability
values computed at the end of the test (t = 48 hours) were

172
Table 7-3.
Partial Results of the Analysis
of Test CT- 2
*** Centrifuge Test CT-2 ***
Acceleration level = 60. g
Initial Height = 12.0 cm
Solids Content = 16.05Z Void Ratio = 14.175
Number of Layers = 10
Reduced Height of the Specimen = 0.791 cm
Initial Conditions
Theoretical
Gradient =
0 .
113
NODE
H ( I )
Z ( I )
BUOY . ST .
EXC.P.P.
EFF
. STR .
GRADIENT
1 1
12 .
.0 0 0 0
0
.7 90 8
0 .
0 0 0 0
0 ,
,0 0 0 0
0 .
0 0 0 0
0 ,
,119 4
10
1 0 .
.80 00
0
.7117
0 .
.1153
0 .
.1222
- 0 .
0 0 69
0 .
.1194
9
9 .
.60 0 0
0
.6326
0 .
2 3 0 7
0 ,
,2 4 4 5
- 0 .
0138
0 .
,1194
8
8 .
.4 0 0 0
0
.5536
0 .
3 4 6 0
0 .
.3 563
- 0 .
0 10 3
0 ,
.0 9 9 1
7
7
.20 0 0
0
.4 7 4 5
0 .
4 6 14
0 .
.4 5 7 7
0 .
0 0 3 7
0 .
.0 99 1
6
6 .
.0 00 0
0
.3 954
0 .
.5 7 67
0 ,
.5592
0 .
0 17 6
0 ,
.0 99 1
5
4
.8 0 0 0
0
.3163
0 .
.6921
0 .
.666 4
0 .
02 57
0 ,
.1329
4
3 .
.60 0 0
0
.23 7 2
0 .
.8 0 7 4
0 .
.8 024
0 .
0 0 50
0 ,
.1329
3
2
.4 0 0 0
0
.1582
0 .
9228
0 .
.93 85
- 0 .
0 15 7
0 .
.1329
2
1
.20 0 0
0
.0 7 9 1
1 ,
,0 3 8 1
1.
.0 7 4 5
- 0 .
0 3 6 4
0 .
.1329
1
0 .
.0 0 0 0
0
.0 0 00
1 .
.1535
1.
.2106
- 0 .
0 57 1
0 .
.1329
N
e w
Time
=
6 0.0
min
New
Height
= 10.90 cm
New
Reduced
Height
o f
the
Specimen
«
0.800
c m
U ( I )
=
1.0295 0 .
5259 0
.15 12 ps i
S ( J )
=
21.77 16.
67
1 7 .
0 4
17.18
17.90
17.83 16 .
0 5
z
NODE
H
e
u
Ef f
. Str .
i
Vs
k
(f t/d ay )
1 1
10
.765
13
.895
0 .
0 18
- 0 .
0 1 8
0
.15 7
0.3432E-03
0
. 1173E + 00
1 0
9
.662
12
.479
0 .
16 0
- 0 .
0 4 5
0
.14 6
0.3161E-03
0
. 1 127E + 00
9
8
.597
12
.447
0 .
2 9 1
- 0 .
0 60
0
.14 3
0.2785E-03
0 .
. 1003E + 00
8
7
.532
12
.573
0 .
4 16
- 0 .
0 7 0
0
.132
0.2410E-03
0 .
. 9851E-01
7
6
.446
12
.918
0 .
5 3 3
- 0 .
0 7 1
0
.12 1
0.2096E-03
0 .
. 8999E-01
6
5
.335
1 3
.10 7
0 .
6 4 2
- 0 .
0 6 5
0
.110
0.1848E-03
0 .
. 8368E-01
5
4
.216
1 3
.180
0 .
7 54
- 0 .
0 6 2
0
.117
0.1621E-03
0 .
6130E-0 1
4
3
.0 89
1 3
.352
0 .
8 6 1
- 0 .
0 53
0
.10 5
0.1419E-03
0 .
5627E-01
3
1
.946
1 3
.409
0 .
958
- 0 .
0 3 5
0
.094
0.1260E-03
0 .
5254E-01
2
0
.902
1 1
.17 7
1 .
0 3 6
0 .
0 0 2
0
.083
0.8264E-04
0 .
3616E-01
1
0
.000
9
.738
1.
097
0 .
0 5 7
0
.074
0.OOOOE+OO
0 .
OOOOE+OO

14
13
12
11
10
9
8
7
6
5
4
a t â–  1 l 2 hrs.
a t â–  4 hrs.
â–¡ t â–  8 hrs.
â–  t * 12 hrs.
® t ■ 24 hrs.
• t * 35 & 48 hrs.
.â–¡1
*: *
O Í ■
■—i—■—»■»»r] ■—■—■—■—i ■■■ ■[ —■—■—■»■ n| ■—«—i—
3 IE-2 IE—1 IE 0
Effective Stress (psi)
(a)
- Constitutive Relationships from Centrifuge Test CT-2.
a) Compressibility; b) Permeability
7.14
173

15
14
13
12
11
10
9
8
7
6
5
4
a t â–  1 hr.
a t â–  2 hrs.
â–¡ t â–  4 hrs.
â–  t â–  8 hrs.
o t * 12 hrs.
• t ■ 24 & 35 hrs,
o â– 
IE-3 IE-2 IE-1 IE 0
Permeabi 1ity (ft/day)
(b)
Figure 7.14—continued
174

175
excluded because very small gradients and solids velocities
exist at this moment, which results in erroneous computation
of the coefficient of permeability.
A comparison of the constitutive relationships obtained
from centrifuge tests CT-1 and CT-2 is presented in Figure
7.15. The agreement between the results of both tests is
very good. These constitutive relationships can be repre¬
sented fairly well by power curves of the form of equations
4.31 and 4.32. A regression analysis with the data of
Figure 7.15 was performed to obtain the corresponding
parameters, with the following results
Compressibility Parameters from tests CT-1 and CT-2:
A = 16.359 B - -0.204 r - -0.940
Permeability Parameters from tests CT-1 and CT-2:
C = 1.029E-06 D = 4.297 r = 0.926
These parameters are for the effective stress in psf, and
the coefficient of permeability in ft/day. The correlation
coefficients obtained indicate a fairly good correlation.
The power functions are also shown in Figure 7.15.
In order to quantify the agreement between the results
of the two tests, the power function parameters of the data
of test CT-2 only were determined. The results of the
regression analysis were
Compressibility Parameters from test CT-2 only:
A = 16.956 B = -0.214 r - -0.933
Permeability Parameters from test CT-2 only:
C - 1 . 862E-06
D -= 3.958
r = 0.903

(a)
- Comparison of CT-1 and CT-2 Results, a) Compressibility
Relationship; b) Permeability Relationship
Figure 7.15

Figure 7.15—continued
177

178
These parameters compare very well with those obtained
with the data of both tests. This result clearly shows the
agreement between the constitutive relationships obtained
from the two tests.
Comparison of CRD and Centrifuge Test Results
During the course of this research two completely
different techniques for the determination of consolidation
properties of slurries were developed, namely the automated
slurry consolidometer and fully monitored centrifugal model
tests. Accordingly, an excellent opportunity is presented
to compare the results of the two techniques and evaluate
their effectiveness.
For the purpose of comparison, two CRD tests were
selected. They are CRD-1 and CRD-3, the two constant rate
of deformation tests with initial solids contents similar to
those of centrifuge tests CT-1 and CT-2. Figure 7.16 shows
the constitutive relationships obtained with all four tests.
The graphs also show the power function curves obtained with
the centrifuge data.
The compressibility plots of Figure 7.16a show a very
good agreement between the centrifuge data and the virgin
zone of the curve of test CRD-3. The latter is the constant
rate of deformation test performed at the slow deformation
rate. This result tends to corroborate a conclusion of
Chapter V, specifically that CRD tests performed at very
slow rates describe better the actual soil behavior because

(a)
Figure 7.16 - Comparison of CRD and Centrifuge Test Results.
a) Compressibility Relationship; b) Permeability Relationship
179

Figure 7.16—continued
180

181
they conform better to the analysis assumptions. As pointed
out before in this chapter, the centrifuge curves do not
show the preconsolidation effect observed in the CRD tests.
The permeability plots of Figure 7.16b, on the other
hand, do not show the same good agreement between CRD and
centrifuge tests. The latter, however, plot parallel to the
virgin zone of the CRD tests. The centrifuge permeabilities
are approximately a half order of magnitude higher than the
CRD permeabilities. It is worth recalling at this point
that the centrifuge permeabilities plotted in Figure 7.16b
represent the "prototype" values. The "model" permeabil¬
ities would be even higher, 80 times in test CT-1 and 60
times in test CT-2 ; thus, the difference between CRD and
"model" permeabilities would be about two orders of magni¬
tude. Although the results of Figure 7.16b do not show a
total agreement, these results at least demonstrate that the
"model" permeability can not be equal to the permeability of
the "prototype", which agrees with other studies (Goforth,
1986).
An explanation for the apparent disagreement between
CRD and centrifuge test results with regard to the permea¬
bility relationship has not been found. However, it is
important to recall that the process occurring in the
centrifuge showed evidence of radial drainage and that an
approximation was made in order to simulate a one-dimensio¬
nal consolidation problem. Nevertheless, a more detailed
study is necessary before a definite explanation can be

182
found. The following sections of this chapter further
address the problem of radial drainage in the centrifuge and
some of its implications.
Effect of Surcharge on Pore Pressure Response
It is believed that one of the factors that may be
promoting radial drainage in the centrifuge tests reported
is the absence of large horizontal confining stresses near
the top of the specimen. The pore pressure profiles
measured in the tests performed in the automated slurry
conso 1idometer did not show any evidence of possible radial
drainage; in these tests, a large horizontal effective
stress surely existed as a result of the large surcharge
being applied by the loading piston.
With this hypothesis in mind, it was decided to perform
a centrifuge test with a sufficient surcharge to prevent the
fast radial dissipation of excess pore pressure taking place
near the top of the specimen. The shape of the excess pore
pressure profiles would readily indicate whether radial
drainage was being prevented. The test was not designed to
obtain solids content profiles, and therefore could not be
used to obtain the soil's constitutive properties.
To apply the surcharge load, a perforated aluminum
plate with a vertical rod in the center was constructed.
Underneath the plate and on top of the slurry, filter paper
is placed to allow free drainage while preventing soil
particle migration. The edge of the plate is wrapped with

183
teflon tape to reduce friction and at the same time prevent
the slurry from being squeezed out around the plate. The
submerged weight of the plate is 257.2 grams (0.5665 lb).
Two surcharge tests were performed as described in
Table 7-1. The first one, test CT-4, was performed at 60
g's, while the second, CT-5, was at 80 g's. To start the
test with the piston already submerged, the initial slurry
height was 11.0 cm, while the water height was kept at 12.0
cm; in this way the zero readings of the transducers will
not be changed. The initial solids content of test CT-4 was
16.04% .
Although it is clear that the "centrifuge weight" of
the plate will change as it displaces away from the center
of rotation, it is assumed that a constant acceleration of
60 g's applies. Using this value, the surcharge load
applied by the plate was computed as 1.445 psi, a value
somewhat larger than the self-weight buoyant stress at the
bottom of the specimen.
The test ran successfully for less than four hours,
when the photograph revealed that the plate had tilted and
sunk. Nevertheless, some useful information could be
obtained from the test results. Figure 7.17 shows the
excess pore pressure profiles obtained from the transducer
readings, along with the theoretical initial buoyant stress
distribution. The curves show the expected behavior under a
surcharge loading. Transducers No. 3 (elevation 9 cm) and

Figure 7.17 - Pore Pressure Profiles for Test CT-4
184

185
No. 2 (elevation 5 cm) record relatively high excess pore
pressures, without exhibiting the fast dissipation attrib¬
uted to radial drainage in tests CT-1 and CT-2. It is not
until t = 3 hours, when the specimen height is slightly
higher than 9 cm, that U3 begins to drop.
Due to the partial failure of test CT-4, the surcharge
system had to be modified to prevent tilting of the loading
plate. This was easily accomplished by constructing an
acrylic cover for the bucket, with a hole in the center to
allow only vertical displacement of the vertical rod
connected to the plate. Figure 7.18 shows a photograph of
the test container with the cover and loading piston
assembled as for an actual test.
Test CT-5 was performed at 80 g's with the modified
surcharge loading system. The specimen initial height was
11.0 cm (12 cm of water), and the initial solids content was
15.95%. With a normal acceleration of 80 g's, the surcharge
load applied to the specimen by the loading plate was
estimated to be 1.927 psi; this value is somewhat larger
than the self-weight buoyant stress at the bottom of the
specimen.
Unfortunately, this test could not be completed
successfully either. Although the plate fitting in the
bucket was initially snug, some slurry started escaping from
the specimen and depositing on top of the plate. After 8
hours of test, there was about 4 mm of sediment on top of
the plate, and the test was stopped.

186
Figure 7.18
Bucket Used in Centrifuge Surcharge Tests

187
Although test CT-5 was not completed, the results led
to important conclusions and the main objective of the test
was fulfilled. Figure 7.19 presents the height-time curve
obtained for the test. The excess pore pressure profiles
obtained from the transducer readings are shown in Figure
7.20, along with the theoretical buoyant stress distribu¬
tion. Some apparent abnormalities are observed in the
figure. The first two profiles (2 and 15 min) show rela¬
tively low excess pore pressures, which increase substan¬
tially at t - 1 hour. An explanation for this inconsistent
trend can be found by comparing the 2 min profile with the
initial buoyant stress distribution. It seems impossible
that in such a short period of time so much excess pore
pressure had been dissipated. Consequently, it is believed
that the first two profiles only reflect part of the plate
surcharge, due to the presence of side friction. As the
piston displaces, some of the friction is released (most
probably the container is not perfectly round), and the
excess pore pressures suddenly increase.
Figure 7.21 shows the curves of excess pore pressure
versus time at all three transducer locations. The curves
clearly show how after some dissipation the excess pore
pressures suddenly increase, most probably as a result of
some friction release. It is very likely that during these
periods of time that the friction was substantially reduced,
some slurry had the chance to escape from the specimen.

Figure 7.19 - Height-Time Relationship for Test CT-5

12
o Theoretical Initial Profila
Figure 7.20 - Pore Pressure Profiles for Test CT-5
189

Excess Pore Pressure (psi)
Figure 7.21 - Pore Pressure with Time for Test CT-5
190

191
Regardless of the friction problem, the excess pore
pressure profiles obtained in test CT-5 (Figure 7.20)
indicate that radial drainage was not occurring in the test.
Similar to the results of test CT-5, and unlike those of
tests CT-1 and CT-2, the excess pore pressures at transdu¬
cers No. 2 and 3 do not dissipate too fast. The curves
behave much as expected in a one - dimensional problem with
surcharge.
Some Comments on the Time Scaling Exponent
The purpose of this section is to present a somewhat
speculative, but definitely valid, analysis about the effect
of radial drainage upon the time scaling exponent and
modelling of models. Although most of the analysis is
theoretical, some experimental results will be presented as
evidence of the points being considered.
First, let us review the basic equations used in
modelling of models theory. If two centrifugal models are
used to model the same prototype, the prototype time
corresponding to a given average solids content can be
exp re s sed as
cp = ^ml^i “ ^tm2^nl (7.4)
where tp is the prototype time,
tmi is the time in model 1,
n^ is the acceleration (g's) in model 1,
tm2 is the time in model 2,
n2 is the acceleration (g's) in model 2, and

192
x is the time scaling exponent.
The right hand side of Equation 7.4 can be rearranged
in the form
(n1/n2)x - tm2/tml
(7.5)
from which the time scaling exponent is obtained as
x
loS(tm2/tml)/1°g(nl/n2)
(7.6)
It is demonstrated in Appendix A and elsewhere (Croce
et al., 1984) that for one - dimensional consolidation the
time scaling exponent is 2. However, an experimental study
presented by Bloomquist and Townsend (1984) found for
Kingsford waste clay an exponent of 1.6 for solids content
up to about 19%, and then increasing to the value of 2 at a
solids content around 21%. These low values of x were
attributed to the existence of hindered settling during most
of the test, becoming pure consolidation only at the very
end of the test.
If unnoticed radial drainage occurs during a centrifu¬
gal model test, the model time required to achieve a given
degree of consolidation would obviously be reduced, as a
result of a faster dissipation process. If the time scaling
exponent were to be evaluated from the knowledge of the
corresponding prototype time, and using the relationship
(7 . 7a)
x - log(tp/tm)/log(n)
(7.7b)
or
the computed exponent x would be higher than the value it
takes without radial drainage. In other words, if the
true” exponent is 2, a model with radial drainage would

193
deceivingly lead to a exponent higher than 2, in order to
obtain the actual prototype time. Bloomquist (1982) used a
prototype-size test to obtain the time scaling exponent.
The IMC tank test consisted of a steel tank 9' x 14' x 22'
deep, in which 20.75 ft of Kingsford clay were deposited at
12.6% solids content and allow to self-weight consolidate
for 403 days. The test was modelled in the centrifuge at 80
g's, obtaining a constant exponent of 1.6. This result
seems to invalidate the above statement concerning the value
of x when this is obtained from the prototype time. How¬
ever, the tank test itself, though representing the proto¬
type, may have been affected by radial drainage considering
its large depth/width ratio.
However, the exponent x is very rarely obtained from
the prototype time (which is the unknown in the problem),
but from the times in two models as expressed in equation
7.6. In this case, the effect of radial drainage upon x
will be different.
During the process of modelling of models, the two
models representing the prototype at different accelerations
will have different heights. Consequently, it is reasonably
valid to believe that they will be affected differently by
radial drainage. Let us assume for a moment that a "per¬
fect" modelling of models led to an exponent of 2, based on
two model times, t^ and t2â–  Using these values in Equation
7.5, results that
(ni/n2)2 = t2/t1
(7.8)

194
If modelling of model tests with radial drainage are
performed, both times would be reduced, but in a different
amount. Let tj^ and t¿ be the new model times influenced by
radial drainage and expressed as
ti - Cl-tl (7.9a)
and t¿ = C2*t2 (7.9b)
where and C2 are different reduction coefficients.
Substituting tj^ and t¿ into equation 7.5 leads to
(n1/n2)x - t¿/ti (7.10)
and using equations 7.8 and 7.9,
(n1/n2)x - (C2t2)/(C1t1) = (C2/C!)(ni/n2)2 (7.11)
Taking the logarithm of equation 7.11, the following
equation results,
x*log(n1/n2) = log(C2/C1) + 2*log(n1/n2) (7.12)
and solving for x,
x = 2 + log ( 02/C]^)/log (n1/n2 ) (7.13a)
or x = 2 - log(C1/C2)/log(n1/n2) (7.13a)
Equation 7.13 shows that if the models were affected in
the same amount by radial drainage (C^ = C2), the exponent
would remain equal to 2. However, it seems logical to
suppose that the shorter model will be affected less by
radial drainage. If, for instance, model 1 is the higher
acceleration model, and therefore the shorter model, then
the coefficient would be closer to 1 than the coefficient
C2. Thus, with the ratios n^/n2 and C-^/C^ both larger than
one, according with Equation 7.13b, the time scaling
exponent would be less than 2.

195
Certainly, equation 7.13 does not have any practical
application. However, it serves the purpose of helping to
visualize how the effect of radial drainage upon the model
times may explain an exponent less than 2. Such an exponent
will not lead to the correct time in the prototype; it only
represents the value of x that satisfies equation 7.10.
Another important consequence of radial drainage upon
modelling of model results can be found in the following
reasoning. If the effect of radial drainage upon a centri¬
fugal model depends on its height, then, two modelling of
models supposedly equivalent (i.e. same acceleration ratio)
may lead to different exponents. For example, a modelling
of models performed with models at lOOg and 50g is expected
to produce an exponent higher than another modelling of
models with accelerations of 50g and 25g but the same
acceleration ratio of 2. This is so because the models in
the first case are relatively shorter and therefore affected
less by radial drainage.
The hypothesis that modelling of models conducted at
different acceleration levels would lead to different
exponents was investigated using the test results reported
by Bloomquist and Townsend (1984). In this study, a model¬
ling of models was done using three models, specifically a 6
cm model at 80 g's, an 8 cm model at 60 g's, and a 12 cm
model at 40 g's. From their data, the model times corres¬
ponding to three different solids content were carefully
obtained as reported in Table 7-4.

196
Table 7-4. Modelling of Model Results
(Bloomquist and Townsend, 1984)
a = 80 2's
a = 60 e's
a = 40 g's
S - 16%
91
151
289
S = 18%
189
330
628
S = 20%
382
713
1382
Two modelling of model analyses were done with these
values. First, the values at 80 g's and 60 g's were used in
one analysis, and secondly, the values at 60 g's and 40 g's.
The exponent obtained from the analyses are reported in
Table 7-5.
Table 7-5. Time Scaling Exponent Obtained
from Data in Table 7-4
80-60 Models
60-40 Models
Si =
16%
1.76
1 . 60
Si =
18%
1 . 94
1 . 59
Si -
20%
2 . 17
1.63
Several conclusions can be drawn from these results.
First, the exponent is always higher in the 80-60 modelling
of models (shorter models). Secondly, this increases with
solids content at a much faster rate in the case of the 80-
60 models, approaching a value close to 2 much earlier than
reported by Bloomquist and Townsend (1984).
The results of a three-model modelling of models can be
interpreted graphically. If the logarithm of equation 7.7a

197
is taken, the following expression is obtained,
l°g(tp) “ l°g(tn,) + x* log(n) (7.14)
Since the prototype time is a constant, say C, equation 7.14
can be rewritten as
log(tm) = -C + x*log(n) (7.15)
Thus, according to equation 7.15, if different model times
are plotted versus the centrifuge accelerations in log-log
scales, the resulting plot is a straight line whose slope is
the exponent x.
Using above interpretation, the values shown in Table
7-5 are plotted in Figure 7.22. For each solids content, a
unique straight line can be easily fit through the data.
However, Figure 7.22 shows the graphical equivalent to doing
two modelling of models with the data. The 80g and 60g
points are joined by one straight line, and the 60g and 40g
points are joined by another. An apparently minor but
consistent change in slope is clearly noticed. The 80-60
line has a larger slope in all three cases, indicating a
higher time scaling exponent.
Finally, and to complement the results of previous
studies with Kingsford waste clay, two of the tests of the
present research were designed to conduct a modelling of
model analysis (Table 7-1). They were test CT-2, performed
at 60 g's with and model height of 12 cm, and test CT-3, run
at 80 g's with an initial height of 9 cm. Their initial
solids content were 16.05% and 16.02%, respectively. Test
CT-2 lasted for 2880 minutes and the final model height was

Model Time (min)
Figure 7.22 - Modelling of Models using Bloomquist and Townsend
(1984) Data

199
6 cm. The duration of test CT-3 was 2115 minutes, with a
final model height of 4.55 cm.
Figure 7.23 presents the plots of average void ratio
versus log time for tests CT-2 and CT-3. The graph shows
the expected behavior, and the final void ratio of the two
models is reasonably close. The time scaling exponent was
obtained for different void ratios, as presented in Table
7-6 .
A very surprising result is obtained from the analysis.
The exponents obtained are extremely low, regardless of the
relatively high solids contents. Except for the values near
the beginning and end of the tests, when it is more likely
to obtain erroneous model times, the exponent increases with
the solids content, as expected.
These modelling of model results appear to be consist¬
ent with the reasoning presented earlier about the effect of
radial drainage on modelling of models. Bloomquist and
Townsend (1984) data contains two tests with models at 80
g's and 60 g's, with heights of 6 cm and 8 cm, respectively.
Their analysis produced exponents of 1.6 and above. The
present modelling of models, on the other hand, was done
with models at the same acceleration levels, but with larger
specimens, specifically 9 cm for the 80g model and 12 cm for
the 60g model. Therefore, it is expected that radial
drainage would be more significant in the latter, thus,
resulting in smaller time scaling exponent.

Model Time (min)
Figure 7.23 - Modelling of Models using Tests CT-2 and CT-3
200

201
Table
Void
Ratio
7-6. Modelling of Models
Solids Time (min)
Content ( % } CT-2
on Tests CT-2
Time (min)
CT- 3
and CT- 3
Exponent
13
17
. 25
51 ,
. 7
33.8
1
.48
12
18
. 42
105 .
. 3
77.0
1
.09
11
19 ,
. 77
202 .
. 1
144 .
1
1
. 18
10
21 .
. 32
332 .
, 7
235 .
4
1
. 20
9
23 .
. 14
536 .
, 1
359 .
6
1
. 39
8
23 .
. 30
859 .
3
542 .
7
1
. 60
7
27 .
. 91
1588 .
4
1042 .
6
1
.46
In summary, there appears to be enough evidence in the
test results reported in this research to believe that some
degree of radial drainage takes place near the top of
centrifugal model specimens. This radial drainage would
definitely reduce the model times, but quantification of the
magnitude of the effect is not possible. The degree of
significance of radial drainage is probably a function of
the specimen height, centrifuge acceleration, and elapsed
time of test. All this introduces some uncertainty about
the validity of the time scaling exponent obtained from
modelling of models. It appears that a deceivingly low
value of x would be obtained from tests with radial drain¬
age. However, some of the evidence presented here is mostly
circumstantial, and further studies are needed to verify
above conclusions.

CHAPTER VIII
COMPARISON OF NUMERICAL AND CENTRIFUGAL PREDICTIONS
Int ro due tion
An important aspect of this research is to use the
obtained constitutive properties of slurries as input
information into large deformation consolidation numerical
analyses. The results of such numerical predictions can
then be validated with the results of centrifugal model
tests .
Several formulations of large strain consolidation
theory have been derived. Among the most popular ones, for
which computer codes have been written, are those by Somogyi
(1979), Cargill (1982), and Yong et al. (1983). McVay et
al. ( 1986) derived a general large-strain one - dimensional
consolidation equation, based on continuity of the separate
phases and balance of momentum of the fluid phase, in terms
of excess pore pressure in combination with the spatial and
material coordinates. They proved that the other forms of
the governing equation can be obtained by simply adopting a
different dependent variable (e.g. void ratio vs. excess
pore pressure) and the appropriate coordinate system (e.g.
reduced vs. spatial coordinates). Several studies (Hernan¬
dez, 1985; Zuloaga, 1986; McVay et al., 1986) have shown
202

203
that good agreement exists between the various approaches,
as long as the same soil properties are used.
For the numerical predictions reported here, the
piecewise linear approach developed by Yong and coworkers
(1983) and later expanded by Zuloaga (1986) was used. An
important advantage of this program is that it allows the
input of the constitutive relationships in the form of data
points, as an alternative to the traditional power curve
parameters.
Many of the features of the program developed by
Zuloaga (1986) UF-McGS, such as continuous filling, sand/
clay mixes, etc., were not necessary for the analyses of the
ponds to be considered here. Therefore, a simplified and
more efficient version of the program, analyzing only
quiescent conditions, was written in Turbo Pascal. The
program is called YONG-TP. This program, which allows a
surcharge, was found to run faster than the original pro¬
gram. A listing of this is included in Appendix I.
A total of five hypothetical ponds were analyzed. All
of the ponds have been modelled in the centrifuge under
quiescent conditions using Kingsford clay. Two of them were
modelled by McClimans (1984). The first one, pond KC80-6/0
in McClimans notation, is a 16-ft high prototype, self¬
weight consolidating from a solids content of 16%. The
second one, pond KC80-10.5/0, is a 27.6-ft high prototype
with initial solids content of 16.3%. Hernandez (1985) used
McClimans centrifuge data to obtain the prototype elapsed

204
time of consolidation. Hernandez reported using an incre¬
mental time scaling exponent as reported by Townsend and
Bloomquist (1983). The sett1ement-time curves as presented
by Hernandez were used for comparison with numerical
predictions.
The other three ponds analyzed correspond to the
centrifuge tests CT-1, CT-2/3, and CT-5 as described in
Table 7-1. Pond CT-2/3 denotes a prototype modelled in the
centrifuge by tests CT-2 and CT-3, used in the modelling of
models. After the results obtained in Chapter VII concern¬
ing the influence of radial drainage on the time scaling
exponent, it was decided to use the theoretical value of 2
to obtain the prototype time for these tests. Test CT-5
offers an specially interesting opportunity of comparing
numerical and centrifugal predictions in a pond where a
surcharge loading is applied. The initial solids content of
all five ponds to be analyzed was around 16%.
The Constitutive Relationships
Through the readily availability of computer programs,
several of which have been adapted to run on personal
computers, the task of predicting the consolidation behavior
of slurry ponds has been greatly simplified. However,
without reliable soil properties the results of these
numerical tools are meaningless. Hernandez (1985) and McVay
et al. (1986) found tremendous disagreement among

205
predictions using different constitutive relationships
reported for Kingsford clay.
It has been found during the development of this
research that the constitutive relationships of remolded
slurries are not unique. Instead, they show a zone similar
to a preconsolidation effect, which is dependent upon the
initial solids content. Therefore, material characteriza¬
tion of the ponds to be analyzed should be based on labora¬
tory tests with initial solids contents compatible to that
of the pond.
Unfortunately, the centrifugal model tests reported in
Chapter VII did not show this preconso 1idation effect for
the reasons already given. Consequently, the results of the
automated slurry conso 1idometer tests were the first choice
to characterize the slurry properties. Because of the
irregular behavior found on the CHG compressibility curves,
these tests were not even considered, leaving the CRD as the
best option. Of the four CRD tests performed, only two of
them had an initial solids content around 16% (Table 5-1).
In addition, test CRD-3 started at a solids content of 16.2%
and the first reading was taken after 2 hours, when the
solids content was about 16.3%. Since the ponds' initial
solids contents are below this value, the results of test
CRD-3 could not be used because the computer program needs
to determine the initial effective stress of the pond
interpolating from the effective stress-void ratio data
points. Thus, the results of test CRD-1, with an initial

206
solids content of 15.3%, were used to characterize Kingsford
waste clay. Ten evenly spaced points were selected from
Figure 5.1 to generate the input constitutive curves for the
program. As an alternative to the data points, the power
curves fit to the experimental data of test CRD-1 will also
be used in the predictions. The corresponding parameters
were given in Chapter V.
Prediction of Ponds KC80-6/0 and KC80-10.5/0
These two ponds are the ones modelled in the centrifuge
by McClimans (1984), and whose prototype behavior was
analyzed and reported by Hernandez (1985). Appendix I
includes, as an example, the output of the program YONG-TP
predicting the behavior of pond KC80-6/0, with the constitu¬
tive relationships (data points) obtained from test CRD-1.
Figure 8.1 presents the settlement predictions of pond
KC80-6/0 obtained using the constitutive relationships
obtained from test CRD-1, as well as the centrifugal model.
One numerical prediction was based on the use of the direct
experimental data points, while the other was obtained using
the corresponding power curve parameters. The agreement
between the prediction using direct data points and the
centrifugal model is very good. In both cases, however, the
total settlement predicted was about 0.5 ft less than that
predicted with the centrifuge. The time needed to produce
the total settlement, as well as the rate of settlement, are
predicted better with the data points. The prediction based

Figure 8.1 - Prediction of Pond KC80-6/0 using Constitutive
Relationships obtained from Test CRD-1
207

208
on the parameters obtained from test CRD-1 bisects the
centrifugal model prediction, initially underpredicting and
later overpredicting the settlement rate.
To verify the output of the Turbo Pascal program used
in the analyses reported in this research, YONG-TP, and to
compare the results of the piecewise linear approach with
Somogyi's implicit scheme (1979), pond KC80-6/0 was analyzed
using the computer programs UF-McGS (Zuloaga, 1986) and QSUS
(Somogyi, 1979). Because of limitations of the latter, the
constitutive relationships of the slurry were represented by
the power curve parameters obtained from test CRD-1. Figure
8.2 presents the results of the three programs. The agree¬
ment among them is excellent.
The settlement predictions of pond KC80-10.5/0 are
presented in Figure 8.3. The agreement between centrifugal
and numerical predictions is good. Again, the use of the
power curve parameters, instead of the experimental data
points, results in the numerical prediction curve bisecting
the centrifugal model results.

-p
<+-
-p
JZ
CD
•ri
Ql
cu
Q-
X
-P
o
-p
o
L
Q_
17
16-
15-
14-
13-
12-
11-
* YONG-TP
^ UF-McGS
â–¡ QSUS
IE 2
“» ■ ■ *—■—» i |
IE 3
Prototype Time (days)
Figure 8.2 - Comparison of YONG-TP, UF-McGS, and QSUS Outputs
IE 4
209

Figure 8.3 - Prediction of Pond KC80-10.5/0 using Constitutive
Relationships obtained from Test CRD-1
210

211
Prediction of Ponds CT-1. CT-2/3. and CT-5
Pond CT-1, a 31.5-ft prototype, was modelled in the
centrifuge by the test with the same name, as reported in
Chapter VII. A numerical prediction was obtained using the
results of test CRD-1 (data points). The results of the
centrifugal model and the computer prediction are presented
in Figure 8.4.
Surprisingly, the agreement between centrifugal and
numerical predictions is very poor. The computer predic¬
tion underestimates both the total magnitude and rate of
settlement. Similar results were obtained in the prediction
of pond CT-2/3 presented in Figure 8.5. In this case, two
centrifugal models were obtained from tests CT-2 and CT-3.
The agreement of the two centrifugal models is very good.
However, the numerical prediction suffers the same short¬
comings found for pond CT-1.
The results of these two predictions led to the believe
that somehow the material used in the centrifuge tests
reported in Chapter VII was different from the one charac¬
terized by the constitutive relationships used in the
predictions. In order to investigate this hypothesis, one
of McClimans centrifuge tests, specifically KC80-10.5/0, was
approximately reproduced using the material tested in
Chapter VII. McClimans test KC80-10.5/0 was performed at 80
g's, with a specimen initial height of 10.5 cm. and initial
solids content of 16.3%. The new test, denoted by CT-6, was

34
32
30
28
26
24
22
20
18
16
14
. *—■—■ ■ ■ i ■ | « ■—■—«—* ■ ■ * i ■ ■—■—■ « * ■ ■ ¡—
1 IE 2 IE 3 IE 4
Prototype Time (days)
Figure 8.4 - Prediction of Pond CT-1 using Constitutive
Relationships obtained from Test CRD-1
212

26
24
22
20
18
16
14
12
10
a Centrifugal Model CT—2
a Contrifugal Model CT-3
â–¡ CR0-1 Dato Points
i • ■ ■—■—i « «
-» a ■ r-
-«—i i «-|
~« ■ ■—i—i—m
IE 2 IE 3
Prototype Time (days)
IE 4
Figure 8.5 - Prediction of Pond CT-2/3 using Constitutive
Relationships obtained from Test CRD-1
ro

214
also performed at 80 g's, with an initial height of 10.7 cm
and solids content of 15.95%.
The settlement plots for both tests are presented in
Figure 8.6. These plots show, leaving no room for doubts,
that the two materials do not behave similarly. The slurry
of test CT-6 has both larger compressibility and larger
pe rme abi1ity.
Given the results of Figure 8.6, the most reasonable
step to follow was to re-analyze ponds CT-1 and CT-2/3 using
the power curve parameters obtained from the same centrifuge
tests. These parameters were given in Chapter VII and are
repeated here for convenience.
A = 16.359 B - -0.204 C = 1.029E-06 D = 4.297
The resulting numerical prediction of pond CT-1 is
compared with the centrifugal model in Figure 8.7. The
numerical model predicts very well both the total settlement
and the time required to achieve this value. With regard to
the rate of settlement, the computer prediction bisects the
centrifugal model curve. This peculiar result is attrib¬
uted, at least in part, to the fact that the permeability
relationship does not include the preconso 1idation zone.
Because of this, the permeability is initially too low, and
toward the end of the test it is too high. It is also very
likely that radial drainage effects, which are only being
approximated, are partially responsible for the initial
disagreement between numerical and centrifugal results.

13
12
11
10
9
8
7
6
5
4
]
Í£
a Test CT-6 Si B 15.95Z
â–¡ KC80-10.5/0 Si - 16.30*
Model Time (min)
â–¡ â–¡ D
IE 4
8.6 - Comparison of Centrifuge Tests KC80-10.5/0 and CT-6
215

34
32
30
28
26
24
22
20
18
16
14
IE 2 IE 3
Prototype Time (days)
IE 4
8.7 - Prediction of Pond CT-1 using Centrifuge Test Parameters
216

217
A comparison between measured and predicted void ratio
profiles for pond CT-1, using the centrifuge parameters, is
presented in Figure 8.8. At the end of the test, the
agreement between the measured void ratios and the values
predicted by the computer program is very good, except near
the top of the pond. Theoretically, the void ratio at the
surface of pond should not change. However, the results of
this and other studies (Been and Sills, 1981; Lin and
Lohnes, 1984) reveal that, without a known reason, the void
ratio at the surface decreases as the pond consolidates.
The measured void ratio profile at a prototype time of
2.9 years is in good agreement with the prediction obtained
at 2 years, only for the bottom half of the pond. In the
upper portion of the pond, the two curves depart from each
other, since the predicted curve must reach the initial void
ratio of 14.53 at the surface.
Figure 8.9 presents the pore pressure profiles pre¬
dicted at four different times for pond CT-1 and using the
centrifuge power curve parameters. In Chapter VII, Figure
7.7 showed the measured excess pore pressure at a time of 2
hours (model time), along with the parabolic distribution
assumed to exist at the center of the specimen. At 80 g's
with a time scaling exponent of 2, two hours in the model
represent about 1.5 years in the prototype.
Using the results of Figure 8.9, the excess pore
pressure distribution at 1.5 years (2 hours in the model)
was obtained. A comparison of the latter with the results

26-
24-
22-
20-
18-
16-
14-
12-
10-
8-
6-
4-
2-
o-
Fi
a Predictad at End of Test
* Measured at End of Test
■ Predicted at t » 2 yrs.
â–¡ Measured at t â–  2.9 yrs.
° Predicted at t ■ 4 yrs.
9 10 il
Void Ratio
r
12
T
13
T
14
15 16
8.8 - Measured and Predicted Void Ratio Profiles for Pond CT-1
218

Elevation in Pond (ft)
Excess Pore Pressure (psf)
Figure 8.9 - Predicted Excess Pore Pressure Profiles for Pond CT-1

220
of Figure 7.7 is shown in Figure 8.10. The predicted
distribution falls right in the middle between the measured
values and the parabolic distribution, except near the top
of the model. This local departure from the general trend
is simply due to the difference between the measured model
height of 9.5 cm and the predicted value of 10.18 cm.
Figure 8.7 showed that the numerical model initially
overpredicts the pond height.
The result of Figure 8.10 is consistent with the
assumption made in Chapter VII to obtain the constitutive
relationships from the centrifuge test data. Specifically,
the assumption was that the excess pore pressure profile was
the average of the measured distribution at the boundary and
the parabolic distribution assumed at the center. In this
way, a problem where radial drainage exists is approximated
by a one - dimensional situation.
The next pond to be analyzed, CT-2/3, is a 23.6-ft
prototype. Figure 8.11 presents the numerical prediction of
this pond using the centrifuge test parameters, along with
the two centrifugal models, CT-2 and CT-3. The prediction
of the total settlement and time for consolidation is
clearly much better than those obtained with the results of
test CRD-1 or the other constitutive relationships proposed
for Kingsford clay. Similar to pond CT-1, the computer
prediction bisects the centrifuge curves.

12
11
10
9
8
7
6
5
4
3
2
1
0
Fi
a Parabolic Distribution
a Transducer Readings
â–¡ Predicted Distribution
Excess Pore Pressure (psi)
re 8.10
Measured and Predicted Excess Pore Pressure Profiles
at a Model Time of 2 hours for Pond CT-1
221

26
24
22
20
18
16
14
12
10
1
•* Centrifugal Model CT~2
a Centrifugal Model CT-3
a Centrifuge Test Parameters
f-O
ro
ro
1 1 1 >>>••! ■ ■■■■'! 1 T I M | W—i
1 IE 2 IE 3 IE 4
Prototype Time (days)
e 8.11 - Prediction of Pond CT-2/3 using Centrifuge Test Parameters

223
A comparison of measured and predicted void ratio
profiles for pond CT-2/3 is presented in Figure 8.12.
Again, the agreement at the end of the test is very good,
except near the top of the pond. The profile measured at a
prototype time of 3.3 years compares better with the one
predicted at 2 years than with that at 4 years. Notice,
however, that the corresponding measured height at 3.3 years
is closer to the height predicted at 2 years. Thus at these
two times the pond is under more similar conditions, which
explains why the void ratio profiles at 2 and 3.3 years are
in better agreement.
The results of the numerical prediction of ponds CT-1
and CT-2/3, using the centrifuge power curve parameters, are
very good. Because these parameters were obtained from the
data collected from tests CT-1 and CT-2, these results were
expected. Nevertheless, they demonstrate the validity of
the numerical approach proposed in Chapter VI to obtain the
constitutive properties of slurries from centrifugal model
tests. However, it is necessary to evaluate the reasonable¬
ness of these constitutive relationships by predicting other
ponds. The remaining of this chapter will analyze the
predictions of ponds CT-5 and CT-6.
Pond CT-5 represents a hypothetical prototype corre¬
sponding to test CT-5, used for comparison with McClimans
test KC80-10.5/0 in Figure 8.6. The prototype height is
28.08 ft and the initial solids content is 15.95%. A
computer prediction of this pond was obtained using the

IB
16
14
12
10
B
6
4
2
0
i p:
8.12 - Measured and Predicted Void Ratio Profiles for Pond CT-2/3
224

225
centrifuge power curve parameters. The centrifugal predic¬
tion was obtained using the time scaling exponent of 2 with
the acceleration level of 80 g's. The results of the
numerical and centrifugal predictions are shown in Figure
8.13. The computer analysis predicts quite well the final
height of the pond and the total time required to achieve
this height. The predicted rate of settlement is also in
quite good agreement with the centrifugal model. Similar to
previous predictions where power curve parameters were used,
the numerical prediction bisects the centrifuge curve.
The last pond to be analyzed is pond CT-5, a 28.9-ft
prototype with a surcharge of 263 psf. The centrifugal
model test of this pond was only performed for 8 hours for
the reasons given in Chapter VII. Nevertheless, this pond
offers an excellent opportunity to validate the numerical
prediction of a slurry pond with a surcharge load.
The pore pressure response observed in test CT-5
(Chapter VII) provides the basis for a more confident use of
a time scaling exponent of 2 to obtain the prototype times
of the centrifugal model. For the numerical prediction, the
centrifuge test parameters were used, based on the analyses
of the previous ponds CT-1, CT-2/3 and CT-6 .
Figure 8.14 compares the numerical and centrifugal
settlement predictions of pond CT-5. The agreement between
the two curves is remarkably good. The predicted excess
pore pressure profiles at various times is compared in
Figure 8.15 with the values measured at the transducers at

30
28
26
24
22
20
18
16
14
12
IE 2 IE 3
Prototype Time (days)
IE 4
8.13 - Prediction of Pond CT-6 using Centrifuge Test Parameters
226

30
28
26
24
22
20
18
16
14
12
10
1
* Centrifugal Model CT-5
â–¡ Numerical Prediction
-I 1 I T I 'â– 
t 1 â–  i i r
IE 2 IE 3
Prototype Time (days)
IE 4
8.14 - Prediction of Pond CT-5 using Centrifuge Test Parameters
227

26
24
22
20
18
16
14
12
10
8
6
4
2
0
•a Measured at t ° 0.7 yr.
a Measured at t ° 5.8 yr.
â–¡ Predicted at t
â–  Predicted at t
o Predicted at t
• Predicted at t
0.5 yr.
1 yr.
4 yr.
6 yr.
1 1 1 1 1— T
150 200 250 300 350 400 450
Excqss Pore Pressurg (psf)
500 MO 600
Figure 8.15 - Measured and Predicted Excess Pore Pressure
Profiles for Test CT-5
228

229
prototype times of 0.7 and 5.8 years. Within the limita¬
tions of the data, the agreement between predicted and
measured pore pressure is quite good.
After stopping test CT-5, two samples were cored and
sliced to determine the void ratio-depth profile. The
centrifuge was stopped shortly after 8 hours of test,
corresponding to a prototype time of about 5.9 years.
Figure 8.16 shows the two profiles obtained, along with the
predicted curves at 4 and 6 years. Considering the diffi¬
culty of the sampling technique, it can be concluded that
the measured profiles exhibit the right behavior and that
their agreement with the predicted results is good. It is
worth mentioning here that, because there was no initial
intention of using this information, the samples for the
determination of the void ratio profile were not obtained
until four days after the end of the test. Thus, some
swelling definitely had occurred in the specimen.

20
18
16
14
12
10
8
6
4
2
0
a Measured at t * 5.9 yrs. (1)
â–¡ Predicted at t â–  4 yrs.
a Measured at t - 5.9 yrs. (2)
â–  Predicted at t * 6 yrs.
~I
8.5
e 8.16 - Measured and Predicted Void Ratio Profiles for Pond CT-5
230

CHAPTER IX
CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH
Summary and Conclusions
1. The main objective of this research was to develop
techniques to obtain the consolidation properties of
slurries, specifically the effective stress-void ratio
relationship and the permeabi1ity-void ratio relationship.
Two techniques were developed. The first one involved the
design and construction of an automated slurry consolidóme-
ter, while the second used centrifugal model tests.
2. The automated slurry conso 1idometer proved to be an
effective technique for determining the constitutive proper¬
ties of slurries. The equipment is fully automated,
requiring human intervention only during setting up and
dismantling of the test.
3. The test chamber is an 8-inch (0.20 m) diameter cast
acrylic cylinder. The specimen height can vary between 4
inches (0.10 m) and 8 inches (0.20 m). The test monitors
the specimen height, pore pressure distribution across the
specimen, load, and total stress at the bottom of the
specimen. A stepping motor is used to produce the load,
231

232
which is transmitted to the specimen through a gear system
and loading piston.
4. A Hewlett-Packard computer and control/data acquisition
system is used to control and monitor the test. The
controlling computer program was written in BASIC. A second
program is used to reduce the data and plot the constitutive
curves at the end of the test. The data reduction analysis
uses well-accepted soil mechanics principles.
5. Two different loading conditions were investigated in the
research, specifically Constant Rate of Deformation (CRD)
and Controlled Hydraulic Gradient (CHG). The CRD test
produced much better results and is recommended as the
standard testing procedure. A typical CRD test lasts
between 3 days and 1 week, depending on the rate of deforma¬
tion and the initial and final conditions of the specimen.
6. The constitutive relationships obtained from the CRD
tests show a "pseudo-preconsolidation" effect, which is a
function of the initial solids content of the slurry. Thus,
it is concluded that the constitutive relationships are not
unique. This particular behavior is attributed to the
initial highly remolded initial structure of the material.
7. In the case of the permeability relationship, the curves
with different initial solids content approach a unique

233
virgin zone for the range of deformation rates investigated.
The compressibility relationship, on the other hand, was
found to be dependent upon the rate of deformation as well
as initial solids content. Therefore, it is recommended
that the test be performed at a slow rate, and values around
0.008 mm/min appear to be appropriate.
8. The results of this research indicate that the constitu¬
tive relationships of slurries can not be represented by the
traditional power curve parameters. Instead, the actual
experimental data points should be used as input data for
computer analysis.
9. The technique proposed to obtain the constitutive
properties from centrifugal model tests has the advantage of
better simulating the stress conditions of an actual pond.
Additionally, the approach is not based on average values as
is the case with the automated slurry consolidation tests.
Instead, actual measurements of excess pore pressure and
void ratio profiles with time are used to obtain the
relationships using the effective stress principle, Darcy's
law, and continuity. A numerical approach, based on updated
Lagrangian coordinates and a material representation of the
specimen, is used to analyze the data. A FORTRAN program
was written for this purpose. However, the approach has
several disadvantages. First, the obtaining of the samples
for solids content measurements is not very accurate.

234
Second, the test does not provide information on the
preconso 1idation zone because it is not possible, with the
technique used, to obtain the solids content profile early
in the test. Nevertheless, the existence of the preconsoli¬
dation zone, at least in the compressibility curve, is
clearly demonstrated by the fact that a condition of zero
initial effective stresses was observed in the tests.
10. The series of centrifuge tests conducted revealed a
problem with radial drainage in the acrylic bucket. Because
of this, an approximation was necessary in order to simulate
a pseudo one - dimensional situation and to be able to use the
numerical approach proposed. The radial drainage evidences
disappeared when a surcharge load was applied to the model.
11. It was demonstrated that the effect of radial drainage
upon the models may explain the obtaining of a time scaling
exponent of less than 2 from a modelling of models analysis.
It is recommended that a value of 2 be used for initial
solids content above 14%-16%.
12. The constitutive relationships of the slurry were
obtained from two centrifuge tests performed at 60 g's and
80 g's. The permeability obtained from the analysis corres¬
ponds to the prototype value, which is n (the acceleration
level) times smaller than the permeability in the model. The

235
agreement between the results of the two tests was very
good .
13. The compressibility relationship obtained from the
centrifuge tests was in good agreement with the results of
the CRD tests performed at a rate of deformation of 0.008
mm/min. This result reaffirms the need to perform the CRD
tests at low deformation rates. On the other hand, the
permeability relationship obtained from the centrifuge tests
plotted parallel to the virgin zone of the CRD curves.
However, the centrifuge permeabilities are about a half
order of magnitude higher. A full explanation of this
apparent discrepancy requires further investigation.
14. Two groups of hypothetical ponds were predicted using a
piecewise linear solution of the governing equation. One
group corresponds to centrifuge tests reported by McClimans
(1984), and the other corresponds to centrifuge tests
conducted as part of this research. The two ponds modelled
by McClimans were predicted using the constitutive relation¬
ships obtained from CRD tests, both in the form of data
points and as power curve parameters. The agreement between
centrifugal and numerical models was good for both ponds.
The rate of settlement was predicted better using the
, constitutive relationships in the form of data points.

236
15. When the CRD constitutive relationships were used to
predict the behavior of the recently conducted centrifuge
tests, the predictions were not good. After some additional
testing, it was concluded that the material used in the
centrifuge tests was different from the more virgin slurry
used in the early CRD tests (certainly different from the
material used by McClimans). This was attributed to several
factors, including aging of the slurry, the continuing
addition of tap water, and the re-use of the same material.
Accordingly, the prediction of the hypothetical ponds
modelled in this research was repeated, this time using the
parameters obtained from the centrifuge tests themselves.
The agreement between centrifugal and numerical models was
quite good, not only for those model ponds used to obtain
the constitutive properties, but also for two different
model ponds, including one with a surcharge. Not only were
the settlement predictions good, but also the predictions of
excess pore pressure and void ratio were reasonably good.
16. In summary, the use of numerical models is an excellent
tool for predicting the consolidation behavior of slurry
ponds. The constitutive input properties needed in the
analysis can be obtained from either of the techniques
developed in this research. However, the CRD automated
slurry consolidation tests are recommended over the centri¬
fugal model tests. The latter technique is more appropriate
for validation of computer results.

237
Suggestions for Future Research
1. A major aspect of the automated slurry consolidation
apparatus requiring improvement is reducing piston friction.
It is recommended that the present acrylic chamber be
replaced by a metal chamber which will maintain a true bore
and piston diameter capability. The chamber should be
teflon coated and the piston edge should be sealed using a
teflon 0-Ring to minimize piston friction and, at the same
time, prevent edge leakage of slurry.
2. The range of the total stress transducer at the bottom of
the specimen needs to be reduced from 3 bars to 1 bar, and
the transducer diaphragm should be flush with the bottom of
the specimen. An accurate reading of this transducer is
crucial to estimating the side friction on the specimen.
3. The range of the pore pressure transducers should also be
improved. On the moving piston, a 1-psi (75 mbar) transdu¬
cer is recommended. The rest of the transducers on the
chamber side should be of 5-psi (350 mbar) to 14.5-psi (1
bar) range. This improvement of the transducer sensitivity
is particularly important if CRD tests are to be performed
at low deformation rates. By the same token, the range of
the load cell should be limited to 100-200 pounds.
4. The significance of using average values to obtain the
slurry properties is an aspect of the automated slurry

238
conso1idome ter that deserves further investigation. This
study can be accomplished by performing several tests with
similar initial conditions. The tests should be stopped at
different times to obtain the solids content profiles.
These and the excess pore pressure profiles with time would
allow the obtaining of constitutive relationships in a way
similar to that used in the centrifuge tests.
5. A more detailed study of the effect of the deformation
rate is needed in order to make a better recommendation
concerning the appropriate values for the CRD test.
6. The effect of the initial specimen height upon the
constitutive properties needs to be investigated; the use of
a smaller specimen (5-10 cm) may be advisable.
7. With respect to centrifugal modelling, the main short¬
coming of the proposed approach to obtain the constitutive
relationships is the determination of the void ratio
profile. The technique used in this research yielded
reasonable values, but it is not applicable during early
stages of the test when the slurry is still very dilute.
Therefore, if the centrifuge approach is to be developed
further, this is the aspect of the test that requires
improvement.

239
8. The results of the centrifuge tests conducted as part of
this research suggest the existence of radial drainage in
the specimen. However, additional testing is necessary to
evaluate this effect and its influence on the time scaling
exponent. Since the evidences of radial drainage were not
observed in the tests with surcharge, it is recommended that
a modelling of models analysis using surcharge be carried
out. Such an analysis would allow a better evaluation of
the time scaling exponent.
9. Finally, it is necessary to test other slurries in order
to corroborate the findings of this research. Such study
should concentrate on the CRD test using the automated
slurry conso 1idometer. However, the centrifuge approach
could be used as a verification tool.

APPENDIX A
TIME SCALING RELATIONSHIP
Introduction
The derivation of the time scaling relationship will be
based on the general governing equation derived by McVay et
a1. (1986). This is
5
fk
6 u]
, 1 -
de
Du
¿e
_TW
1 + e
da '
Dt
0 (A . 1)
where u is the excess pore pressure,
e is the spatial or convective coordinate,
k is the coefficient of permeability,
7W is the unit weight of water,
e is the void ratio,
o' is the effective stress,
t is the time, and
^U- denotes the material derivative
X
To begin, it is necessary to express several basic
scaling relationships. If n is the scale factor, such that
a length in the prototype, lp, and a length in the model,
lm, are related by
1p/1m “ n (A.2)
240

241
then, in order to produce equal stresses in model and
prototype, their accelerations must be related by
(ag)m/(ag)p = n (A.3)
where (ag)m is the acceleration of gravity in the prototype,
i . e . g, and
(ag)p is the normal acceleration of the model in the
centrifuge.
Since the density of a material is independent of
gravity, it follows from Equation A.3 that
7m/7p = n (A.4)
where ym and 7p are the unit weights in the model and
prototype, respectively.
Equations A.2 through A.4 do not only imply that the
total and effective stresses will be equal in the model and
prototype, but also the pore pressures will be equal. In
particular, for the excess pore pressure,
um = up (A.5)
Permeability Scaling Factor
To derive the scaling factor relating the model and
prototype permeabilities, Mitchell's equation of the
coefficient of permeability is used. This is
k = K ..PttJU (A. 6)
4w
where pw ¿s the water density,
¿iw is the water viscosity,
ag is the acceleration of gravity of centrifuge, and

242
K is the absolute permeability, which depends only on
the geometry of the soil skeleton.
Since K, pw, and are the same in the model and the
prototype, it follows from Equation A.6 that
(A. 7)
Replacing Equation A.2 into Equation A.7 leads to
(A.8)
The same result is obtained if a more general equation
for k, known as Kozeny-Carmen, is used. Goforth ( 1986 ) has
also proved that the coefficient of permeability in the
model is n times larger than in the prototype, as long as
the hydraulic potential is defined as energy per unit
weight. Such a definition is the one exclusively used in
Soil Mechanics.
Governing Equation in the Centrifuge
If the first term of Equation A.l is written for the
prototype, then the scaling factors already known can be
used to express the term for the model. The process is
carried out in the following equation.
kn 6un
- 5
"(km/n)
^ um
^em
^em
_(7w>p 5GP
_( <7„)m/n)
^ em
d6P J
dGP
and since from Equation A.2,
1
(A.10)
n

243
then Equation A.9 is simplified to
8
" kD 6ud"
<-o
II
6uml
5EP
(lw)p ^ep
1
oV
m
3!
—1
E
W
£
?
?~
(A.11)
Proceeding in the same way with the second term of Equation
A.l (without expanding the material derivative), and
considering than the void ratio will the same in the model
and prototype, leads to
1 + e,
de,
da,
DUj
D tT
de,
X
1 + em
da
m
X
dt
dt
(A.12)
Replacing equations A.11 and A.12 into equation A.l, and
O
multiplying by n , leads to
8
^m
8 um
1
dem
Dum
^ em
Sem
1 + em
Dtm
n
2 dt
HL
dt,
0
(A.13)
Equation A.13, the governing equation in the centrifuge,
will be identical to the equation in the prototype, i.e.
equation A.l, if
n
2.
= 1
(A.14)
Integrating this ordinary differential equation, and
considering that at tm =0, tp = 0, the time scaling
relationship is finally obtained as
tp = n2,tm (A.15)
In summary, it is demonstrated that in order for the
differential equation governing the one - dimensional consoli¬
dation process to hold in the centrifuge, it is necessary
that the elapsed times of consolidation in the model and
prototype be related by equation A.15. In other words, the
time scaling exponent must be 2.

APPENDIX B
LVDT-PIVOTING ARM CALIBRATION
In Figure B-l, position 1 represents an ideal horizon¬
tal of the pivoting arm, while position 2 represents the arm
after the specimen has deformed an amount D-^ .
Figure B-l. Two Positions of Pivoting Arm
The factory calibration of the LVDT, FC in Volts/in, would
yield the displacement of the LVDT tip, D2, as
D2 - AV/FC (B.l)
where AV is the corresponding voltage change in Volts. From
basic proportionality, the deformation of the specimen can
be obtained from
D-l - (11/12) • (AV/FC) = AV/CC (B . 2 )
where CC represents the converted calibration of the LVDT,
given by
CC = (12/11)*FC (B . 3)
244

245
The dimensions 1 ^ and ]_2 were accurately measured as
121.2 mm and 35.6 mm, respectively. For our LVDT, with a
factory calibration of 10.138 Volts/in, the converted
calibration is
CC = (35.6/121.2)•10.138 = 2.978 V/in (B.4a)
or CC = 0.117 V/mm (B.4b)
Furthermore, the following is a proof that the conver¬
sion factor, 1 /12 > is independent of any initial inclina¬
tion of the arm. In Figure B-2, position 1 is again the arm
in its horizontal position, but position 2 represents its
initial position. Distances a and b represent the devia¬
tions of the arm from its horizontal position. When the
specimen deforms an amount c, the arm reaches position 3.
Figure B-2. Initial Inclination of Pivoting Arm
Again, from basic proportionality we know that
a/b = 1p/12 (B.5)
but also
(a+c)/(b+d) = li/l2 (B.6)
Then, from the properties of proportions, it is also true
that
c/d - 1 ]_/12
( B . 7 )

246
Thus, the deformation of the specimen c can be obtained from
the displacement of the LVDT tip, d, using the calibration
converted by the arm ratio li/l2> regardless of any initial
inclination of the arm.
Finally, it was anticipated that the round shape of the
LVDT tip would introduce an error in the calibration. This
is so because it would not be the same point that would be
in contact with the arm as the specimen deforms. Thus, the
round tip was replaced with a knife-edged tip to eliminate
the problem.

APPENDIX C
ANALYSIS OF NOISE EFFECT IN THE TRANSDUCERS RESPONSE
This appendix presents the analysis undertaken to study
the noise effect on the pressure transducers and load cell
response. The study included the use of analog and digital
filters in the HP-6940B Multiprogrammer, and the use of a
more advanced data acquisition unit, the HP-3497A.
To produce a low pass analog filter, a capacitor C is
connected across the output leads of each transducer. The
cut-off frequency of the filter is given by
fc = 1/(2 ttRq C ) (C.l)
where R0 is the nominal output impedance of the device.
Since the output of the transducers used in the test is not
frequency dependent, there is no risk of loosing information
in the response by using a capacitor too large. The cut-off
frequency, however, will be limited by the Nyquist sampling
theorem (Malmstadt et al., 1981), which states that if a
band-limited dc signal is sampled at a rate that is twice
the highest frequency component in the signal, the sample
values exactly describe the original signal. For the
hardware/software configuration being used in the study, it
was estimated a time interval between readings of 0.131
seconds, which corresponds to a sampling rate of about 7.6
247

248
Hz. With this limitation, the cut-off frequency of the
filter must be lower than 3.8 Hz, using the minimum factor
of 2 .
For the pressure transducers, with a nominal output
impedance of 1000 0, a cut-off frequency of 3.8 Hz leads to
a minimum capacitance of about 42 pF. For the load cell,
with a nominal output impedance of 351.5 Q, the minimum
capacitance would be about 120 ¿¿F. Based on these results,
a 47 nF capacitor was installed in each pressure transducer
and a 122 /¿F (100 /¿F and 22 /¿F in parallel) capacitor was
installed in the load cell. Considering that the voltage
across a capacitor cannot change instantly, it is important
to estimate the percentage of the voltage applied that has
charged the capacitor by the time the next reading is taken.
This is a function of the ratio t/RC, where t is the elapsed
time of charging, and RC is referred to as the time constant
of the circuit. Using the time interval between readings of
0.131 seconds and the value of RC for each circuit, the
following values are computed
Pressure Transducers: 0.131/(1000 47E-6) = 2.79
Load Cell: 0.131/(351.5 122E-6) = 3.05
According to Malmstadt et al. (1981) (Table 6-1, page 144),
these values correspond to voltage percentages across the
capacitors of about 93.5% for the pressure transducers and
95.2% for the load cell. Such values are not considered
completely acceptable since, for practical purposes, a
capacitor is considered fully charged when t/RC ~ 5. Even

249
so, these capacitors were used as the best filters, since it
was necessary to make a trade-off with the sampling theorem.
After several preliminary tests, it was found that the
noise level was still unacceptable. Therefore, it was
decided to undertake the study described in this appendix.
The study consisted of taking 50 consecutive readings, while
keeping the pressure constant (about 5 cm of water) in
pressure transducer No. 1, and the load constant (about 15
lb) in the load cell. A total of seven tests were done for
each device; five of them used the Multiprogrammer with
three different capacitors (analog filters), no capacitor at
all, and two types of digital filter; the seventh test was
done with the HP-3497A monitoring the devices. The average,
standard deviation, and coefficient of variation (COV) were
computed for each test.
The two digital filters used in the study were a
nonrecursive 7-point filter, and a recursive first-order low
pass filter (Kassab, 1984). In the first case, the filter
output is computed from the input samples by a least-square
fitting; for a 7-point filter, the output at time nT is
given by equation C.2.
Y(nT) - 1/21 [-2X(nT-3T) + 3X(nT-2T) + 6X(nT-T) + 7X(nT)
-2X(nT+3T) + 3X(nT+2T) + 6X(nT+T)] (C.2)
where T is the time interval between samples
n is an integer, and
X(nT-3T), for example, denotes the input sample
taken 3 time intervals before the current time nT.

250
In the case of a recursive first-order low-pass digital
filter, on the other hand, the output of the filter is
computed from the input samples as well as previous samples
of the output. Recursive filters simulate better the
equivalent analog filters, but they are subjected to
possible instability (Kassab, 1984). For the digital filter
used here, the equation for the output is
Y(nT) = (aT)X(nT) + (e'aT)[Y(nT-T)] (C.3)
where a is the reciprocal of the RC time constant
The results of the study are summarized in Table C-l.
From this table, it is clear that the largest scatter occurs
when no filter is used in the HP-6940B and that, the larger
the capacitor, the more uniform the response is. Similarly,
digital filtering reduces the scatter of the response but
the effect is smaller than with analog filters; the recur¬
sive filter worked better than the nonrecursive. The
average values differed slightly from one device to the
other, but this effect is not considered important since it
is the voltage change that determines the pressure or load
measured.
Figure C.l shows the response observed with no filter,
a 220 /xF analog filter, and the use of the HP- 3497A for
pressure transducer No. 1. The voltage range in the abscise
of the plot corresponds to a pressure of about 0.16 psi.

251
Table C.l - Summary of Transducers Response
Using Various Filtering Techniques
Device
Average
Standard
C . 0 . V .
Used
Reading
Deviation
in
220 y. F
19.620
0.0131
0.0666
100 nF
19.620
0.0149
0.0759
47 nF
19.298
0.0197
0.1022
No Filter
19.122
0.1832
0.9578
Rec. Digital
19.597
0.1165
0.5948
Nonrec. Digital
19.379
0.1592
0.8214
HP-3497A
19.493
0.0036
0.0184
(a)
Pressure
Transducer No. 1
Device
Average
Standard
C . 0 . V
Used
Reading
Deviation
ill
220 /¿F
0.4300
0.0113
2.63
100 n F
0.4240
0.0101
2.37
47 mF
0.4245
0.0155
3.66
No Filter
0.4455
0.0543
12 .19
Rec. Digital
0.4728
0.0123
2.61
Nonrec. Digital
0.4606
0.0381
8.27
HP-3497A
0.2499
0.000235
0.09
(b) Load Cell
Figure C.2 shows similar information for the load cell.
In this case, the abscise range corresponds to a load of
about 3 pounds. The results found in the study reported in
this appendix clearly indicate that the best transducer
response is obtained with the HP-3497A. These results, in
conjunction with the problems associated with the use of
capacitors in analog filters, led to the decision of
replacing the HP-6940B Multiprogrammer by the HP-3497A to
monitor all the test devices. The HP-6940B would be devoted
exclusively to control the stepper motor.

Fipure C.1 — Response of Pressure Transducer No.
OUTPUT VOLTAGE Cmv)
M M
CD CD
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19.7

i;:ure C.2 - Response of Load Cell
OUTPUT VOLTAGE (mv)
ro
CO
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(O
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esz

APPENDIX D
AUTOMATED SLURRY CONSOLIDOMETER CONTROLLING
AND MONITORING PROGRAM (SLURRY1)
SLURRY1
Flowchart
Main Program
(T777T)
254

255

256

257
CHG

258

259
End of main program

260
Listing of SLURRY1
10 REM COMPUTER-CONTROLLED SLURRY-CONSOLIDATION TEST FILE: SLURRY1
20 DIM XLOW (6) , XHIGH (6) , PROBIDS [ 80 ] , PRINTERS [ 300 ] ,LINE1$[20] ,LINE2$[20]
30 DIM SERIALNUMBERSLOW(25),EQUIPMENTNAMESLOWS(25)[30] ! hp manual p 117
40 DIM CALIBRALOW(25),UNITSLOWS(25)[15],B$[15],AS[30]
50 DIM SERIALNUMBERSHIGH(25),EQUIPMENTNAMESHIGHS(25 ) [30]
60 DIM CALIBRAHIGH(25),UNITSHIGHS(25)[15]
70 IOBUFFER PRINTERS
80 REM
90 DISP TAB (5);"What Test do you want to run?"
100 DISP TAB (5)¡"Enter CRD for Constant Rate of Deformation Test, or"
110 DISP TAB (5);" CHG for Controlled Hydraulic Gradient Test"
120 INPUT TESTS
130 IF TEST$="CRD" OR TESTS="CHG" THEN GOTO 150
140 DISP TAB (5);"ERROR ENTERING TEST TYPE!" @ GOTO 100
150 DISP TAB (5),-"Enter Problem Identification - 80 Characters Maximum"
160 INPUT PROBIDS
170 DISP TAB (5);”Name of Output File is”;
180 INPUT SLURRYOUTS
190 REM ** The DATA FILE is not created until later when the required number of records is known
**
200 DISP
210 DISP TAB (5)¡"Do you want to produce a printout";
220 DISP TAB (5)¡"Answer Y or N";
230 INPUT PRINTOUTS
240 PRINTER IS 1
250 IF FRINTOUT$="N" THEN GOTO 330
260 PRINTER IS 8,220
270 IF TESTS="CRD" THEN PRINT TAB (5);"CONSTANT RATE OF DEFORMATION TEST"
280 IF TEST$="CHG" THEN PRINT TAB (5);"CONTROLLED HYDRAULIC GRADIENT TEST"
290 PRINT TAB (5)¡"OUTPUT INFORMATION"
300 PRINT " "
310 PRINT TAB (5);"TEST IDENTIFICATION: "¡PROBIDS
320 REM
330 GOSUB CALIBRATIONS ! Read Calibration Factors of all Devices
332 IF SERIALNUMBERSLOW(5)=73169 THEN MAXLOAD=200 @ GOTO 390
334 IF SERIALNUMBERSLOW(5)=49650 THEN MAXLOAD=1000 @ GOTO 390
336 DISP "Serial number of load cell does not correspond"
337 DISP "to either 200-lb or 1000-lb load cell"
338 DISP "Program is being aborted" @ STOP
340 REM
350 REM ********************************************************************
360 REM ************************ INPUT DATA ********************************
370 REM ********************************************************************
380 REM
390 DISP TAB (5);"Initial Sample Height in (cm)";
400 INPUT HI
410 AREA—.36 ! SAMPLE AREA IN ft“2 USED FOR COMPUTING THE PPR IN CRD TEST
420 DISP TAB (5);"Initial Solids Content in (%)";
430 INPUT SI
435 DISP TAB (5);"Specific Gravity of Solids, Gs";

261
440 INPUT GS
450 EI=GS*(100/SI-l) ! INITIAL VOID RATIO
460 GAMMA—(GS+EI)/(1+EI)*62.4 ! Initial unit weight in pcf
470 WEIGHT=GAMMA*AREA*HI/30.48 ! Initial weight in pounds
480 REM
490 REM
500 IF TEST$="CHG" THEN GOTO 1230
510 REM
520 REM *********************************************************************
530
REM ****************
CONSTANT RATE OF DEFORMATION ROUTINE ***************
540
550
560
REM *********************************************************************
REM
DISP
570
DISP
"SELECT OPTION
(1-5) FOR RATE OF DEFORMATION”
580
DISP
"RATE (mm/min)
OPTION"
590
DISP
" 0.004
1"
600
DISP
" 0.008
2"
610
DISP
" 0.02
3"
620
DISP
o
o
4"
630
DISP
" 0.06
5"
640
INPUT
FACTOR
650 IF FACTOR=5 THEN FACTOR=15
660 IF FACTOR=4 THEN FACTOR-10
670 IF FACTOR=3 THEN FACTOR=5
680 RATE*.004*FACTOR ! APPROXIMATED RATE OF DEFORMATION IN mra/min
690 NMIN=120*FACTOR ! NUMBER OF STEPS PER MINUTE
700 N=INT (NMIN/120) ! NUMBER OF STEPS PER HALF A SECOND
710 DELTATIME*INT (.1*HI*10/(1+EI)/RATE) ! SUGGESTED VALUE IN MINUTES
720 DISP USING 730 j DELTATIME
730 IMAGE "SUGGESTED TIME INTERVAL BETWEEN READINGS TO PRODUCE"/"CHANGES IN VOID RATIO OF ABOUT
0.1 IS ",DD," min"
740 DISP TAB (5);"Do you want to change this value - Y or N";
750 INPUT CHANGE 1$
760 IF CHANGE1$*"N" THEN GOTO 790
770 DISP TAB (5)¡"Enter Value of Time Interval between Readings (min)"
780 INPUT DELTATIME
790 SF=35 @ EF=GS*(100/SF-l) @ DELTAH=HI*(EI-EF)/(1+EI) ! in cm
800 TMAXHR=DELTAH*10/(RATE*60)
810 DISP USING 820 ; TMAXHR
820 IMAGE "SUGGESTED DURATION OF THE TEST TO END"/"AT A SOLIDS CONTENT OF ABOUT 35% IS ",DDD.DD,"
hrs"
830 DISP TAB (5);"Do you want to change this value - Y or N";
840 INPUT CHANGE2S
850 IF CHANGE2$="N" THEN GOTO 880
860 DISP TAB (5);"Enter Duration of the Test (hrs)"
870 INPUT TMAXHR
880 TMAX=TMAXHR*60 ! DURATION OF THE TEST IN MINUTES
890 REM
900 REM ** CREATE DATA FILE ACCORDING TO No. OF READINGS TO BE TAKEN **
910 NoREADINGS=INT (TMAX/DELTATIME)+l
920 NoRECORDS=NoREADINGS+2 ! 2 EXTRA RECORDS ARE REQUIRED FOR PROBIDS, HI, SI
930 CREATE SLURRYOUTS,NoRECORDS,72

262
940 ASSIGN# 2 TO SLURRYOUTS
950 PRINT# 2 ; PROBIDS,HI,SI
960 REM
970 GOSUB INITIALIZATION ! TAKES INITIAL READINGS AND PRINTS GENERAL TEST INFORMATION AND TABLE
HEADING
980 IREAD=1 ! COUNTER FOR TAKING READINGS AT TIME = IREAD*DELTATIME
990 ISTEP=0 ! TIME KEEPER FOR STEPPING THE MOTOR EVERY HALF A SECOND
1000 SETTIME 0,0 ! INITIATES ELAPSED TIME COUNT OF THE TEST
1010 DISP
1020 DISP "TEST STARTING-
1030 REM INITIATE STEPPING OF THE MOTOR
1040 GOSUB STEPPING
1050 GOSUB RUNTIME ! COMPUTE ELAPSED TIME OF THE TEST
1060 IF ELAPSEDTIME 1070 REM TAKE READINGS OF LOW AND HIGH VOLTAGE DEVICES
1080 DISP
1090 TIMEREAD=ELAPSEDTIME
1100 DISP "TIME OF READING No.";IREAD;" = ";TIMEREAD
1110 GOSUB READLOWVOLT
1120 GOSUB READHIGHVOLT
1130 GOSUB CONVERTDATA
1140 GOSUB TESTEND ! CHECK IF TEST IS TO BE STOPPED AT THIS MOMENT
1150 IREAD=IREAD+1
1160 GOSUB RUNTIME ! COMPUTE ELAPSED TIME OF THE TEST
1170 IF ELAPSEDTIME>= ISTEP THEN GOTO 1040
1180 GOTO 1050
1190 REM
1200 REM **********************************************************************
1210 REM *************** CONTROLLED HYDRAULIC GRADIENT ROUTINE ****************
1220 REM **********************************************************************
1230 DISP TAB (5);"What is the Gradient desired in the test";
1240 INPUT DESIREDGRADIENT
1250 DISP TAB (5);”What is the allowed variation in the gradient (2)";
1260 INPUT EPSILON
1270 DISP TAB (5);"Enter Time Interval between Readings (min)"
1280 INPUT DELTATIME
1290 SF=35 @ EF=GS*(100/SF-l) @ DELTAH=HI*(EI-EF)/(1+EI) ! SAMPLE DEFORMATION NEEDED TO REACH A
FINAL SOLID CONTENT OF 352
1300 REM
1310 DISP TAB (5) ¡"Enter duration of the test (hrs)"
1320 INPUT TMAXHR
1330 TMAX=TMAXHR*60 ! DURATION OF THE TEST IN MINUTES
1340 REM ** CREATE DATA FILE ACCORDING TO THE No. OF READINGS TO BE TAKEN **
1350 NoREADINGS=INT (TMAX/DELTATIME)+l
1360 NoRECORDS=NoREADINGS+2 ! 2 EXTRA RECORDS ARE REQUIRED FOR PROBIDS, HI, SI
1370 CREATE SLURRYOUTS,NoRECORDS,72
1380 ASSIGN# 2 TO SLURRYOUTS
1390 PRINT# 2 ; PROBIDS,HI,SI
1400 GOSUB INITIALIZATION ! TAKES INITIAL READINGS AND PRINTS GRAL. INFO.
1410 IREAD=0 ! COUNTER FOR TAKING READINGS AT TIME = IREAD*DELTATIME
1420 NTOT=0 ! TOTAL NUMBER OF MOTOR-STEPS
1430 DEFORMSTEPS=0

263
1440 PREVIOUSGRADIENT=0
1450 ACTIVATEOS”"YES” @ N=2047 ! MAXIMUM NUMBER OF STEPS ALLOWED FOR THE MOTOR
1460 REM ACTIVATEOS”"YES" MEANS THE LAST GRADIENT CHANGE COMPUTED IS DUE TO
1470 REM THE STEPPING OF THE MOTOR; IF SO THE No. OF STEPS PER UNIT GRADIENT
1480 REM (SPUG) WILL BE COMPUTED AND USED FOR ESTIMATING NEXT VALUE OF N
1490 SETTIME 0,0 ! INITIATES ELAPSED TIME COUNT OF THE TEST
1500 DISP
1510 DISP "TEST STARTING"
1520 DISP " PRESSURE1 (psi) HEIGHT(cm) GRADIENT ERROR (%)”
1530 GOSUB STEPPING @ NTOT=NTOT+N ! ACTIVATES THE MOTOR N STEPS
1540 WAIT 10000
1545 IF IREAD=0 THEN WAIT 10000 ! WAIT LONGER IF GRADIENT HAS NOT BEEN REACHED
1546 ! BECAUSE LOADING GOES TOO FAST AND NEED
1547 ! TO ALLOW TIME FOR DISSIPATION OF U4
1550 CLEAR 709
1560 OUTPUT 709 ;"VR1"
1570 OUTPUT 709 ;”AI01"
1580 ENTER 709 ; X
1590 XLOW(1)=1000*X ! Reading of transducer No. 1 in mv
1600 PRESSURE1=ABS (XLOW(1)-LV10)/CALIBRALOW(1) ! POREPRESSURE AT THE BOTTOM OF THE SAMPLE
1610 OUTPUT 709 ;"AI04"
1620 ENTER 709 ; X
1630 XLOW(4)=X*1000 ! Reading of transducer No. 4 in mv
1640 REM
1650 GOSUB READHIGHVOLT
1660 DEFORMATION=ABS (XHIGH(1)-HV10)/CALIBRAHIGH(1) ! in mm
1670 HYDROPRESSURE=62.4*DEFORMATION/304.8/144
1680 PRESSURE4”(XLOW(4)-LV40)/CALIBRALOWC4)-HYDROPRESSURE
1690 IF PRESSURE4<0 THEN PRESSURE4=0
1700 ! DISP "DEFORMATION =";DEFORMATION;"mm"
1710 H=HI-DEFORMATION/10 ! SAMPLE HEIGHT IN cm
1720 GRADIENT”(PRESSURE1-PRESSURE4)*144/(H/30.48)/62.4 ! CURRENT GRADIENT
1730 IF ACTIVATEOS”"NO" THEN GOTO 1780
1740 DELTAGRAD=GRADIENT-FREVIOUSGRADIENT
1750 IF DELTAGRADo 0 THEN GOTO 1770
1760 SPUG=9999 @ GOTO 1780 ! SPUG made very large because DELTAGRAD=0
1770 SPUG=ABS (N/DELTAGRAD)
1780 GRADERROR=100*(DESIREDGRADIENT-GRADIENT)/DESIREDGRADIENT ! GRADIENT OFFSET IN %
1790 DISP USING 1800 ; PRESSURE1;PRESSURE4;H;GRADIENT;GRADERROR
1800 IMAGE 5(DDDD.DDDD)
1810 IF ABS (GRADERROR)«EPSILON THEN GOTO 1890
1820 N=SPUG*(DESIREDGRADIENT-GRADIENT) ! NEW No. OF STEPS TO APPROACH THE DESIRED GRADIENT
1830 N=INT (N) ! N CAN BE POSITIVE (FORWARD) OR NEGATIVE (BACKWARD)
1840 IF N>2047 THEN N=2047
1850 IF N<-2047 THEN N=-2047
1860 DISP "NEW No. OF STEPS IS ";N
1870 PREVIOUSGRADIENT”GRADIENT @ ACTIVATEDS="YES"
1880 GOTO 1530
1890 ACTIVATEOS”"NO"
1900 IF IREAD>0 THEN GOTO 1960
1910 PRINT USING 1920 ; TIME /60
1920 IMAGE "TIME REQUIRED TO REACH THE DESIRED GRADIENT WAS",DDD.DD," min"

264
1930 PRINT "NUMBER OF MOTOR-STEPS REQUIRED WAS";NTOT
1940 LINEC0UNTER=LINEC0UNTER+2
1950 REM
I960 GOSUB RUNTIME ! COMPUTE ELAPSED TIME OF THE TEST
1970 IF IREAD*DELTATIME<= ELAPSEDTIME THEN GOTO 1990
1980 GOTO 1540 ! TO COMPUTE AND CHECK CURRENT GRADIENT
1990 TIMEREAD=ELAPSEDTIME
2000 DISP TAB (5);"TIME OF READING No.";IREAD;" = "¡TIMEREAD
2010 GOSUB READLOWVOLT ! READ ALL LOW VOLTAGE DEVICES
2020 GOSUB READHIGHVOLT
2030 GOSUB CONVERTDATA
2040 GOSUB TESTEND
2050 IREAD=IREAD+1
2060 GOTO 1540
2070 REM
2080 REM **********************************************************************
2090 REM ******************** SUBROUTINE INITIALIZATION ***********************
2100 REM **********************************************************************
2110 INITIALIZATION: ! THIS SUBROUTINE TAKES THE INITIAL READINGS AND PRINTS
2120 REM THE GENERAL TEST INFORMATION AND TABLE HEADING
2130 REM
2140 DISP "TAKING INITIAL READINGS AND GETTING READY TO START TEST-
2150 REM
2160 GOSUB READLOWVOLT
2170 LV10=XLOW(1) ! Zero Reading of low-voltage device 2 - POREPRESSURE # 1
2180 LV20=XLOW(2) ! 3 - POREPRESSURE # 2
2190 LV30=XLOW(3) ! " " 4 - POREPRESSURE # 3
2200 LV4 0=XLOW( 4) ! 5 - POREPRESSURE # 4
2210 DISP
2220 DISP "Drain water and fill chamber with slurry"
2230 DISP "Set up LVDT and Load Cell”
2240 DISP "Press the CONT key when done to proceed with the test"
2250 PAUSE
2260 OUTPUT 709 ;"AIO0"
2270 ENTER 709 ; X
2280 LV00=1000*X ! Zero Reading for the Total Stress
2290 OUTPUT 709 ;"AI5"
2300 ENTER 709 ; X
2310 LV50=1000*X ! Zero Reading for the Load Cell
2320 REM
2330 GOSUB READHIGHVOLT
2340 HV10=XHIGH(1) ! Zero Reading for LVDT
2350 PRINT " "
2360 PRINT TAB (5);"INITIAL HEIGHT = ";HI;"cm"
2370 PRINT TAB (5)¡"INITIAL SOLIDS CONTENT = ";SI;"%"
2380 PRINT USING 2390 ; El
2390 IMAGE 4X,"INITIAL VOID RATIO = ".DD.DDD
2400 IF PRINTOUTS—"N" THEN RETURN
2410 PRINT ” ”
2420 PRINT USING 2430
2430 IMAGE 5XTRANSDUCER FOR:",7X,"T.S.",10X,"PP 1",10X,"PP 2",10X,"PP 3",10X,"PP 4",10X,"L.C.
10X,"LVDT"

265
2440 PRINT USING 2450 ; CALIBRALOW(0),CALIBRALOW(1) ,CALIBRALOW(2),CALIBRALOW(3),CALIBRALOW(4),
CALIBRALOW(5) ,CALIBRAHIGH(1)
2450 IMAGE 5X,"CALIBRATIONS7(4X,D.DDDDe)
2460 PRINT USING 2470 ; LV00,LV10,LV20,LV30,LV40,LV50,HV10
2470 IMAGE 5X,"ZERO READING7(7X,ODD.DDD)
2480 PRINT " "
2490 PRINT TAB (5);"DURATION OF THE TEST = " ;TMAXHR;"hrs","INTERVAL BETWEEN READINGS =";DELTATIME
"min"
2500 PRINT " "
2510 IF TEST$="CRD" THEN PRINT TAB (5)¡"APPROX. RATE OF DEFORMATION =";RATE;"mm/min"
2520 IF TEST$="CHG" THEN PRINT TAB (5);"AVERAGE GRADIENT KEPT AT";DESIREDGRADIENTEPSILON;
"Z"
2530 PRINT ” "
2540 LINE1$=”======== ===== =" @ LINE2S=" ”
2550 PRINT USING 2560 ; LINE1S,LINE 1$,LINE1S,LINE 1$,LINE 1$,LINElS,LINE1S
2560 IMAGE 5X, 7 (20A), "=========== ••
2570 PRINT USING 2580
2580 IMAGE 5X,"READING",5X,"TIME",13X,"LOAD",13X,"TOTAL STRESS",7X,"POREPRESSURE 1",7X,"POREP-
RESSURE 2",7X,"POREPRESSURE 3",7X,"POREPRESSURE 4",4X,"DEFORMATION"
2590 PRINT USING 2600
2600 IMAGE 7X,"No.",6X,"(min)",7X,"(mV)",6X,"(lbs)",5(6X,"(mV)",6X,"(psi)"),7X,"(mm)"
2610 PRINT USING 2620 ; LINE2S,LINE2S,LINE2S,LINE2S,LINE2S,LINE2S,LINE2S
2620 IMAGE 5X,7(20A)," "
2630 LINECOUNTER=21
2640 RETURN
2650 REM *******************************************************************
2660 REM ******************** SUBROUTINE RUNTIME ***************************
2670 REM *******************************************************************
2680 RUNTIME: ! THIS SUBROUTINE COMPUTES THE ELAPSED TIME OF TEST IN MINUTES
2690 IF DATE >0 THEN GOTO 2720
2700 ELAPSEDTIME=TIME /60
2710 RETURN
2720 ELAPSEDTIME=DATE *1440+TIME /60
2730 RETURN
2740 REM
2750 REM *******************************************************************
2760 REM ******************** SUBROUTINE STEPPING **************************
2770 REM *******************************************************************
2780 STEPPING: ! SUBROUTINE THAT ACTIVITATES THE STEPPING MOTOR TO TURN
2790 ! N STEPS
2800 C=SPOLL (723)
2810 ENTER 723 ; C
2820 NoSTEPS=N
2830 IF N<-2047 OR N>2047 THEN GOTO 2910
2840 IF N<0 THEN NoSTEPS=2048+ABS (N) ! N<0 MAKES THE MOTOR TO TURN BACKWARD
2850 NS-DTOS (NoSTEPS)
2860 A=VAL (NS)
2870 C=SPOLL (723)
2880 OUTPUT 723 ;"00040TI",A,"T" @ IF TEST$="CHG" THEN RETURN
2890 ISTEP=ISTEP+.5/60
2900 RETURN
2910 PRINT "NUMBER OF STEPS IS OUT OF RANGE"

266
2920 STOP
2930 REM
2940 REM
2950 REM *******************************************************************
2960 REM ********************** SUBROUTINE READLOWVOLT *********************
2970 REM *******************************************************************
2980 READLOWVOLT: ! THIS SUBROUTINE READS THE LOW-RANGE VOLTAGE DEVICES:
2990 REM PRESSURE TRANSDUCERS AND LOAD CELL
3000 REM USING THE HP-3497
3010 CLEAR 709
3020 OUTPUT 709 ;"VR1"
3030 OUTPUT 709 ;"AF0AL5AC0"
3040 FOR 1=0 TO 5
3050 IF I>0 THEN OUTPUT 709 ;"AS" ! MOVE TO READ NEXT CHANNEL
3060 OUTPUT 709 ;"VT3" ! CAUSES THE VOLTMETER TO TRIGGER AND TAKE A READING
3070 ENTER 709 ; X
3080 XLOW(I)=1000*X ! READING OF THE FIVE LOW-RANGE VOLTAGE DEVICES IN mv
3090 NEXT I
3100 RETURN
3110 REM
3120 REM
3130 REM **********************************************************************
3140 REM *********************** SUBROUTINE READHIGHVOLT **********************
3150 REM **********************************************************************
3160 REM
3170 READHIGHVOLT: ! THIS SUBROUTINE READS ONE HIGH-RANGE VOLTAGE DEVICE
3180 CLEAR 709
3190 OUTPUT 709 ;"VR3"
3200 OUTPUT 709 ;"AI11" ! Channel 11 is to be read
3210 ENTER 709 ; XHIGH(l)
3220 REM
3230 RETURN
3240 REM
3250 REM ******************************************************************
3260 REM **************** CONVERTDATA SUBROUTINE **************************
3270 REM ******************************************************************
3280 REM THIS SUBROUTINE CONVERTS THE VOLTAGE READINGS INTO THEIR CORRESPONDING
3290 REM PHYSICAL VALUE USING THE CALIBRATION FACTORS PROVIDED
3300 CONVERTDATA: !
3310 IF TEST$="CHG" THEN GOTO 3380
3320 GOSUB RUNTIME ! COMPUTE ELAPSED TIME OF TEST
3330 IF ELAPSEDTIMEdSTEP THEN GOTO 3380 ! IF TIME TO STEP THE MOTOR HAS BEEN
3340 GOSUB STEPPING ! REACHED GO TO SUBROUTINE STEPPING
3350 GOTO 3320
3360 REM
3370 REM ONE HIGH-VOLTAGE DEVICE IS BEING USED - LVDT
3380 DEFORMATION=ABS (XHIGH<1)-HV10)/CALIBRAHIGH(1) ! in mm
3390 DISP "DEFORMATION = DEFORMATION;"mm"
3400 H=HI-DEFORMATION/10 ! CURRENT HEIGHT IN cm
3410 e=H*(1+EI)/HI-1
3420 S=100/(l+e/GS)
3430 DISP "SOLIDS CONTENT =";S;"J"

267
3440 REM FOUR LOW-VOLTAGE DEVICES ARE BEING USED
3450 LOADCELL=(LV50-XLOW(5))/CALIBRALOW(5)
3460 DISP "LOAD (lb) = LOADCELL
3470 TOTALSTRESS=(XLOW(0)-LV00)/CALIBRALOW(0)
3480 PP1=(XLOW(1)-LV10)/CALIBRALOW(1)
3490 IF TESTS="CRD" THEN PPR=100*PP1*144/((LOADCELL+WEIGHT)/AREA)
3500 PP2=(XLOW(2)-LV20)/CALIBRALOW(2)
3510 PP3=(XLOW(3)-LV30)/CALIBRALOW(3)
3520 HYDROPRESSURE=62.4*DEFORMATION/304.8/144 ! ADDITIONAL HYDROSTATIC PRESSURE FOR TRANSDUCER No
4 IN psi
3530 PP4=(XLOW(4)-LV40)/CALIBRALOW(4)-HYDROPRESSURE
3540 IF PP4<0 THEN PP4=0
3550 DISP "TOTAL STRESS (psi) =";TOTALSTRESS
3560 DISP
3570 DISP "PWP # 4 —";PP4
3580 DISP "PWP # 3 =";PP3
3590 DISP "PWP it 2 =";PP2
3600 DISP "PWP # 1 =”; PP1
3610 DISP
3620 IF TEST$="CRD" THEN DISP "PORE PRESSURE RATIO =";PPR;"%"
3630 REM
3640 PRINT# 2 ; IREAD,TIMEREAD,LOADCELL,TOTALSTRESS,PP1,PP2,PP3,PP4,DEFORMATION
3650 IF PRINTOUTS="N” THEN GOTO 3750
3660 IF LINECOUNTER<60 THEN GOTO 3720
3670 PRINT USING 2560 ; LINE IS,LINE 1$,LINE1S,LINElS,LINElS,LINE IS,LINE1S
3680 PRINT USING 2580
3690 PRINT USING 2600
3700 PRINT USING 2620 ; LINE2S,LINE2S,LINE2S,LINE2S,LINE2S,LINE2S,LINE2S
3710 LINECOUNTER=4
3720 OUTPUT PRINTERS USING 3730 ; IREAD,TIMEREAD,XLOW(5),LOADCELL,XLOW(0),TOTALSTRESS,XLOW<1),PP1-
,XLOW(2),PP2,XLOW(3),PP3,XLOW(4),PP4,DEFORMATION
3730 IMAGE #,5X,4D,4X,DDDDD.DD,5X,DDD.DDD,3X,DDD.DDD,5(4X,DDD.DDD,3X,DD.DDDD),5X,DDD.DDDD
3740 TRANSFER PRINTERS TO 8 INTR g LINECOUNTER=LINECOUNTER+l
3750 RETURN
3760 REM
3770 REM *********************************************************************
3780 REM ********************* TESTEND SUBROUTINE ****************************
3790 REM *********************************************************************
3800 TESTEND: ! THIS SUBROUTINE DECIDES WHEN TO STOP THE TEST FOR A VARIETY OF
3810 REM REASONS
3820 REM
3830 TESTEND: ! THIS SUBROUTINE DECIDES WHEN TO STOP THE TEST FOR A VARIETY OF
3840 REM REASONS
3850 REM CHECK FOR TMAX
3860 IF TIMEREAD>TMAX THEN GOTO 4000
3870 REM
3880 REM CHECK FOR MAXIMUM LOAD
3890 IF LOADCELL>MAXLOAD THEN GOTO 4010
3900 REM
3910 REM CHECK FOR MAXIMUM PRESSURE IN TRANSDUCER No. 1 (1 bar RANGE)
3920 IF PP1>15 THEN GOTO 4020
3930 REM

268
3940 REM CHECK FOR MAXIMUM PRESSURE IN TRANSDUCER No. 4 (5 psi RANGE)
3950 IF PP4>5 THEN GOTO 4030
3960 REM
3970 REM CHECK FOR MAXIMUM DEFORMATION
3980 IF DEFORMATION>DELTAH*10 THEN GOTO 4040
3990 RETURN
4000 PRINT TAB (5)¡"NORMAL TERMINATION - MAXIMUM TIME OF TEST REACHED" @ GOTO 4050
4010 PRINT TAB (5);"ABNORMAL TERMINATION - MAXIMUM ALLOWABLE LOAD EXCEEDED" @ GOTO 4050
4020 PRINT TAB (5);"ABNORMAL TERMINATION - TRANSDUCER # 1 EXCEEDED MAX PRESSURE" @ GOTO 4050
4030 PRINT TAB (5);"ABNORMAL TERMINATION - TRANSDUCER # 4 EXCEEDED MAX PRESSURE" @ GOTO 4050
4040 PRINT TAB (5)¡"NORMAL TERMINATION - DEFORMATION CORRESPONDING TO A SOLIDS CONTENT OF 35% WAS
EXCEEDED” @ GOTO 4050
4050 ASSIGN# 2 TO *
4060 STOP
4070 END
4080 REM ********************************************************************
4090 CALIBRATIONS:
4100 ASSIGN# 1 TO "CALIBRATIO:D700"
4110 NoLOWDEVICES=6 ! Test is using 6 low-voltage (mV) devices
4120 FOR 1=0 TO NoLOWDEVICES-1
4130 READ# 1 ; SERIALNUMBERSLOW(I),EQUIPMENTNAMESLOWS(I)
4140 READ# 1 ; CALIBRALOW(I),UNITSLOWS(I)
4150 NEXT I
4160 READ# 1 ; SERIALNUMBERSHIGH(1),EQUIPMENTNAMESHIGHS(1),CALIBRAHIGH(1),UNITSHIGHS(1)
4170 GOSUB CALDISPLAY ! Display on screen calibration information
4180 DISP
4190 DISP TAB (5) ¡"Do you want to change any calibration?"
4200 DISP TAB (5)¡"Answer Y or N"
4210 INPUT REVIEWS
4220 IF REVIEW$="Y" THEN GOTO 4250
4230 ASSIGN# 1 TO *
4240 RETURN
4250 DISP TAB (5)¡"Input Index (0,1,...) of Low-Voltage Device to modify, or"
4260 DISP TAB (5);"Input -1 if LVDT Calibration is to be modified, or"
4270 DISP TAB (5);"Input "¡NoLOWDEVICES;” if adding a Low-Voltage Device"
4280 INPUT CODE
4290 IF CODE>-1 THEN GOTO 4370
4300 DISP "Input new LVDT Serial Number"
4310 INPUT SERIALNUMBERSHIGH(1)
4320 DISP "Input new LVDT name" @ INPUT EQUIPMENTNAMESHIGHS(1)
4330 DISP TAB (5)¡"Input new LVDT Calibration in Volts/mm"
4340 INPUT CALIBRAHIGH(1)
4350 GOSUB CALSTORAGE
4360 GOTO 4170
4370 DISP TAB (5);"Device No. "¡CODE
4380 DISP TAB (5)¡"Input the new serial number"
4390 INPUT SERIALNUMBERSLOW(CODE)
4400 DISP
4410 DISP TAB (5);"Input the name of the Equipment in 30 characters or less"
4420 DISP TAB (5)¡"or press RETURN if unchanged"
4430 INPUT AS
4440 IF A$="" THEN GOTO 4470

269
A450 EQUIPMENTNAMESLOWS(CODE)=AS
4460 REM
4470 DISP
4480 DISP TAB (5)¡"Input the Calibration Factor”
4490 INPUT CALIBRALOW(CODE)
4500 DISP
4510 DISP TAB (5)¡"Input the units for the calibration factor in 15 characters or less"
4520 DISP TAB (5)¡"or press RETURN if unchanged"
4530 INPUT B$
4540 IF B$="" THEN GOTO 4570
4550 UNITSLOWS(CODE)=B$
4560 IF BS="" THEN GOTO 4570
4570 IF CODE=NoLOWDEVICES THEN NoLOWDEVICES=CODE+l
4580 GOSUB CALSTORAGE
4590 GOTO 4170
4600 REM *********************************************************************
4610 CALSTORAGE:
4620 ASSIGN# 1 TO "CALIBRATIO:D700"
4630 FOR 1=0 TO NoLOWDEVICES-1
4640 PRINT# 1 ; SERIALNUMBERSLOW(I),EQUIPMENTNAMESLOWS(I)
4650 PRINT# 1 ; CALIBRALOW(I),UNITSLOWS(I)
4660 NEXT I
4670 PRINT# 1 ; SERIALNUMBERSHIGH(1),EQUIPMENTNAMESHIGHS(1)
4680 PRINT# 1 ; CALIBRAHIGH(1),UNITSHIGHS(1)
4690 RETURN
4700 REM
4710 REM **********************************************************************
4720 CALDISPLAY:
4730 DISP TAB (4);"Calibration Information"
4740 DISP TAB (4);"Index";TAB (12);"S/N";TAB (22);"Name of Equipment";TAB (52);"Calibration
Factor"
4750 DISP TAB (4);" "¡TAB (12);" "¡TAB (22);" "¡TAB (52);"
4760 FOR 1=0 TO NoLOWDEVICES-1
4770 DISP TAB (4);I;TAB (12);SERIALNUMBERSLOW(I);TAB (22);EQUIPMENTNAMESLOWS(I);TAB (52);CALIBRA¬
LOW (I);TAB (62);UNITSLOWS(I)
4780 NEXT I
4790 DISP TAB (4);"10";TAB (12);SERIALNUMBERSHIGH(1);TAB (22);EQUIPMENTNAMESHIGHS(1);TAB (52);-
CALIBRAHIGH(1);TAB (62);UNITSHIGHS(1)
4800 RETURN

APPENDIX E
AUTOMATED SLURRY CONSOLIDOMETER
DATA REDUCTION PROGRAM (SLURRY2)
10 REM DATA REDUCTION PROGRAM FOR CONSTANT RATE OF DEFORMATION TEST DATA
20 DIM EFFSTRESSPSF(500),VOIDRATIO(500),PERMEABILITY(500),PERMFTDAY(500),X(500),Y(500),K(500),EFF
STRESSKGCM2(500),U(4),H(4),Z(4),ES(4)
30 DIM PROBIDSI80],LINE1$[20],LINE2$[20]
34 MASS STORAGE IS ":D701"
35 DISP "PLACE DISK WITH DATA IN DRIVE D701 (RIGHT HAND SIDE) AND"
40 DISP "ENTER NAME OF THE INPUT DATA FILE";
50 INPUT CRDATAS
60 ASSIGN# 1 TO CRDATAS
70 DISP "NUMBER OF DATA POINTS IS";
80 INPUT N
81 DISP @ DISP "THE OUTPUT DATA FILE WILL BE DENOTED ";CRDATAS;"R"
83 CRDOUTPUT$=CRDATA$&"R"
84 NoRECORDS=N+l
85 CREATE CRDOUTPUTS,NoRECORDS,24
86 ASSIGN# 2 TO CRDOUTPUTS
87 PRINT# 2 ; N
90 PRINTER IS 1
100 DISP "Do you want to produce a printout ?"
110 DISP "Answer Y or N"
120 INPUT PRINTERS
130 IF PRINTER$="Y" THEN PRINTER IS 8,220
140 READ# 1 ; PROBIDS,HI,SI
150 DISP "DO YOU WANT TO CHANGE THE INITIAL SOLIDS CONTENT ?"
160 DISP "Answer Y or N"
170 INPUT YN$
180 IF YN$="N" THEN GOTO 205
190 DISP "ENTER CORRECT VALUE OF Si"
200 INPUT SI
205 DISP "Enter Estimated Piston Friction in lbs"
206 INPUT FRICTION
207 DISP "Enter Specific Gravity of Solids Gs”
208 INPUT GS
210 PRINT "SLURRY CONSOLIDATION TEST * DATA REDUCTION"
220 PRINT PROBIDS
230 PRINT " "
250 EI=GS*(100/SI-l) ! INITIAL VOID RATIO
260 GAMMA»62.4*(GS+EI)/(1+EI) ! INITIAL UNIT WEIGHT IN pcf
270 AREA».36 ! SAMPLE AREA IN ft~2
280 WEIGHT=GAMMA*AREA*HI/30.48 ! SAMPLE WEIGHT IN lbs
290 ! TOTALPP=GAMMA*HI/30.48/144 ! TOTAL PORE PRESSURE AT THE BOTTOM IN psi
300 ! HYDROPP=62.4*HI/30.48/144 ! HYDROSTATIC PORE PRESSURE AT THE BOTTOM IN psi
310 ! EXCESSPP=TOTALPP-HYDROPP ! EXCESS PORE PRESSURE AT THE BOTTOM IN psi
270

271
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
â–  "s'
600
610
20X,
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760
770
780
790
800
810
PRINT "SAMPLE GENERAL INFORMATION"
PRINT "INITIAL HEIGHT (cm) =";HI
PRINT "INITIAL SOLIDS CONTENT =";SI;" %"
PRINT USING 360 ; El
IMAGE "INITIAL VOID RATIO = ”,DD.DDD
PRINT " "
PRINT USING 390 ; GAMMA
IMAGE "INITIAL UNIT WEIGHT (pcf) =",DD.DD
PRINT USING 410 ; WEIGHT
IMAGE "SAMPLE TOTAL WEIGHT (lbs) =",DD.DD
PRINT "SAMPLE AREA (ft~2) =";AREA
PRINT "ESTIMATED PISTON FRICTION (lbs) =";FRICTION
PRINT "CONDITIONS AT THE BOTTOM OF THE SAMPLE BEFORE LOADING"
PRINT USING 450 ; TOTALPP
IMAGE "TOTAL POREPRESSURE (psi) =",DD.DDD
PRINT USING 470 ; HYDROPP
IMAGE "HYDROSTATIC POREPRESSURE (psi) =",DD.DDD
PRINT USING 490 ; EXCESSPP
IMAGE "EXCESS POREPRESSURE (psi) =”,DD.DDD
PRINT " "
REM **************** DATA REDUCTION ROUTINE ***************************
IF PRINTER$="N" THEN GOTO 650
LINE1$="========== = ="
LINE2S=" "
PRINT USING 570 ; LINElS,LINElS,LINElS,LINElS,LINElS,LINElS,LINE1S,LINElS
IMAGE 8(20A),"==="
PRINT USING 590
IMAGE "READING TIME",6X,"LOAD STRESS",5X,"DEFORMATION HEIGHT",9X,"EFFECTIVE STRESS",14X-
,14X,"S",11X,"i",13X,"PERMEABILITY"
PRINT USING 610
IMAGE 2X,"No.",5X,"(min)",8X,"(psi)",11X,"(mm)",10X,"(cm)",9X,"(psi)",10X,"(psf)",24X,"(%)",-
"(cm/sec)",7X,"(ft/day)"
PRINT USING 630 ; LINE2S,LINE2S,LINE2S,LINE2$,LINE2S,LINE2S,LINE2S,LINE2S
IMAGE 8(20A)," "
COUNTER=16
OLDTIME=0
OLDHT=HI
OLDGRAD=0
H(l)=1.235 @ H(2)=6.235 @ H(3)=11.235 ! Elevation of transducers in cm - H(4)=H
FOR 1=1 TO N
READ# 1 ; IREAD,TIMEREAD,LOADCELL,TOTALSTRESS,U(1),U(2),U(3),U(4).DEFORMATION
H=HI-DEFORMATION/10 ! HEIGHT IN cm
H(4 )=H
LOADSTRESS=(LOADCELL-FRICTION)/AREA/144 ! in psi
VOIDRATIO(I)=H*(1+EI)/HI-1 ! Avg. void ratio corresponding to height H
S=100/(1+VOIDRATIO(I)/GS) ! Avg. Solids Content in %
EE=.014217*(GS“1)/(1+VOIDRATIO(I))
FOR J=1 TO 4
Z(J)=H-H(J)
BUOYANTSTRESS=EE*Z(J) ! in psi
ES(J)=LOADSTRESS+BUOYANTSTRESS-U(J) ! Eff. Stress at each point
IF LOADSTRESS
272
815 IF TOTALSTRESS<0 THEN TOTALSTRESS=0
820 ES(J)=ES(J)-(LOADSTRESS-TOTALSTRESS)*Z(J)/H ! Reduction for side friction
825 IF ES(J)<0 THEN ES(J)=0
830 NEXT J
840 IF Z(3)<0 THEN GOTO 870 ! DOES NOT INCLUDE TRANSD. No. 3
850 ESAVG=(H(l)*ES(l)+2.5*(ES(l)+2*ES(2)+ES(3))+Z(3)*(ES(3)+ES(4))/2)/H ! 4 TRANSDUCERS
860 GOTO 880
870 IF Z(2)<0 THEN GOTO 878 ! DOES NOT INCLUDE TRANSD. No. 2
875 ESAVG=(H(l)*ES(l)+2.5*(ES(l)+ES(2))+Z(2)*(ES(2)+ES(4))/2)/H ! 3 TRANSDUCERS
876 GOTO 880
878 ESAVG”(H(l)*ES(l)+Z(l)*(ES(l)+ES(4))/2)/H ! 2 TRANSDUCERS
880 EFFSTRESSPSI=ESAVG ! Avg. Effective Stress in psi
890 EFFSTRESSKGCM2(I)=EFFSTRESSPSI/14.19352
900 EFFSTRESSPSF(I)“EFFSTRESSPSI*144
910 GRADIENT3(U(1)-U(4))* 144/(H/30.48)/62.4 ! Avg. Gradient across the sample
920 AVGGRADIENT3(GRADIENT+OLDGRAD)/2 ! Time average
930 AVGSOLVELOCITY3(OLDHT-H)/((TIMEREAD-OLDTIME)*60)/2
940 PERMEABILITY (I )=AVGSOLVELOCITY/AVGGRADIENT ! cm/sec BASED ON AVERAGE VALUES
950 PERMFTDAY(I)“PERMEABILITY(I)*86400/30.48 ! k in ft/day
960 OLDHT=H
970 OLDTIME=TIMEREAD
980 OLDGRAD=GRADIENT
990 IF PRINTERS=”N" THEN GOTO 1086
1000 IF COUNTER<60 THEN GOTO 1060
1010 PRINT USING 570 ; LINElS,LINElS,LINElS,LINE IS,LINE 1$,LINElS,LINElS,LINE1S
1020 PRINT USING 590
1030 PRINT USING 610
1040 PRINT USING 630 ; LINE2S,LINE2S,LINE2S,LINE2S,LINE2S,LINE2S,LINE2S,LINE2S
1050 COUNTER-4
1060 PRINT USING 1080 ; IREAD , TIMEREAD , LOADSTRESS , DEFORMATION , H , EFFSTRESSPSI, EFFSTRESSPSF (I-
VOIDRATIO(I),S,GRADIENT,PERMEABILITY(I),PERMFTDAY(I)
1070 COUNTER=COUNTER+l
1080 IMAGE DDDD,5X.DDDDD.D,4X.DDD.DDD,8X,DDD.DDD,10X,DD.DD,7X,D.DDDe,6X,D.DDDe,8X,DD.DDD,7X,-
DD.DDD,6X,DD.DDD,6X,D.DDDe,6X,D.DDDe
1084 REM STORES VOID RATIO, EFF. STRESS, AND PERMEABILITY IN REDUCED DATA FILE
1086 PRINT# 2 ; VOIDRATIO(I),EFFSTRESSPSF(I),PERMFTDAY(I)
1090 NEXT I
1100 ASSIGN# 1 TO * ! CLOSES COMMUNICATION TO INPUT DATA FILE
1105 ASSIGN# 2 TO * ! CLOSES COMMUNICATION TO OUTPUT DATA FILE
1106 MASS STORAGE IS ":D700" ! REASSIGN DEFAULT DRIVE
1110 REM
1120 DISP "NUMBER OF INITIAL POINTS TO EXCLUDE FROM REGRESSION";
1130 INPUT NI
1140 PRINT " "
1150 PRINT "(k-e) and (p-e) curves generated for points";NI+1;"to";N
1160 REM
1170 NN=N-NI
1180 FOR I-NI+l TO N
1190 Y(I-NI)=LGT (VOIDRATIO(I))
1200 X(I-NI)=LGT (EFFSTRESSPSF(I))
1210 NEXT I
1220 GOSUB REGRESSION

273
1230 A=10~ALFA
1240 B=BETA
1250 R1=R
1260 REM
1270 FOR I=NI+1 TO N
1280 Y(I-NI)=LGT (PERMFTDAY(I))
1290 X(I-NI)=LGT (VOIDRATIO(I))
1300 NEXT I
1310 GOSUB REGRESSION
1320 C=10'ALFA
1330 D=BETA
1340 R2=R
1350 PRINT " "
1360 PRINT USING 1370 ; A,B,R1
1370 IMAGE "COMPRESSIBILITY PARAMETERS"/"A = ",DDD.DDD,10X,"B = ",DDD.ODD/"r = ",DD.DDD
1380 PRINT USING 1390 ; C,D,R2
1390 IMAGE /"PERMEABILITY PARAMETERS"/"C - ",D.DDDe,10X,”D = ",DDD.DDD/"r = ",DD.DDD
1400 GOTO 1590
1410 REGRESSION:
1420 SUMX=0 @ SUMY=0 @ SUMX2=0 @ SUMY2=0 @ SUMXY=0
1430 FOR 1=1 TO NN
1440 SUMX=SUMX+X(I)
1450 SUMY=SUMY+Y(I)
1460 SUMX2=SUMX2+X(I)*2
1470 SUMY2=SUMY2+Y(I)*2
1480 SUMXY=SUMXY+X(I)*Y(I)
1490 NEXT I
1500 XAVG=SUMX/NN
1510 YAVG=SUMY/NN
1520 BETA=(NN*SUMXY-SUMX*SUMY)/(NN*SUMX2-SUMX*2)
1530 ALFA=YAVG-BETA*XAVG
1540 REM
1550 SXX=SUMX2-SUMX“2/NN
1560 SYY=SUMY2-SUMY*2/NN
1570 R=BETA*(SXX/SYY)" . 5
1580 RETURN
1590 DISP
1600 DISP "PRESS THE *CONT* KEY TO PROCEED WITH PLOTTING ROUTINE"
1610 DISP "AND PRESS IT AGAIN AFTER EACH PLOT IS DONE"
1620 PAUSE
1630 VOIDRATIO(0)=EI
1640 REM *********************** PLOTTING ROUTINE *****************************
1650 REM ***** PLOT OF VOID RATIO VS. LOG PERMEABILITY (cm/sec) or (ft/day)****
1660 DISP "Do you want to plot e-LOG k (cm/sec) - Y or N";
1670 INPUT PLOT1S
1680 DISP "Do you want to plot e-LOG k (ft/day) - Y or N";
1690 INPUT PLOT2S
1700 DISP "Do you want to plot e-LOG p (psf) - Y or N";
1710 INPUT PLOT3S
1720 DISP "Do you want to plot LOG k (ft/day)-LOG e - Y or N";
1730 INPUT PLOT4$
1740 DISP "Do you want to plot LOG e-LOG p (psf) - Y or N";

274
1750 INPUT PLOT5S
1760 IF PL0T1$="N" THEN GOTO 1840
1770 FOR I=NI+1 TO N
1780 K(I)“PERMEABILITY(I)
1790 NEXT I
1800 NUMPLOTS=l
1810 GOTO 1890
1820 PAUSE
1830 GCLEAR g CLEAR
1840 IF PL0T2$="N” THEN GOTO 2670
1850 FOR I=NI+1 TO N
1860 K(I)=PERMFTDAY(I)
1870 NEXT I
1880 NUMPLOTS=2
1890 GCLEAR
1900 CLEAR
1910 DISP "CRT (C) OR PLOTTER (P) OUTPUT";
1920 INPUT OUTPTS
1930 ZZ=1
1940 IF OUTPT$="P" THEN ZZ=705
1950 PLOTTER IS ZZ
1960 EMAX=INT (VOIDRATIO(NI+1)+1) ! MAX. VOID RADIO FOR SCALE OF Y AXIS
1970 EMIN=INT (VOIDRATIO(N)) ! MIN. VOID RATIO FOR Y-AXIS SCALE
1980 KMAX=INT (LGT (K(NI+1))+1) ! MAX. PERMEABILITY FOR X-AXIS SCALE
1990 KMIN=INT (LGT (K(N))) ! MIN. PERMEABILITY FOR X-AXIS SCALE
2000 LOCATE 15,125,20,80
2010 SCALE KMIN,KMAX,EMIN,EMAX
2020 CSIZE 4
2030 FRAME
2040 LORG 4
2050 MOVE (KMIN+KMAX)/2,EMAX+(EMAX-EMIN)/15
2060 LABEL PROBIDS
2070 CSIZE 3
2080 LORG 5
2090 MOVE KMIN+(KMAX-KMIN)/4,EMAX+(EMAX-EMIN)/30
2100 LABEL "Hi =",HI,”cm"
2110 MOVE (KMIN+KMAX)/2,EMAX+(EMAX-EMIN)/30
2120 LABEL "Si =",SI,"%"
2130 MOVE KMIN+(KMAX-KMIN)A.75,EMAX+(EMAX-EMIN)/30
2140 LABEL USING 2150 ; El
2150 IMAGE "ei = ",DD.DD
2160 FOR J=1 TO KMAX-KMIN+1
2170 FOR K=2 TO 10
2180 X=LGT (lO*(J+KMIN-1)*K)
2190 PLOT X,EMAX
2200 PLOT X,EMIN,0
2210 NEXT K
2220 LORG 5
2230 MOVE J+KMIN-1,EMIN-(EMAX-EMIN)/30
2240 CSIZE 3
2250 LABEL "10"
2260 MOVE J+KMIN-1+(KMAX-KMIN)/60,EMIN-(EMAX-EMIN)/30

275
2270 Z=J+KMIN-1
2280 ZZ$=VAL$ (Z)
2290 LORG 1
2300 CSIZE 2
2310 LABEL ZZ$
2320 NEXT J
2330 MOVE (KMIN+KMAX)/2,EMIN-(EMAX-EMIN)/10
2340 LORG 6
2350 CSIZE 4
2360 IF NUMPLOTS=l THEN LABEL "COEFFICIENT OF PERMEABILITY (cm/sec)”
2370 IF NUMPLOTS—2 THEN LABEL "COEFFICIENT OF PERMEABILITY (ft/day)"
2380 YINCR=(EMAX-EMIN)/10
2390 LORG 8
2400 FOR K=EMIN TO EMAX STEP YINCR
2410 MOVE KMIN,K
2420 DRAW KMAX.K
2430 MOVE KMIN-(KMAX-KMIN) /40 ,K
2440 KK$=VAL$ (K)
2450 CSIZE 3
2460 LABEL KK$
2470 NEXT K
2480 MOVE KMIN-(KMAX-KMIN)/10,(EMAX+EMIN)/2
2490 LDIR 0,1
2500 LORG 4
2510 CSIZE 4
2520 LABEL "VOID RATIO"
2530 LDIR -1,0
2540 LORG 5
2550 FOR I-NI+1 TO N
2560 X=LGT (K(I))
2570 IF X>KMAX THEN GOTO 2600
2580 MOVE X,(VOIDRATIO(I)+VOIDRATIO 2590 LABEL "+"
2600 NEXT I
2610 IF NUMPLOTS=2 THEN GOTO 2630
2620 GOTO 1820
2630 PEN 0
2640 PAUSE
2650 GCLEAR @ CLEAR
2660 REM ********* PLOT OF VOID RATIO VS. LOG EFFECTIVE STRESS (psf) **********
2670 IF PLOT3S="N” THEN GOTO 3380
2680 GCLEAR
2690 CLEAR
2700 DISP "CRT (C) OR PLOTTER (P) OUTPUT";
2710 INPUT OUTPTS
2720 ZZ=1
2730 IF OUTPT$-"P" THEN ZZ=705
2740 PLOTTER IS ZZ
2750 LOCATE 15,125,20,80
2760 XMIN=INT (LGT (EFFSTRESSPSF(NI+1)))
2770 XMAX=INT (LGT (EFFSTRESSPSF(N))+l)
2780 EMAX=INT (VOIDRATIO(NI+1)+l)

276
2790 EMIN=INT (VOIDRATIO(N))
2800 SCALE XMIN,XMAX,EMIN,EMAX
2810 CSIZE 4
2820 FRAME
2830 LORG 4
2840 MOVE (XMIN+XMAX)/2,EMAX+(EMAX-EMIN)/15
2850 LABEL PROBIDS
2860 CSIZE 3
2870 LORG 5
2880 MOVE XMIN+(XMAX-XMIN)/4,EMAX+(EMAX-EMIN)/30
2890 LABEL "Hi =",HI,"cm"
2900 MOVE XMIN+(XMAX-XMIN)/2,EMAX+(EMAX-EMIN) / 30
2910 LABEL "Si =",SI,"Z"
2920 MOVE XMIN+.75*(XMAX-XMIN),EMAX+(EMAX-EMIN)/30
2930 LABEL USING 2940 ; El
2940 IMAGE "ei = ",DD.DD
2950 FOR J=1 TO XMAX-XMIN+1
2960 FOR K=2 TO 10
2970 X=LGT (10*(J+XMIN-1)*K)
2980 PLOT X,EMAX
2990 PLOT X,EMIN,0
3000 NEXT K
3010 LORG 5
3020 MOVE J+XMIN-1,EMIN-(EMAX-EMIN)/30
3030 CSIZE 3
3040 Z-10*(J+XMIN-1)
3050 ZZ$=VAL$ (Z)
3060 LABEL ZZS
3070 NEXT J
3080 MOVE (XMAX+XMIN)/2,EMIN-(EMAX-EMIN)/10
3090 LORG 6
3100 CSIZE 4
3110 LABEL "EFFECTIVE STRESS (psf)"
3120 YINCR=(EMAX-EMIN)/10
3130 LORG 8
3140 FOR K=EMIN TO EMAX STEP YINCR
3150 MOVE XMIN,K
3160 DRAW XMAX,K
3170 MOVE XMIN-(XMAX-XMIN)/40,K
3180 KK$=VAL$ (K)
3190 CSIZE 3
3200 LABEL KK$
3210 NEXT K
3220 MOVE XMIN-(XMAX-XMIN)/10,(EMAX+EMIN)/2
3230 LDIR 0,1
3240 LORG 4
3250 CSIZE 4
3260 LABEL "VOID RATIO"
3270 LDIR -1,0
3280 LORG 5
3290 FOR I=NI+1 TO N
3300 X=LGT (EFFSTRESSPSF(I))

277
3310
3320
3330
3340
3350
3360
3370
3380
3390
3400
3410
3420
3430
3440
3450
3460
3470
3480
3490
3500
3510
3520
3530
3540
3550
3560
3570
3580
3590
3600
3610
3620
3630
3640
3650
3660
3670
3680
3690
3700
3710
3720
3730
3740
3750
3760
3770
3780
3790
3800
3810
3820
IF X MOVE X,VOIDRATIO(I)
LABEL "+"
NEXT I
PEN 0
PAUSE
GOLEAR @ CLEAR
REM ******************* PLOT OF LOG k (ft/day) vs.LOG e *****************
IF PLOT4$="N” THEN GOTO 4210
FOR I-NI+1 TO N
K(I )“PERMFTDAY(I)
NEXT I
GOLEAR
CLEAR
DISP "CRT (C) OR PLOTTER (P) OUTPUT";
INPUT OUTPTS
ZZ“1
IF OUTPT$="P” THEN ZZ=705
PLOTTER IS ZZ
EMAX=INT (LGT (VOIDRATIO(NI+l))+l) ! MAX. VOID RATIO FOR X-AXIS SCALE
EMIN=INT (LGT (VOIDRATIO(N))) ! MIN.
KMAX=INT (LGT (PERMFTDAY(NI+1))+l) ! MAX PERMEABILITY FOR Y-AXIS SCALE
KMIN=INT (LGT (PERMFTDAY(N))) ! MIN. PERMEABILITY FOR Y-AXIS SCALE
LOCATE 15,125,20,80
SCALE EMIN,EMAX,KMIN,KMAX
CSIZE 4
FRAME
LORG 4
MOVE (EMIN+EMAX)/2,KMAX+(KMAX-KMIN)/15
LABEL PROBIDS
CSIZE 3
LORG 5
MOVE EMIN+(EMAX-EMIN) /4 , KMAX+ (KMAX-KMIN) /30
LABEL "Hi =",HI,"cm"
MOVE (EMIN+EMAX)/2,KMAX+(KMAX-KMIN)/30
LABEL "Si =",SI,"%"
MOVE EMIN+(EMAX-EMIN)*.75,KMAX+(KMAX-KMIN)/30
LABEL USING 2150 ; El
IMAGE "ei = ",DD.DD
FOR J=1 TO EMAX-EMIN+1
FOR K=2 TO 10
X=LGT (10*(J+EMIN-1)*K)
PLOT X,KMAX
PLOT X,KMIN,0
NEXT K
LORG 5
MOVE J+EMIN-1,KMIN-(KMAX-KMIN)/30
CSIZE 3
Z=10“(J+EMIN-1)
ZZS-VALS (Z)
LABEL ZZS
NEXT J

278
3830 MOVE (EMIN+EMAX)/2,KMIN-(KMAX-KMIN)/10
3840 LORG 6
3850 CSIZE 4
3860 LABEL "VOID RATIO"
3870 FOR J=1 TO KMAX-KMIN+1
3880 FOR K=2 TO 10
3890 X=LGT (10*(J+KMIN-1)*K)
3900 MOVE EMIN,X
3910 DRAW EMAX.X
3920 NEXT K
3930 LORG 5
3940 MOVE EMIN-(EMAX-EMIN)/20,J+KMIN-1
3950 CSIZE 3
3960 LABEL ”10"
3970 MOVE EMIN-(EMAX-EMIN)/30,J+KMIN-1+(KMAX-KMIN)/60
3980 Z=J+KMIN-1
3990 ZZ$=VAL$ (Z)
4000 LORG 1
4010 CSIZE 2
4020 LABEL ZZS
4030 NEXT J
4040 MOVE EMIN- (EMAX-EMIN ) / 10 , (KMAX+KMIN ) /2
4050 LDIR 0,1
4060 LORG 4
4070 CSIZE 4
4080 LABEL "k (ft/day)"
4090 LDIR -1,0
4100 LORG 5
4110 FOR I=NI+1 TO N
4120 Y=LGT (PERMFTDAY(I))
4130 IF Y>KMAX THEN GOTO 4160
4140 MOVE LGT ((VOIDRATIO(Il+VOIDRATIO(I-1))/2),Y
4150 LABEL
4160 NEXT I
4170 FEN 0
4180 PAUSE
4190 IF PLOT5$="N" THEN GOTO 4950
4200 REM ******* PLOT OF LOG VOID RATIO VS. LOG EFFECTIVE STRESS (psf) *******
4210 IF PLOT5$="N” THEN GOTO 4950
4220 GCLEAR
4230 CLEAR
4240 DISP "CRT (C) OR PLOTTER (P) OUTPUT";
4250 INPUT OUTPTS
4260 ZZ=1
4270 IF OUTPT$="P" THEN ZZ=705
4280 PLOTTER IS ZZ
4290 LOCATE 15,125,20,80
4300 XMIN—INT (LGT (EFFSTRESSPSF(NI+1)))
4310 XMAX=INT (LGT (EFFSTRESSPSF(N) ) + l)
4320 EMAX=INT (LGT (VOIDRATIO(NI+l))+l) ! MAX. VOID RATIO FOR Y-AXIS SCALE
4330 EMIN=INT (LGT (VOIDRATIO(N))) ! MIN.
4340 SCALE XMIN,XMAX,EMIN,EMAX

279
4350 CSIZE 4
4360 FRAME
4370 LORG 4
4380 MOVE (XMIN+XMAX)/2,EMAX+(EMAX-EMIN)/15
4390 LABEL PROBIDS
4400 CSIZE 3
4410 LORG 5
4420 MOVE XMIN+(XMAX-XMIN)/4,EMAX+(EMAX-EMIN) /30
4430 LABEL "Hi =",HI,"cm"
4440 MOVE XMIN+(XMAX-XMIN) / 2,EMAX+(EMAX-EMIN)/30
4450 LABEL "Si =",SI,"Z"
4460 MOVE XMIN+.75*(XMAX-XMIN),EMAX+(EMAX-EMIN)/30
4470 LABEL USING 2940 ; El
4480 IMAGE "ei = ",DD.DD
4490 FOR J=1 TO XMAX-XMIN+1
4500 FOR K=2 TO 10
4510 X=LGT (10*(J+XMIN-1)*K)
4520 PLOT X.EMAX
4530 PLOT X,EMIN,0
4540 NEXT K
4550 LORG 5
4560 MOVE J+XMIN-1,EMIN-(EMAX-EMIN)/30
4570 CSIZE 3
4580 Z=10*(J+XMIN-1)
4590 ZZS=VAL$ (Z)
4600 LABEL ZZS
4610 NEXT J
4620 MOVE (XMAX+XMIN)/2,EMIN-(EMAX-EMIN)/10
4630 LORG 6
4640 CSIZE 4
4650 LABEL "EFFECTIVE STRESS (psf)"
4660 FOR J=1 TO EMAX-EMIN+1
4670 FOR K=2 TO 10
4680 X=LGT (10*(J+EMIN-1)*K)
4690 MOVE XMIN,X
4700 DRAW XMAX.X
4710 NEXT K
4720 LORG 5
4730 MOVE XMIN-(XMAX-XMIN) /20 ,J+EMIN-1
4740 CSIZE 3
4750 Z=10“(J+EMIN-1)
4760 ZZS=VALS (Z)
4770 LABEL ZZS
4780 NEXT J
4790 MOVE XMIN-(XMAX-XMIN)/10,(EMAX+EMIN)/2
4800 LDIR 0.1
4810 LORG 4
4820 CSIZE 4
4830 LABEL "VOID RATIO"
4840 LDIR -1,0
4850 LORG 5
4860 FOR I=NI+1 TO N

280
4870 X=LGT (EFFSTRESSPSF(I))
4880 IF X 4890 MOVE X, LGT (VOIDRATIOd ))
4900 LABEL
4910 NEXT I
4920 PEN 0
4930 PAUSE
4940 GOLEAR @ CLEAR
4950 DISP "PLOTTING COMPLETE" @ END

APPENDIX F
TRANSDUCER CALIBRATION IN THE CENTRIFUGE
Before using the PDCR 81 transducers with confidence in
the centrifuge, it was necessary to investigate their
performance in this high acceleration environment. For this
purpose, a dummy test with a specimen of 12 cm of tap water
was conducted to evaluate the calibration factor of each
transducer.
In the test, the transducers readings were first taken
at 1-g. The centrifuge was then accelerated to angular
speeds corresponding to average normal accelerations of 40
g's, 60 g's, and 80 g's. At each acceleration, the readings
of the transducers were taken and recorded. Four other
readings for each transducer were taken when the centrifuge
was decelerated and stopped.
For a given angular speed, w, the hydrostatic pressure
that exists at any point in the water is given by (Goforth,
1986)
p = Tg 2 ‘(r2 ‘ ri) where rw = unit weight of water, assumed as 62.4 pcf,
g - 32.2 ft/sec^ = acceleration of gravity,
r1, r2 “ distances from center of rotation.
281

282
Figure F.l gives the values and interpretetation of
and r2 for transducer No. 1. Table F-l gives the values of
the pressures computed with equation F.l, and the value at
1-g. It also includes the pair of readings taken at each
acceleration level. A plot of the transducer readings
versus the pressure for transducer No. 1 is shown in Figure
F.2. A linear regression done with these data gave a slope
of 6.540 mV/psi with a correlation coefficient of 0.99998,
while the factory calibration is 6.370 mV/psi. The differ¬
ence between these values is of 2.7%
A similar analysis was done with transducer No. 2, and
the results are shown in Figure F.3, Table F-2, and Figure
F.4. The slope obtained from the linear regression analysis
was of 7.463 mV/psi with a correlation coefficient of
0.99997. The factory calibration of this transducer is
7.418 mV/psi, which represents a difference of only 0.6%.
The calibration analysis of transducer No. 3 is
summarized in Figure F.5, Table F-3, and Figure F.6. The
centrifuge calibration obtained from the linear regression
analysis was 11.79 mV/psi with a correlation coefficient of
0.995, while the factory calibration is 12.80 mV/psi. This
represents a difference of 7.9%.
Above results prove that the transducers perform well
in the centrifuge. Furthermore, since the difference
between the centrifuge and factory calibrations was only
about 8% in the worst case, it can be concluded that the
factory calibrations hold in the centrifuge environment.

283
,12 cm
k H
3 2 1
Figure F.l - Radii and for Transducer No. 1
Table F-l. Calibration Data for Transducer No. 1
( g ' s )
w ( r . p . m . )
P (psi)
Reading
(mV)
1
_
0.156
-18.2,
-18.8
40
186
6.231
21.35,
21.55
60
228
9.363
41.65,
41.85
80
263
12.458
62.00,
61.95
Figure F.2
Calibration Plot for Transducer No. 1

284
.12 cm.
H H
Figure F.3 - Radii rp and r2 for Transducer No. 2
Table F-2. Calibration Data for Transducer No. 2
(g' s)
w ( r . p . in . )
P
(ps i )
Reading
(mV)
1
-
0
.099
- 24 ,
. 65 , -
24 .
. 70
40
186
3
.893
3 .
â–  65,
4 ,
, 05
60
228
5
. 849
18 ,
• 15 ,
18 .
. 45
80
263
7
.783
32 .
, 70,
32 .
, 65
- Calibration Plot for Transducer No. 2
Figure F.4

285
c m
H
—□ □ ET
Figure F.5 - Radii rp and for Transducer NcF. ^
Table F-3. Calibration Data for Transducer No. 3
(g' s)
w ( r . p . m . )
P
(ps i )
Reading
(mV)
1
_
0
. 0426
5 .
. 95 ,
6 .
. 80
40
186
1
.635
25 .
• 65 ,
26 .
. 00
60
228
2
.457
35 .
.50,
35 .
. 20
80
263
3
. 269
44 ,
• 55 ,
44 ,
. 05

APPENDIX G
CENTRIFUGE MONITORING PROGRAM
5 REM - PROGRAM "CENTRIFUGE" USED TO MONITOR THE PRESSURE TRANSDUCERS
10 DIM CALIBRATION(3),ZEROREADINGÍ3),READING(3),PRESSURE(3),TR(6),TESTIDS[80],LINE1$[20],LINE2$
[20]
20 CALIBRATION(1)=6.37 ! TRANSDUCER No. 1
30 CALIBRATION(2)=7.418 ! TRANSDUCER No. 2
40 CALIBRATION(3)=12.8 ! TRANSDUCER No. 3
50 TR(1)=2 @ TR(2)=4 @ TR(3)=8 @ TR(4)=15 @ TR(5)=30 @ TR(6)=60
60 IREAD=1
70 PRINTER IS 8,220
80 DISP "INPUT TEST IDENTIFICATION (80 character max.)";
90 INPUT TESTIDS
100 DISP "INPUT SAMPLE HEIGHT (cm)";
110 INPUT HI
120 DISP "INPUT INITIAL SOLIDS CONTENT (%)";
130 INPUT SI
140 GS=2.71
150 EI=GS*(100/SI-l)
160 DISP "INPUT ACCELERATION LEVEL (g’s)";
170 INPUT ACC
180 GOSUB ZEROREAD ! TO OBTAIN ZERO READINGS FOR THE ACC. LEVEL
190
200
210
220
(NOT USED)
' ¡TESTIDS
" ¡HI
= " ; SI
DISP "INPUT NAME OF OUTPUT FILE"
INPUT OUTFILES
CREATE OUTFILES,100,40
ASSIGN# 1 TO OUTFILES
230 PRINT TAB (5)¡"TEST IDENTIFICATION:
240 PRINT " "
250 PRINT TAB (5)¡"INITIAL HEIGHT (cm) =
260 PRINT TAB (5);"INITIAL SOLIDS CONTENT (%)
270 PRINT USING 280 ; El
280 IMAGE 4X,"INITIAL VOID RATIO = ".DD.DDD
290 PRINT TAB (5);"ACCELERATION (g’s) =";ACC
300 PRINT ” ”
310 PRINT USING 320
320 IMAGE 5X,"TRANSDUCER FOR:",7X,"PP 1",10X,"PP 2",10X,"PP 3"
330 PRINT USING 340 ; CALIBRATION(1),CALIBRATION(2),CALIBRATION(3)
340 IMAGE 5X,"CALIBRATION:”,2X,3(5X,D.DDDe)
350 PRINT USING 360 ; ZEROREADING (1), ZEROREADING ( 2 ), ZEROREADING( 3 )
360 IMAGE 5X,"ZERO READING:",3(7X,ODD.DDD)
370 PRINT " "
380 LINE1 $="====================" @ LINE2S—" "
390 PRINT USING 400 ; LINElS,LINElS,LINElS,LINE1S
400 IMAGE 5X, 4 (20A), "
410 PRINT USING 420
286

287
420 IMAGE 5X,"READING",5X,"TIME",10X,"PORE PRESSURE l",12X,"PORE PRESSURE 2",12X,"P0RE PRESSURE 3"
430 PRINT USING 440
440 IMAGE 7X,"No.”,6X,"(min)",3(9X,"(mV)",9X,"(psi)")
450 PRINT USING 460 ; LINE2$,LINE2S,LINE2S,LINE2$
460 IMAGE 5X , 4 (20A), " "
470 DISP "The program will now be PAUSED"
480 DISP "After pressing the CONT key the program"
490 DISP "will wait 1 minute before setting t=0”
500 PAUSE
510 DISP
520 WAIT 60000
530 DISP "TEST STARTING"
540 SETTIME 0,0
550 IF IREAD<7 THEN TIMEREAD=TR(IREAD) ! Initial 6 times for readings
560 IF IREAD>= 7 THEN TIMEREAD=TIMEREAD+60 ! After 1 hr take readings every hr
570 GOSUB RUNTIME
580 IF ELAPSEDTIME 590 REM Take Reading of Three Transducers
600 CLEAR 709
610 OUTPUT 709 ;"VR1"
620 OUTPUT 709 ;"AF1AL3AC1" ! Reading channels 1 to 3
630 FOR 1=1 TO 3
640 IF I>1 THEN OUTPUT 709 ;"AS" ! Move to read next channel
650 OUTPUT 709 ;"VT3" ! Causes the voltmeter to trigger and take a reading
660 ENTER 709 ; X
670 READINGd)=1000*X ! Voltmeter reading in milivolts
680 NEXT I
690 REM Compute excess pore pressure at each transducer
700 FOR 1=1 TO 3
710 PRESSURE(I)=(READING(I)-ZEROREADING(I))/CALIBRATION(I)
720 NEXT I
730 PRINT USING 740 ; IREAD,TIMEREAD,READING(1),PRESSURE(1),READING(2),PRESSURE(2),READING(3),-
PRESSURE(3)
740 IMAGE 5X,4D,5X,DDDD.DD,3(7X,DDD.DDD,5X,DDD.DDDD)
750 ! PRINT# 1; TIMEREAD,READING(1),PRESSURE(1),READING(2),PRESSURE(2),READING(3),PRESSURE(3)
760 IREAD=IREAD+1
770 GOTO 550
780 REM
790 REM ********************************************************************
800 REM ******************* SUBROUTINE RUNTIME *****************************
810 REM ********************************************************************
820 RUNTIME: ! THIS SUBROUTINE COMPUTES THE ELAPSED TIME OF TEST IN MINUTES
830 IF DATE >0 THEN GOTO 860
840 ELAPSEDTIME=TIME /60
850 RETURN
860 ELAPSEDTIME=DATE *1440+TIME /60
870 RETURN
880 REM
890 REM ********************************************************************
900 REM ******************* SUBROUTINE ZEROREAD ****************************
910 REM ********************************************************************
920 ZEROREAD: ! THIS SUBROUTINE ASSIGNS THE ZERO READINGS FOR THE THREE

288
930 ! TRANSDUCERS FOR A PARTICULAR ACCELERATION LEVEL
940 ! VALUES REPRESENT THE AVERAGE OF 5 READINGS OVER A PERIOD OF 30 MINUTES
950 ! THE COEFF. OF VARIATION (C.O.V.) IS GIVEN IN EVERY CASE
960 IF ACC=40 THEN GOTO 1030
970 IF ACC=60 THEN GOTO 1080
980 IF ACC=80 THEN GOTO 1130
990 DISP "INVALID ACCELERATION LEVEL"
1000 DISP "INPUT CORRECT VALUE (g’s)";
1010 INPUT ACC
1020 GOTO 960
1030 REM - ZERO READINGS FOR 40g
1040 ZEROREADINGU)=21.244 ! C.O.V.=0.45%
1050 ZEROREADING(2)=4.279 ! C.O.V.=0.70%
1060 ZEROREADINGt3)=25.341 ! C.O.V.=1.43%
1070 RETURN
1080 REM - ZERO READINGS FOR 60g
1090 ZEROREADINGU )=41.913 ! C.O.V.=0.23%
1100 ZEROREADINGC2) = 19.145 ! C.O.V.=0.72%
1110 ZEROREADING(3)=35.308 ! C.O.V.=0.25%
1120 RETURN
1130 REM - ZERO READINGS FOR 80g
1140 ZEROREADINGU )=61.729 ! C . O. V. =0.086%
1150 ZEROREADING(2)=33.329 ! C.O.V.=0.48%
1160 ZEROREADINGU)=44.253 ! C.O.V.=0.44%
1170 RETURN

APPENDIX H
CENTRIFUGE DATA REDUCTION PROGRAM AND OUTPUT LISTINGS
Data Reduction Propram
C THIS PROGRAM ANALYZES THE DATA FROM CENTRIFUGE TESTING TO OBTAIN
C THE COMPRESSIBILITY AND PERMEABILITY RELATIONSHIPS
DIMENSION H(20,15),Z(20),SIGB(20),S(10), EH (10),XL(10),A(10),Y(4),
&UY(3),GR(4),HT(15),VS(20,15),PERM(20,15)
DIMENSIONTIMEMIN(15),U(20,15),EFFSTR(20,15),E(20,15),GRAD(20,15)
CHARACTER *1 BATCHS
CHARACTER *12 DATAS,PRINTS
CHARACTER *60 TESTIDS
WRITE(*,26)
26 FORMAT(5X,’Is the data already on disk (Y/N)?’)
READ(*,60) BATCHS
60 FORMAT(Al)
C
IF (BATCHS.EQ.’Y’.OR.BATCHS.EQ.’y’) THEN
WRITE(*,27 )
27 FORMAT(5XEnter name of data file’)
READ(*,61) DATAS
61 FORMATCA12)
OPEN(UNIT=1,FILE-DATAS,STATUS»’UNKNOWN’)
READ(1,46) TESTIDS
READ(1,*) ACC,HI,SI,N,(UY(I),1=1,3)
ELSE
WRITE!*,8)
8 FORMAT(5X,'Enter Test Identification (max. 60 characters)’)
READ(*,46) TESTIDS
46 FORMAT(A60)
WRITE(*,11)
11 FORMAT(5X,’Input Centrifuge Acceleration (g)’)
READ(*,*) ACC
WRITE(*,1)
1 FORMAT(5X,’Input Initial Specimen Height (cm)’)
READ(*,* ) HI
WRITE(*,2)
2 FORMAT(5X,’Input Initial Solids Content (%)’)
READ(*,* ) SI
WRITE(*,3)
3 FORMAT(5X,’Input number of layers’)
READ(*,* ) N
WRITE(*,5)
5 FORMAT(5X,’Input initial exc. Pore Pressures, Ul, U2, U3 (psi)’)
READ!*,*) (UY(I), 1=1,3)
289

290
WRITE(*,40)
40 FORMAT(5XEnter name of file to store data')
READ(*,61) DATAS
OPEN(UNIT-1,FILE=DATAS,STATUS-’UNKNOWN’)
WRITE(1,*) TESTIDS,ACC,HI,SI,N,(UY(I),1=1,3)
ENDIF
C
WRITE(*,62)
62 FORMAT(5X,’Enter name of output file’)
READ(*,70) PRINTS
OPEN(UNIT=2,FILE=PRINTS,STATUS-’UNKNOWN')
70 FORMAT(A12)
C
GS-2.71
C
C COMPUTE INITIAL CONDITIONS
K-l
TIMEMIN(1)=0.0
EI=GS*(100./SI-1. )
C THEORETICAL INITIAL GRADIENT = BUOYANT UNIT WT./WATER UNIT WT.
GRADT0-(GS-1) /(1+EI)
DH-HI/FLOAT(N)
DZ-DH/(1.+EI)
C COMPUTE CONVECTIVE AND REDUCED COORDINATES OF EACH NODE
DO 150 1=1,N+l
H(I,1)-(FLOAT(I)-1.)*DH
Z(I)=(FLOAT(I)-1.)*DZ
150 CONTINUE
C MATERIAL HEIGHT OF THE SPECIMEN IN cm
ZT-Z(N+l)
C COMPUTE BUOYANT STRESS (psi) AT EACH NODE
DO 200 1=1,N+l
SIGB(I)=ACC*(GS-1.)*62.4*(ZT-Z(I))/30.48/144.
200 CONTINUE
C
C COMPUTE INITIAL GRADIENT AND EXCESS PORE PRESSURE AT EACH NODE
CALL GRADIENT (UY,Y,GR,HI,ACC)
DO 17 1=1,N+l
CALL PPGRAD (H(I,1),U(I,1),GRAD(I,1),UY,Y,GR,ACC)
C COMPUTE INITIAL EFF. STRESS
EFFSTR(I,1)=SIGB(I)-U(I,1)
17 CONTINUE
C
C PRINTING TEST INFORMATION AND TABLE OF INITIAL CONDITIONS
WRITE(2,41) TESTIDS
41 FORMAT(/5X.A60)
WRITE(2,63) ACC,HI,SI,El,N
63 FORMAT(/5X,’Acceleration level =’,F5.0,' g*,/5XInitial Height
&,F5.1,’ cm’,/5X,’Solids Content = ’,F5.2,’X’,5X,’Void Ratio = ’,
&F6.3,/5X,’Number of Layers =’,I3)
WRITE(2,64) ZT
64 FORMAT(/5X,'Reduced Height of the Specimen =’,F6.3,’ cm’)

291
WRITE(2,45) GRADTO
45 FORMAT(/5XInitial Conditions’/5XTheoretical Gradient
WRITE(2,30)
30 FORMAK/’ NODE H(I) Z(I) BUOY . ST . EXC . P . P .
&,’ GRADIENT’)
C
DO 31 I-l.N+l
II=N+2-I
WRITE(2,32) II,H(11,1),Z(II),SIGB(II),U(II,1),EFFSTR(II,
& GRAD(II,1)
32 FORMAT(15,6F10.4 )
31 CONTINUE
C
C BEGINNING OF TIME ITERATIONS
C
100 K-K+l
IF (BATCHS.EQ.’Y’. OR.BATCHS.EQ.’y’) THEN
READ(UNIT=1,END=55,FMT=*) TIMEHR,HT(K),M,(S(J),J=1,M)
&1,3 )
GOTO 56
55 CALL INPUT (TIMEHR,HT(K),M,S,UY)
BACKSPACE(UNIT=1)
WRITE(1,*) TIMEHR,HT(K),M,(S(J),J=1,M),(UY(I),1=1,3)
56 CONTINUE
ELSE
CALL INPUT (TIMEHR,HT(K),M,S,UY)
WRITE(1,*) TIMEHR,HT(K),M,(S(J),J=1,M),(UY(I),1=1,3)
ENDIF
C
WRITE(*,99) TIMEHR
99 FORMAK/5X,’Analyzing data for time =’,F5.1,’ hr.’)
TIMEMIN(K)=TIMEHR*60
DO 10 J=1,M
10 EH(J)=GS*(100./S(J)-1.)
C
CALL GRADIENT (UY,Y,GR,HT(K),ACC)
C ASSIGN VALUES TO XL(J)
DO 420 J=1,M-2
420 XL(J)=2.0
XL(M-l)=HT(K)-2*(M-2)
C COMPUTE CUMULATIVE A(J)=AREA UNDER l/(l+e) vs. H
C A(J) IS THE AREA UP TO POINT J
A(1)=0.0
DO 490 J=2,M
A(J)=A(J-l)+0.5*(l/(1+EH(J-l))+l/(1+EH(J)))*XL(J-1)
490 CONTINUE
C
C HERE BEGINS THE LOOP THAT ANALYZES EACH MATERIAL NODE
DO 500 I-l.N+l
IF (I.EQ.l) THEN
H (1, K) = 0.0
E(1,K) = EH(1)
= ’,F6.3)
EFF.STR.’
.).
(UY(I),1=

292
ELSE
C LOCATE REGION WHERE POINT i FALLS
KK=2
530 IF (Z(I).LE.A(KK).OR.KK.EQ.M) GO TO 550
KK“KK+1
GO TO 530
550 J=KK-1
C THIS MEANS POINT i IS BETWEEN J AND J+l
C NEXT SOLVE FOR x TO OBTAIN NEW SPATIAL COORDINATE OF i
aa= (1./(1.+EH(J))-l./(l.+EH(J+l)))/XL(J)
b=-2./(1.+EH(J))
c-2.*(Z(I)-A(J))
C COMPUTE ROOTS OF THE QUADRATIC EQUATION
DISCR=(b**2-4.*aa*c)
Xl=(-b+SQRT(DISCR))/(2.*aa)
X2= (-b-SQRT(DISCR))/(2.*aa)
C IF (XI.GT.0.AND.Xl.LT.XL(J)) THEN
C X=X1
C ELSE
C IF (X2.GT.0.AND.X2.LT.XLCJ)) THEN
X=X2
C ELSE
C WRITE(*,21)
C 21 FORMAT(5X,'TROUBLE EVALUATING X’)
C ENDIF
C ENDIF
C COMPUTE NEW CONVECTIVE COORDINATE OF NODE i
H(I,K)=2.*FLOAT(J-1)+X
F“1./(1,+EH(J))-(X/XL(J))*(1./(1,+EH(J))-l./(l.+EHCJ+l)))
C COMPUTE NEW VOID RATIO OF NODE i
E(I,K)=1./F-1.
ENDIF
C COMPUTE EXCESS PORE PRESSURE AND GRADIENT AT NODE i
CALL PPGRAD (H(I,K),UMEAS,GRMEAS,UY,Y,GR,ACC)
CALL PARABOLA (HT(K),H(I,K),UPARAB,GRAPAR,UY(1),ACC)
U(I,K)=(UMEAS+UPARAB)/2
GRAD(I,K)=(GRMEAS+GRAPAR)/2
C COMPUTE EFF. STRESS AT NODE i
EFFSTR(I,K)=SIGB(I)-U(I,K)
C COMPUTE SOLIDS VELOCITY IN cm/sec
VS(I,K)~(H(I,K-1)-H(I,K))/(TIMEMIN(K)-TIMEMIN(K-l))/60.
AVGRAD=(GRAD(I,K)+GRAD(I,K-1)) /2 .
C COMPUTE COEFF. OF PERMEABILITY OF THE PROTOTYPE (ft/day)
PERM(I,K)=VS(I, K)/AVGRAD‘86400./30.48/ACC
500 CONTINUE
C
WRITE(2,33) TIMEMIN(K),HT(K)
33 FORMAT(//5X,'New Time = ’,F6.1,’ min’,10X,’New Height = ’,F5.2,
&’ cm’ )
WRITE(2,65) A(M)
65 FORMAT(5XNew Reduced Height of the Specimen =’,F6.3,’ cm’)
WRITE(2,25)

293
25 FORMAT(/' NODE H e u Eff.Str. i Vs
& k (ft/day)’)
DO 22 1=1,N+l
II=N+2-I
WRITE(2,23) II,H(II,K),E(II,K),U(II,K),EFFSTR(II,K),GRAD(II,K),
&VSCII,K),PERM(II,K)
23 FORMAT(I5,5F8.3,2E12.4)
22 CONTINUE
C
C GO BACK TO ANALYZE NEW TIME-STEP
GO TO 100
END
C
SUBROUTINE GRADIENT (UY,Y,GR,HT,ACC)
C THIS SUBROUTINES COMPUTES THE GRADIENT BETWEEN Ul, U2, AND U3
DIMENSION UY(3),Y(4),GR(4)
Y(1)=1.0
Y C 2) = 4.0
IF (UY(3).EQ,0.) THEN
Y(3 )=HT- (Y(1 )+Y(2) )
GR(4)=0.0
ELSE
Y(3 ) = 4.0
Y(4)=HT-(Y(l)+Y(2)+Y(3))
GR(4) = (UY(3)*14 4.)/(Y(4 )/30.48)/(62.4*ACC)
ENDIF
GR(2)=(UY(l)-UY(2))*144./(Y(2)/30.48)/(62.4*ACC)
GR(3)=(UY(2)-UY(3))*144./(Y(3)/30.48)/(62.4*ACC)
GR(1)=GR(2)
RETURN
END
C
SUBROUTINE PPGRAD (H,U,GRAD,UY,Y,GR,ACC)
C THIS SUBROUTINE COMPUTES THE EXCESS PORE PRESSURE AND GRADIENT AT THE
C MATERIAL NODES, BASED ON THE RECORDED PORE PRESSURES Ul, U2, AND U3
DIMENSION UY(3),Y(4),GR(4)
IF (H.LT.Y(l)) THEN
GRAD=GR(1)
U=UY(1)+GR(1)*(62.4*ACC)*((Y(l)-H)/30.48)/144.
ENDIF
IF (H.GT.Y(l).AND.H.LT.(Y(l)+Y(2))) THEN
GRAD=GR(2)
U=UY(1)-GR(2)*(62.4 *ACC)*((H-Y(l))/30.48)/144.
ENDIF
IF (H.GT. GRAD=GR(3)
U=UY(2)-GR(3)*(62.4*ACC)*((H-Y(1)-Y(2))/30.48)/144.
ENDIF
IF (H.GT.(Y(l)+Y(2)+Y(3))) THEN
GRAD=GR(4)
U=UY(3)-GR(4)*(62.4*ACC)*((H-Y(1)-Y(2)-Y(3))/30.48)/144 .
ENDIF

294
RETURN
END
SUBROUTINE INPUT (TIMEHR,HT,M,S,UY)
C THIS SUBROUTINE READS FROM THE KEYBOARD THE DATA FOR A GIVEN TIME-STEP
DIMENSION S(10),UY(3)
WRITE(*,6)
6 FORMAT(/5XInput new time to analyze (hr)’,/5X,
& 'or Input a zero if finished’)
READ*, TIMEHR
IF (TIMEHR.EQ.O.) THEN
WRITE!*,16)
WRITEÍ2,16)
16 FORMAT(/5X,'ANALYSIS COMPLETED’)
CLOSE(UNIT=1)
CLOSE(UNIT=2)
STOP
ELSE
WRITE!*,7)
7 FORMAT(5X,’Input the new specimen height (cm)’)
READ*, HT
WRITE(*,9 )
9 FORMAT(5X,’Input No. of points defining the Solids Content Profi
12
&
13
&
READ*, M
WRITE!*,12)
FORMAT(5X,’Enter Solids Contents S(1),S(2) S(M)’,/5X,
'where S(l) is the value at the bottom’)
READ*, (S(J),J—1,M)
WRITE!*,13)
FORMAT(5XInput U1.U2.U3 (psi)’,/5X,
’If surface is below Transducer No. 3, enter U3 = O’)
READ*, (UY(I),1-1,3)
ENDIF
RETURN
END
C
SUBROUTINE PARABOLA (H,Y,U,GRADIENT,U1,ACC)
C THIS SUBROUTINE COMPUTES THE EXCESS PORE PRESSURE AND GRADIENT AT THE C
MATERIAL NODES ASSUMING A PARABOLIC DISTRIBUTION
C Coefficient A is in [psi/cm2]
C Coefficient C is in [psi]
C U is the excess pore pressure in [psi]
C SLOPE is in [pcf]
C GRADIENT is the dimensionless MODEL hydraulic gradient
A=-U1/(H**2-1. )
C“-A*(H**2)
U=A*(Y**2)+C
SLOPE=2.*A*Y*(1*4.*30.48)
GRADIENT=ABS(SLOPE/(ACC*62.4))
RETURN
END

295
Data Reduction Output of Test CT-1
*** Centrifuge Test CT-1 ***
Acceleration level = 80. g
Initial Height = 12.0 cm
Solids Content = 15.72% Void Ratio = 14.535
Number of Layers = 10
Reduced Height of the Specimen = 0.772 cm
Initial Conditions
Theoretical Gradient =
NODE H(I) Z(I)
0.110
BUOY.ST
EXC.P.P.
EFF.STR.
GRADIENT
11
12.0000
0.7725
0.0000
0.0000
0.0000
0.1119
10
10.8000
0.6952
0.1502
0.1527
-0.0024
0.1119
9
9.6000
0.6180
0.3005
0.3054
-0.0049
0.1119
8
8.4000
0.5407
0.4507
0.4501
0.0006
0.1002
7
7.2000
0.4635
0.6009
0.5869
0.0140
0.1002
6
6.0000
0.3862
0.7512
0.7237
0.0275
0.1002
5
4.8000
0.3090
0.9014
0.8664
0.0350
0.1262
4
3.6000
0.2317
1.0516
1.0386
0.0130
0.1262
3
2.4000
0.1545
1.2019
1.2109
-0.0090
0.1262
2
1.2000
0.0772
1.3521
1.3831
-0.0310
0.1262
1
0.0000
0.0000
1.5024
1.5553
-0.0530
0.1262
New
Time -
60.0 min
New Height
* 10.20 cm
New Reduced Height of the Specimen = 0.768 cm
U(I) = 1.266 0.624 0.152 psi
S(J) = 22.19 16.86 17.65 18.68 16.29 %
NODE
H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
10.263
13.998
-0.012
0.012
0 . 167
0.4824E-03
0.1228E+00
10
9.152
12.830
0.191
-0.041
0. 155
0.4578E-03
0.1218E+00
9
8.121
11.898
0.362
-0.061
0 . 140
0.4109E-03
0.1158E+00
8
7 . 123
12.050
0.514
-0.063
0 . 129
0.3546E-03
0.1097E+00
7
6.104
12.356
0.657
-0.056
0 . 118
0.3046E-03
0.9899E-01
6
5.065
12.506
0.790
-0.038
0 . 107
0.2596E-03
0.8895E-01
5
4.017
12.642
0.931
-0.029
0.114
0.2175E-03
0.6419E-01
4
2.949
13.013
1.062
-0.011
0 . 102
0.1808E-03
0.5605E-01
3
1.853
12.987
1.183
0.019
0.091
0.1518E-03
0.4963E-01
2
0.861
10.877
1.279
0.073
0.080
0.9413E-04
0.3237E-01
1
0.000
9.503
1.352
0.150
0.071
0.OOOOE+OO
0.OOOOE+OO

296
New Time =
120.0
min
New
Height
= 9.A 5 cm
New Reduced Height
of the
Specimen
= 0.783
I cm
U(I) - 1.
1351 0.
A A 7 0 .
0513 psi
S(J) = 23
.85 19.
1A 18.
5A 19.A6
20.05
18.00 Z
NODE
H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
9.305
12.17A
0.026
-0.026
0 . 155
0.2661E-03
0.5859E-01
10
8.330
11.125
0.187
-0.037
0 . 138
0.2283E-03
0.5537E-01
9
7 . A 11
10.92A
0.325
-0.025
0 . 127
0.1972E-03
0.5237E-01
8
6 . A 82
11.115
0 . A 5A
-0.003
0.117
0.1780E-03
0.5137E-01
7
5.538
11.369
0.57A
0.027
0.106
0.1571E-03
0.A973E-01
6
A . 570
11.702
0.700
0.051
0.127
0.1377E-03
0.A172E-01
5
3.579
11.808
0.837
0.06A
0.116
0.1216E-03
0.37A8E-01
A
2.598
11.582
0.961
0.091
0.105
0.97A3E-0A
0.3329E-01
3
1.6A3
10.836
1.069
0.133
0.09A
0.5850E-0A
0.22AAE-01
2
0.780
9.579
1.157
0.196
0.08A
0.2260E-0A
0.97A6E-02
1
0.000
8.653
1.228
0.275
0.076
0.0000E+00
0.OOOOE+OO
New Time =
2A0.0
min
N ew
Height
= 8.55 cm
New Reduced Height of the
Specimen
= 0.776 cm
U (I} = 1.
077 0 .
3789 0
psi
S(J) = 27
.61 22
.19 20.
17 19.89
18.86
Z
NODE
H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
8.505
11.6A5
0.008
-0.008
0.159
0.1112E-03
0.2510E-01
10
7.5A0
11.353
0 . 175
-0.025
0 . 1A6
0.1098E-03
0.27AAE-01
9
6.596
11.081
0.325
-0.025
0.13A
0.1132E-03
0.3075E-01
8
5.672
10.883
0 . A59
-0.009
0 . 121
0.1126E-03
0.33A9E-01
7
A . 757
10.797
0.588
0.013
0 . 139
0.108AE-03
0.3132E-01
6
3.650
10.62A
0.725
0.026
0. 127
0.9998E-0A
0.2783E-01
5
2.97 A
10.065
0.8A6
0.055
0.116
0.8A00E-0A
0.2567E-01
A
2.139
9.579
0.951
0 . 101
0.105
0.6386E-0A
0.2157E-01
3
1.357
8.591
1.0A0
0.162
0.095
0.3965E-0A
0.1A89E-01
2
0.650
7.755
1. 112
0.2A0
0.085
0.1799E-0A
0.751AE-02
1
0.000
7.105
1.172
0.331
0.077
0.0000E+00
0.0000E+00

297
New
1 Time =
480.0
min
New
Height
= 7.55 cm
New
i Reduced Height
of the
Specimen
= 0.792 cm
U(I) = 0.
77 0.1759 0
psi
S(J) = 29
.41 26.
74 23 .
04 21.23
19.09
Z
NODE
H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
7.306
11.236
0.033
-0.033
0.119
0.8330E-04
0.2129E-01
10
6.394
10.387
0.151
0.000
0.108
0.7953E-04
0.2223E-01
9
5.540
9.807
0.250
0.050
0.097
0.7334E-04
0.225 IE-01
8
4 . 721
9.392
0.347
0.103
0.122
0.6601E-04
0.1919E-01
7
3.933
8.988
0.453
0.148
0 . 113
0.5722E-04
0.1609E-01
6
3.188
8.321
0.544
0.207
0.104
0.4594E-04
0.1409E-01
5
2.490
7.773
0.624
0.278
0.095
0.3361E-04
0.1128E-01
4
1.831
7.338
0.692
0.359
0.087
0.2139E-04
0.7885E-02
3
1.199
7.030
0.752
0.450
0.080
0.1102E-04
0.4481E-02
2
0.589
6.754
0.805
0.547
0.072
0.4240E-05
0.1906E-02
1
0.000
6.505
0.851
0.651
0.065
0.0000E+00
0.0000E+00
New Time =
720.0
min
New
Height
= 6.95 cm
New Reduced Height
of the
Specimen
= 0.790 cm
U(I) = 0.
4397 0
0 psi
S(J) = 30
.80 28.
53 25.
34 20.88
19.22
Z
NODE H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
6.739
11.122
0.013
-0.013
0.055
0.3934E-04
0.1605E-01
10
5.844
10.050
0.066
0.084
0.048
0.3821E-04
0.1743E-01
9
5.032
9.034
0 . 107
0.194
0.041
0.3529E-04
0.1807E-01
8
4.288
8.255
0 . 178
0.273
0.083
0.3011E-04
0 . 1037E-01
7
3.596
7.714
0.242
0.359
0.078
0.2343E-04
0.8714E-02
6
2.939
7.308
0.298
0.454
0.072
0.1733E-04
0.6972E-02
5
2.311
6.953
0.347
0.554
0.067
0.1244E-04
0.5421E-02
4
1.708
6.678
0.392
0.660
0.062
0.8492E-05
0.4020E-02
3
1.124
6.466
0.432
0.770
0.058
0.5216E-05
0.2692E-02
2
0.554
6.270
0.467
0.885
0.053
0.2409E-05
0.1363E-02
1
0.000
6.089
0.499
1.003
0.048
0.OOOOE+OO
0.0000E+00

298
New Time =
1320.0
min
New
Height
= 6.20 cm
New Reduced Height
of the
Specimen
= 0.791 cm
a
h-i
II
o
1364 0
0 psi
S(J) = 32
.21 30.
64 28.
18 20.57
Z
NODE H
e
u
Eff.Str.
i
Vs
k (ft/day)
11 5.991
9.996
0.005
-0.005
0.019
0.2076E-04
0.1981E-01
10 5.203
8.523
0.021
0.130
0.017
0.1781E-04
0.1958E-01
9 4.508
7.518
0.041
0.259
0.029
0.1453E-04
0.1460E-01
8 3.880
6.856
0.062
0.389
0.027
0.1133E-04
0.7250E-02
7 3.283
6.611
0.080
0.521
0.026
0.8703E-05
0.5975E-02
6 2.703
6.388
0.096
0.655
0.024
0.6540E-05
0.4828E-02
5 2.141
6.184
0.110
0.791
0.022
0.4733E-05
0.3766E-02
4 1.592
6.042
0.124
0.928
0.020
0.3238E-05
0.2785E-02
3 1.052
5.924
0.135
1.067
0.018
0.1976E-05
0.1846E-02
2 0.522
5.811
0.146
1.206
0.017
0.9040E-06
0.9216E-03
1 0.000
5.704
0.155
1.347
0.015
0.0000E+00
0.OOOOE+OO
New
1 Time =
2280.0
min
N ew
Height
“ 5.95 cm
New
1 Reduced Height
of the
Specimen
= 0.789
1 cm
U(I) = 0.
0068 0
0 psi
S(J) = 33
.56 31.
77 28.
66 20.29
Z
NODE
H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
5.761
10.105
0.000
0.000
0.001
0.3995E-05
0.1402E-01
10
4.979
8.311
0.001
0.149
0.002
0.3892E-05
0.1509E-01
9
4.306
7.176
0.002
0.298
0.001
0.3509E-05
0.8041E-02
8
3.703
6.593
0.003
0.447
0.001
0.3071E-05
0.7555E-02
7
3.127
6.313
0.004
0.597
0.001
0.2694E-05
0.7124E-02
6
2.572
6.062
0.005
0.746
0.001
0.2274E-05
0.6485E-02
5
2.036
5.835
0.006
0.896
0.001
0.1820E-05
0.5619E-02
4
1.513
5.703
0.006
1.045
0.001
0.1363E-05
0.4578E-02
3
1.000
5.585
0.007
1.195
0.001
0.9087E-06
0.3339E-02
2
0.496
5.472
0.007
1.345
0.001
0.4542E-06
0.1839E-02
1
0.000
5.365
0.008
1.495
0.001
0.OOOOE+OO
0.0000E+00
ANALYSIS COMPLETED

299
Data Reduction Output of Test CT-2
*** Centrifuge Test CT-2 ***
Acceleration level = 60. g
Initial Height = 12.0 cm
Solids Content = 16.05% Void Ratio = 14.175
Number of Layers = 10
Reduced Height of the Specimen = 0.791 cm
Initial Conditions
Theoretical Gradient =
NODE H(I) Z(I)
0.113
BUOY.ST.
EXC.P.P.
. EFF.STR.
GRADIENT
11
12.0000
0.7908
0.0000
0.0000
0.0000
0.1194
10
10.8000
0.7117
0.1153
0.1222
-0.0069
0.1194
9
9.6000
0.6326
0.2307
0.2445
-0.0138
0.1194
6
8.4000
0.5536
0.3460
0.3563
-0.0103
0.0991
7
7.2000
0.4745
0.4614
0.4577
0.0037
0.0991
6
6.0000
0.3954
0.5767
0.5592
0.0176
0.0991
5
4.8000
0.3163
0.6921
0.6664
0.0257
0.1329
4
3.6000
0.2372
0.8074
0.8024
0.0050
0.1329
3
2.4000
0.1582
0.9228
0.9385
-0.0157
0.1329
2
1.2000
0.0791
1.0381
1.0745
-0.0364
0.1329
1
0.0000
0.0000
1.1535
1.2106
-0.0571
0.1329
New
T ime =
60.0 min
New
' Height
= 10.90 cm
New Reduced Height of the Specimen = 0.800 cm
U(I) = 1.0295 0.5259 0.1512 psi
S(J) = 21
.77 16.
.67 17.
04 17.18
17.90
17.83 16.
05 %
NODE
H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
10.765
13.895
0.018
-0.018
0 . 157
0.3432E-03
0.1173E+00
10
9.662
12.479
0.160
-0.045
0 . 146
0.3161E-03
0.1127E+00
9
8.597
12.447
0.291
-0.060
0.143
0.2785E-03
0.1003E+00
8
7.532
12.573
0.416
-0.070
0 . 132
0.2410E-03
0.9851E-01
7
6.446
12.918
0.533
-0.071
0 . 121
0.2096E-03
0.8999E-01
6
5.335
13.107
0.642
-0.065
0 . 110
0.1848E-03
0.8368E-01
5
4.216
13.180
0.754
-0.062
0 . 117
0.1621E-03
0.6130E-01
4
3.089
13.352
0.861
-0.053
0 . 105
0.1419E-03
0.5627E-01
3
1.946
13.409
0.958
-0.035
0.094
0.1260E-03
0.5254E-01
2
0.902
11.177
1.036
0.002
0.083
0.8264E-04
0.3616E-01
1
0.000
9.738
1.097
0.057
0.074
0.0000E+00
0.OOOOE+OO

300
New Time =
120.0
min
New
Height
= 10.15 cm
New Reduced Height
of the
Specimen
= 0.788 cm
U(I) - 0.
8717 0.
4020 0
.0485 psi
SCJ) - 22
;.91 17.
83 17.
96 18.06
19.44
16.05 %
NODE
H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
10.200
14.260
-0.005
0.005
0.127
0.1568E-03
0.5222E-01
10
9.066
12.532
0.112
0.003
0.116
0.1656E-03
0.5993E-01
9
8.047
11.283
0.230
0.001
0.132
0.1528E-03
0.5241E-01
8
7.062
11.708
0.337
0.009
0.123
0.1305E-03
0.4844E-01
7
6.036
12.275
0.440
0.022
0 . 112
0.1139E-03
0.4615E-01
6
4.983
12.338
0.536
0.041
0.119
0.9782E-04
0.4049E-01
5
3.926
12.383
0.638
0.054
0 . 108
0.8062E-04
0.3383E-01
4
2.866
12.441
0.731
0.076
0.098
0.6207E-04
0.2890E-01
3
1.804
12.062
0.815
0 . 108
0.087
0.3964E-04
0.2074E-01
2
0.845
10.313
0.882
0.156
0.077
0.1603E-04
0.9449E-02
1
0.000
9.119
0.935
0.219
0.069
0.0000E+00
0.0000E+00
New Time =
240.0
min
New
Height
= 9.25 cm
New Reduced Height
of the
Specimen
= 0.764 cm
U(I) - 0.
7998 0.
3321 0
psi
S(J) = 25
i.53 20.
00 18.
21 18.84
19.37
16.05 Z
NODE H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
9.667
15.471
-0.037
0.037
0.107
0.7396E-04
0.2985E-01
10
8.504
12.303
0.092
0.024
0.140
0.7807E-04
0.2886E-01
9
7.511
11.375
0.206
0.025
0 . 129
0.7446E-04
0.2691E-01
8
6.525
11.569
0.310
0.036
0.118
0.7464E-04
0.2930E-01
7
5.523
11.790
0.406
0.055
0 . 107
0.7122E-04
0.3069E-01
6
4.501
12.044
0.504
0.073
0 . 118
0.6682E-04
0.2662E-01
5
3.470
11.791
0.603
0.089
0 . 107
0.6332E-04
0.2781E-01
4
2.485
11.138
0.688
0.119
0.096
0.5282E-04
0.2577E-01
3
1.559
10.038
0.760
0.162
0.086
0.3396E-04
0.1858E-01
2
0.738
8.801
0.817
0.221
0.077
0.1484E-04
0.9103E-02
1
0.000
7.905
0.863
0.291
0.069
0.0000E+00
0.OOOOE+OO

301
New
Time =
480.0
min
New
Height
= 8.10 cm
New
Reduced Height
of the
Specimen
= 0.774
cm
U(I) = 0.
7096 0.
2525 0
psi
S(J) = 27
.51 24.
58 21.
11 20.12
18.79
Z
NODE
H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
8.312
11.817
-0.019
0.019
0.107
0.9415E-04
0.4153E-01
10
7.317
11.340
0.098
0.017
0. 142
0.8237E-04
0.2759E-01
9
6.359
10.912
0.209
0.022
0 . 130
0.8003E-04
0.2923E-01
8
5.431
10.572
0.307
0.039
0 . 118
0.7596E-04
0.3043E-01
7
4.527
10.287
0.401
0.060
0 . 125
0.6912E-04
0.2811E-01
6
3.650
9.761
0.491
0.086
0 . 114
0.5915E-04
0.2405E-01
5
2.830
8.991
0.567
0.126
0.103
0.4443E-04
0.1995E-01
4
2.066
8.365
0.631
0.177
0.094
0.2912E-04
0.1451E-01
3
1.345
7.895
0.685
0.237
0.084
0.1490E-04
0.8273E-02
2
0.657
7.493
0.732
0.306
0.075
0.5593E-05
0.3473E-02
1
0.000
7.141
0.772
0.381
0.067
0.OOOOE+OO
0.OOOOE+OO
New Time =
720.0
min
New
Height
= 7.A 0 cm
New Reduced Height
of the
Specimen
= 0.756 cm
U(I) - 0.
5194 0.
1349 0
psi
S(J) - 28
.60 26.
30 22.
98 20.29
17.24
z
NODE H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
7.909
14.125
-0.038
0.038
0.090
0.2795E-04
0.1344E-01
10
6.808
11.902
0.057
0.058
0 . 110
0.3538E-04
0.1326E-01
9
5.849
10.511
0.143
0.088
0.099
0.3543E-04
0.1463E-01
8
4.968
9.784
0.214
0.132
0. 113
0.3217E-04
0.1320E-01
7
4 . 140
9.178
0.291
0.171
0.103
0.2692E-04
0.1113E-01
6
3.360
8.553
0.356
0.220
0.094
0.2015E-04
0.9137E-02
5
2.626
8.011
0.413
0.279
0.086
0 . 1418E-04
0.7068E-02
4
1.932
7.563
0.461
0.346
0.078
0.9276E-05
0.5102E-02
3
1.267
7.271
0.504
0.419
0.071
0.5393E-05
0.3288E-02
2
0.623
7.006
0.540
0.498
0.063
0.2357E-05
0.1604E-02
1
0.000
6.766
0.572
0.581
0.056
0.OOOOE+OO
0.OOOOE+OO

302
New Time =
1««0.0
min
New
Height
= 6.45 cm
New Reduced Height
of the
Specimen
= 0.781 cm
o
II
M
o
2960 0.
0265 0
psi
S(J) = 31
.11 29.
22 27.
43 21.33
18.34
Z
NODE H
e
u
Eff.Str.
i
Vs
k ( f t / d ay)
11 6.586
12.856
-0.006
0.006
0.056
0.3063E-04
0.1984E-01
10 5.666
9.394
0.042
0.074
0.059
0.2644E-04
0.1477E-01
9 «.893
8.228
0.081
0.149
0.081
0.2213E-04
0.1158E-01
8 «.198
7.383
0.128
0.218
0.075
0.1783E-04
0.8960E-02
7 3.553
7.026
0.168
0.294
0.070
0 . 1358E-04
0.741IE-02
6 2.926
6.833
0.204
0.373
0.065
0.1003E-04
0.5964E-02
5 2.31«
6.65«
0.236
0.456
0.059
0.7225E-05
0.4697E-02
« 1.716
6.479
0.265
0.543
0.054
0.5013E-05
0.3578E-02
3 1.131
6.309
0.291
0.632
0.049
0.3143E-05
0.2478E-02
2 0.559
6.150
0.313
0.725
0.044
0.1481E-05
0.1300E-02
1 0.000
6.001
0.333
0.820
0.039
0.0000E+00
0.OOOOE+OO
New
- Time =
2100.0
min
New
Height
= 6.10 cm
New
1 Reduced Height
of the
Specimen
- 0.781
cm
U(I) = 0.
1494 0
0 psi
S(J) = 31
.85 30.
86 28.
37 20.24
Z
NODE
H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
6.213
10.996
-0.003
0.003
0.030
0.9413E-05
0.1030E-01
10
5.353
8.948
0.018
0.098
0.026
0.7893E-05
0.8771E-02
9
4.620
7.684
0.040
0.191
0.044
0.6888E-05
0.5184E-02
8
3.970
6.829
0.063
0.283
0.041
0.5764E-05
0.4676E-02
7
3.361
6.578
0.084
0.377
0.038
0.4867E-05
0.4258E-02
6
2.771
6.350
0.103
0.474
0.035
0.3936E-05
0.3726E-02
5
2.198
6.141
0.119
0.573
0.033
0.2940E-05
0.3027E-02
4
1.639
6.021
0 . 134
0.673
0.030
0.1942E-05
0.2185E-02
3
1.087
5.944
0 . 147
0.775
0.027
0.1122E-05
0.1390E-02
2
0.540
5.870
0.159
0.879
0.025
0.4802E-06
0.6597E-03
1
0.000
5.799
0.170
0.983
0.022
0.OOOOE+OO
0.OOOOE+OO

303
New Time =
2880.0
min
New
Height
= 6.00 cm
New Reduced Height
of the
Specimen
= 0.773
1 cm
U(I) = 0.
0382 0
0 psi
S(J) = 32
.14 30.
73 28.
48 20.46
X
NODE H
e
u
Eff.Str.
i
Vs
k (ft/day)
11
6.210
11.145
-0.001
0.001
0.008
0.6911E-07
0.1719E-03
10
5.344
8.972
0.004
0.111
0.007
0.1963E-06
0.5667E-03
9
4.611
7.661
0.010
0.221
0.011
0.1910E-06
0.3239E-03
8
3.964
6.792
0.016
0.330
0.011
0.1310E-06
0.2391E-03
7
3.356
6.567
0.021
0.440
0.010
0.8996E-07
0.1769E-03
6
2.766
6.360
0.026
0.551
0.009
0.8977E-07
0.1909E-03
5
2.192
6.170
0.030
0.662
0.008
0.1239E-06
0.2859E-03
4
1.631
6.034
0.034
0.773
0.008
0.1697E-06
0.4275E-03
3
1.079
5.925
0.038
0.885
0.007
0.1645E-06
0.4554E-03
2
0.535
5.821
0.041
0.997
0.006
0.1066E-06
0.3271E-03
1
0.000
5.722
0.044
1. 110
0.006
0.OOOOE+OO
0.0000E+00
ANALYSIS COMPLETED

APPENDIX I
NUMERICAL PREDICTION PROGRAM AND
EXAMPLE OUTPUT LISTINGS
Listing of Program YONG-TP
Program Yong;
LABEL
1,2,3, A, 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22;
VAR
SI,El,HI,G2,UMAX,BINC,AAA,BB,CC,DD,HT,PRI,FISC,RO,ROT,DH2,BOTT: REAL;
AINC,OLDA,ALPHA,ALPHAINV,A,SLOAD,DH,ZZZ,TB,COEF,TM,AID,ATY,DHI,U,ANINCR,SURCH: REAL;
DSC,DEV,DSP,DK: ARRAY[1..50] OF REAL;
HH,EEV,H,E,UE,SSUW,SP,EA,TK,AV,CV,T,EF: ARRAY[1..26] OF REAL;
DELU,UET,SPF,SCFF,HZ,EFF,SPIN,EIN,ZF,ZI,UEI,HIH,Eli,SPI: ARRAY[1..26] OF REAL;
AFISC,TIME,HEIGHT,DEGCONS: ARRAYU..20] OF REAL;
N,NP,NDP,I,J,KKK,NE,II,JJ,NZZZ,NPN,NN,NoPRINTS: INTEGER;
ABCD,InputCorrect,Run: Char;
Data,Outl: Text; {Name of I/O variables}
Name,DataFile,OutFilel: String[15];
Title: String[80];
CONST
GAMMAW=62.A;
FUNCTION Power(x,y: Real): Real; {Evaluates x”y}
Begin
Power:=EXP(y*LN(x));
End; {Power}
FUNCTION log(xx: Real): Real; {Evaluates log(xx)}
Begin
log:=0.4343*LN(xx) ;
End; {log}
Procedure PrintResults;
BEGIN
{*** Printing of Complete Results File: Outl ***}
Wr iteln(Out1);
Writeln(Outl,’Time = *,ATD:0:2,' days = ’,ATY:0:3,’ years’);
Writeln(Out1,’Elevation Void Ratio Eff. Stress Exc. Pore Press.’);
Write In (Outl,’ ’);
For I:=1 to NP Do
Writeln(Outl,HH[I]:8:2,EF[I]:12:2,SPF[I]:10:2,UET[I]:15:2);
Writeln(Out1,’New Height of Pond =’,HT:5:3);
Writeln(Out1,’Ave. Degree of Consolidation = ’,U:5:2, ’%’);
Writeln(’Time (days) = *,ATD:5:2,’ Height (ft) = ’,HT:5:2,’ U(Z) = ’,U:5:2)
END;
304

305
Procedure DegreeofConsol;
Label
19,20,21;
BEGIN
{*** Conversion of present Updated Lagrangian Coord, to Material ***}
ZF[NP]:=0.0;
DH2:=HH[1]/N;
NPN:=NP-3;
NN:=NP-2;
ZF[N]: = ((HH[N]-HH[NP])/2) *((1/(1+EF[NP])) + (1/(1+EF[N] ))) ;
BOTT:=(HH[N]-HH[NP])/((2*(1+EF[NP]))+(2*(1+EF[N])));
For I:=1 to NN Do
ZF[I];=BOTT+(HH[I]-HH[1+1])/((2*(1+EF[I]))+(2*(1+EF[1+1])));
For I:—1 to NPN Do
Begin
JJ:=NP-I-2;
For J:=l to JJ Do
ZF[I]:=ZF[I)+(HH[J+I]-HH[J+I+l])/((2*(1+EF[J+I]))+(2*(1+EF[J+I+l])));
End;
{*** Conversion of Lagrangian (initial) coord, to Material coord. ***}
DHI:=HIH111/N;
ZI[NP]:=0.0;
ZI[N]:=(DHI/2)*((l/(1+EII[NP]))+(1/(1+EIItN])));
BOTT;=DHI /((2*(1+EII[NP]))+(2*(l+EII[N])));
For I:=1 to NN Do
ZI[I]:=BOTT+DHI/((2*(1+EII[I]))+(2*(1+EII[1+1])));
For I:—1 to NPN Do
Begin
JJ:=NP-I-2;
For J:=l to JJ Do
ZI[I]:=ZI[I]+DHI/((2*(1+EII[J+I]))+(2*(1+EII[J+I+l])));
End;
EIN[1]:=EII[1];
J:-1;
For I:=2 to NP Do
Begin
19:If ZI[J] <= ZF[I] THEN GOTO 20;
J:=J+1;
GOTO 19;
20:EIN[I]:=EII[J]-(ZF[I]-ZI[J])*(ElI[J]-Eli[J-1])/(ZI[J]-ZI[J-l]);
End;
{*** Calculation of Effective Stress at end of Analysis ***}
For I:—1 to NP Do
SPIN[I]:=SPF[I]+UET[I];
{*** Calculation of void ratio at end of analysis ***}
For I:=1 to NP Do
Begin
For J:=l to NDP Do
If DSP[J] > SPIN[I] then Goto 21;
Writeln(’SPIN is out of the e-p-k data range’);
21:EFF[I]:—DEV[ J-1] + ((DEV[J]-DEV[J-1])*LOG(SPIN[I]/DSP[J-1])/LOG(DSP[J]/DSP[J-l]));
{WRITELN(SPIN[I]); }

306
End;
{*** Calculate the Average degree of Consolidation ***}
ROT:=(EIN[1]-EF[1]) /(2*(1+EIN[1]))+(EIN[NP]-EF[NP])/(2*(1+EIN[NP]));
R0:=(EIN[1]-EFF[1])/(2*(1+EIN[1]))+(EINtNP]-EFF[NP])/(2*(1+EIN[NP]));
For I:=2 to N Do
Begin
ROT:=ROT+(EIN[I]-EF[I])/(1+EIN[I] ) ;
RO : =RO+ (EIN [ I ] -EFF [ I ] ) / C 1+EIN [ I ] );
End;
U:=100*(ROT/RO);
END;
BEGIN
CLRSCR;
KKK:= 0;
{*** Input Data Routine **+}
7:Writeln(’Do you want to run Batch or Interactive? (B/I) ’);
ReadIn(Run);
If Run = ’B’ Then Goto 10;
If Run = ’I’ Then Goto 8;
Goto 7;
{*** Batch Data Input ***}
10:Writeln(’Input name of data file');
Writeln(’.DAT will be added by pgm’);
Readln(Name);
DataFile:=Name+’.DAT’;
Assign(Data,DataFile);
Reset(Data);
Readln(Data,Title);
Readln(Data,HI,SI,UMAX,SURCH) ;
Readln(Data,N,G2);
Readln(Data.NDP);
Readln(Data,ABCD);
If (ABCD = ’Y’) OR (ABCD = ’y’)
Then Readln(Data,AAA,BB,CC,DD)
Else
Begin
For I:=1 to NDP Do
Readln(Data,DSCtI],DSP[I],DK[I]);
End;
Close(Data);
Goto 2;
{*** Interactive Data Input ***}
8:Writeln(’Input Problem Title (80 char, max)’);
Readln(Title);
Writeln(’Input the initial height of the pond (ft)’);
Readln(HI);
Writeln(’Input the initial solids content (%)’);
Readln(SI);
Writeln('Input the max simulation time (yrs)’);
Readln(TIMAX);

307
Writeln('Input
Readin(SURCB);
WritelnC'Input
Readin(N);
WritelnC’Input
Readln(G2);
Writeln(’Input
the pond surcharge (psf)’);
the number of layers (25 max)’);
the specific gravity of clay’);
the number of points defining the
e-p and e-k
curves’);
Readln(NDP);
WriteC’Do you wish to input A,B,C,D parameters? (Y/N) ’);
Readin(ABCD);
IF (ABCD = ’Y’) or (ABCD = ’y’)
THEN
BEGIN
WritelnC’Input A’);
Readin(AAA);
Writeln(’Input B’);
Readin(BB) ;
Writeln(’Input C’);
Readin(CC);
Writeln(’Input D’);
Readln(DD);
END
ELSE
Begin
WritelnC’Input Experimental Data Points of’);
WritelnC ’ Solids Content (31), Eff. Stress (psf), and Permeability (ft/day)’);
FOR I:=1 TO NDP DO
Readin(DSC[I],DSP[I],DK[I]);
End;
WritelnC’Input name of file to store data’);
WritelnC’.DAT will be added by pgm.’);
Readin(Name);
DataFile:=Name+’.DAT’;
Assign(Data, DataFile);
Rewrite(Data); {Creates disk file to store data}
2: WritelnC’Summary of Inputs’);
Writeln(’l) Initial Pond height (ft) = ’,HI:5:2);
Writeln(’2) Initial Solids Content (%) = ’,SI:5:2);
Writeln(’3) Maximum Simulation Time (yrs) = ’,TIMAX:5:2);
Writeln(’4) Pond surcharge (psf) = ’,SURCH:5:2);
WritelnC’5) Number of layers = ’,N);
Writeln(’6) Specific Gravity of Clay = ’,G2:3:2);
WritelnC’7) Number of points defining the e-p and e-k curves
IF (ABCD = ’Y’) or (ABCD = ’y’)
Then
Begin
WritelnC’8) A = ’,AAA:5:2);
Writeln(’9) B = ’,BB:4:3);
WritelnC 10) C = ’ ,CC) ;
Writeln(’ll) D = ’,DD:5:2);
’,NDP);
End

308
Else
Begin
Writeln(’Exp. Mechanical Properties (Sol. Content, Eff. Stress, Permeability)');
FOR I:—1 to NDP DO
Writeln(1+7,’) *,DSC[I],DSP[I],DK[I]);
END;
Writeln(’Are all the values correct? (Y/N) ’);
Readln(InputCorrect);
If InputCorrect = ’N’
THEN
Begin
Writeln(’Input the number preceeding the incorrect parameter’);
Writeln(’and press the RETURN key’);
Writeln(’Input the corrected value and press the RETURN key once more’);
Readln(KKK);
If KKK=1 THEN Readln(HI);
If KKK=2 THEN Readln(SI);
If KKK=3 THEN Readln(TIMAX);
If KKK=4 THEN Readln(SURCH);
If KKK=5 THEN Readln(N);
If KKK=6 THEN Readln(G2);
If KKK=7 THEN Readln(NDP);
If KKK<8 THEN GOTO 2;
If (ABCD = ’Y’) or (ABCD = ’y’)
THEN
Begin
If KKK=8 THEN Readln(AAA);
If KKK=9 THEN Readln(BB);
If KKK=10 THEN Readln(CC);
If KKK=11 THEN Readln(DD);
End
ELSE
Readln(DSC[KKK-7),DSP[KKK-7),DK[KKK-7]);
GOTO 2;
End
ELSE
Begin
If (Run = ’B’) and (KKK = 0) Then Goto 9;
If Run = ’B’ Then Rewrite(Data);
WriteIn(Data,Title);
Writeln(Data,HI,SI.TIMAX,SURCH);
WriteIn(Data,N,G2);
Writeln(Data,NDP);
WriteIn(Data,ABCD);
IF (ABCD = ’Y’) or (ABCD = ’y’)
THEN Writeln(Data,AAA,BB,CC,DD)
ELSE
Begin
For I:-l to NDP Do
WriteIn(Data,DSC[I],DSP[I],DK[I]);
End;
End;

309
Close(Data);
9 :Writeln(’Output file: '.Name,1 .OUT');
WritelnC ’);
OutFilel:=Name+’.OUT';
Assign(Out1,OutFilel); Rewrite(Out1);
Writeln(Outl,Title); Writeln(Out 1,’ ’);
Writeln(Out1,’Summary of Data’);
Writeln (Outl, ’ ' );
Writeln(Outl,’1) Initial Pond height (ft) = ’,HI:0:2);
Wr iteln(Outl, ’ 2) Initial Solids Content (¡E) = ’,SI:0:2);
Writeln(Outl,’3) Maximum Simulation Time (yrs) = ',UMAX:0:2);
Writeln(Outl4) Pond Surcharge (psf) = ’,SURCH:0:2);
Writeln(Outl5) Number of layers = ’,N);
Writeln(Outl6) Specific Gravity of Clay = ’,G2:0:2);
Writeln(Outl7) Number of points defining the e-p-k curves = ’,NDP);
If (ABCD = ’ Y ’ ) or (ABCD = ’y’)
Then
Begin
Writeln(Outl,’8) A = ’,AAA:0:2);
Writeln(Outl,19) B = ’,BB:0:3);
WriteIn(Outl,’10) C = ’,CC);
Writeln(Outl,’11) D = ',DD:0:2) ;
End
Else
Begin
Writeln(Outl,’Exp. Data Points (Sol. Cont.(%), Eff. Stress (psf), Permeab.(ft/day)’);
For I:=1 to NDP Do
Writeln(Outl,DSC[I],DSP[I],DK[I]);
End;
Writeln(Outl,’ ’ ) ;
{*** Initialization Routine ***)
Writeln(’Input time (yrs) for first output of results’);
Writeln(’Subsequent outputs at twice the previous time’);
Readln(BINC);
Writeln(’Input inverse of ALPHA, e.g. 6 means ALPHA=l/6’);
Readln(ALPHAINV);
El:=G2*(100/SI-1); {Initial void ratio of the pond)
NE:=2; {Initial number of nodal points}
* Init
ial pond profile
HH [ 1 ] :
“HI;
EEV[1]
: “El;
HH[NE]
: =0 . ;
EEV[2]
: =EI;
{*** Generation of data points from A,B,C,D parameters ***}
If (ABCD = ’Y’) or (ABCD = ’y’)
THEN
Begin
DSC[1]:=SI-2;
If SURCH > 0. Then DSC[1];=SI-4.;
DEV[1]:=G2*(100/DSC[1]-1);

310
ANINCR:=(DEV[1]-1)/NDP; {Min. void ratio assumed as 1.}
FOR II:=2 TO (NDP+I) DO
Begin
DSP[II-1J:=Power(DEV[II-l]/AAA,1/BB); {Eff. Stress (psf)}
DK[II-1]:=CC*Power(DEV[II-l],DD); {Permeability (ft/day)}
DEV[II]:=DEV[II-1]-ANINCR;
End;
End
ELSE
Begin
For II;=1 to NDP DO
DEV[II]:=G2*(100/DSC[II]-1);
End;
AINC:=BINC; {First time interval for outputting the results}
ALPHA:=1/ALPHAINV; {Time step control factor, between 0. and 0.5}
WRITELN(OUTl,'ALPHA = 1 /’,ALPHAINV:0;0);
WRITELN(0UT1,' ’);
A:=0.; {Initialization for time interval between iterations}
NZZZ: =1;
NoPRINTS:=0;
{*** Initial Effective Stress: SLOAD ***}
For JJ:=1 to NDP DO
If DEV[JJ] < El THEN GOTO 3;
3: SLOAD:=SURCH+Power(10,(log(DSP[JJ-1])+((EI-DEV[JJ-1])*(log(DSP[JJ]/DSPtJJ-1]))/(DEV[JJ]-DEV[JJ-1]))))
{*** Compute Elevation of each layer ***}
DH:=HH[1]/N;
ZZZ:=1.0;
TB:=0.25;
{*** Main iteration process begins here *ftft}
REPEAT
NP:=N+1; {Number of nodal points}
H[NP]:-0.0;
FOR II:=1 TO N DO
Begin
JJ:=NP-II;
H[JJ]:=II*DH; {Elevation of each node}
End;
{*** Compute Void Ratio of each nodal point E[I] ***}
E[1]:=EEV[1];
JJ:=1;
FOR II:=2 TO NP DO
Begin
5:IF (NZZZ > 1) and (II = NP) THEN GOTO 4;
IF HH[ JJ] <= H[II ] THEN GOTO 6;
JJ:=JJ+1; GOTO 5;
6:E[II]:=EEV[JJ-1]+(H[II]-HH[JJ-1])*(EEV[JJ)-EEV[JJ-1])/(HH[JJ]-HH[JJ-1]);
4 : End;
UE[1]:«0.;
If (NZZZ > 1) Then E[NP]:=EEV[NP];

311
{*** Compute Stress due to Submerged unit weight ***}
SSUW[1]:=SLOAD;
For I:=2 to NP Do
SSUWtl]:=SSUW[I-1]+62.4*(H[I-1]-H[I))*(G2-1)/(1+0.5*(E[I-1]+E[I]));
{*** Compute Effective Stress at nodal points ***}
For I:-l to NP Do
BEGIN
For JJ:=1 to NDP Do
If (DEV[JJ] < E[I]) THEN GOTO 12;
Writeln(’Void Ratio of a nodal point outside the range of e-p-k data’);
GOTO 22;
12:SP[I]:“Power(10,(log(DSP[JJ-1])+(EtI1-DEV[JJ-1))*(log(DSP[JJ]/DSP[JJ-1]))/(DEV[JJ]-DEV[JJ-1])));
END;
{*** Compute Permeability and Compressibility of different layers ***}
For I:=1 to N Do
EA[I): =0.5*(E[I]+E[I + 1]) ;
For I:=1 to N Do
BEGIN
For JJ:=1 to NDP Do
If DEV[JJ] < EA[I] Then Goto 13;
Writeln('Average Void Ratio of a layer outside the range of e-p-k data’);
GOTO 22;
13:TK[I]:“Power(10,(log(DK[JJ-1]/8.64E+4) + (EA[I]-DEV[JJ-1])*(log(DK[JJ)/DK[JJ-1)))/(DEV £JJ]-DEV(JJ-1]))
{*** TK is in ft/sec ***)
COEF:=log(DSP[JJ]/DSP[JJ-1])/(DEV[JJ]-DEV[JJ-1]);
AV[I]:=Power(10 ,(-log(DSP[JJ-1])-COEF*(EA[I]-DEV[JJ-1])))/(2.303+COEF);
END;
For I:“l to N Do
Begin
CV[I]:=-TK[I]*(1.+EA[I])/(AV[I]* 6 2.A);
End;
{*** Compute minimum time for this iteration ***}
TM:=31.536E+06;
ALPHA:=1/ALPHAINV;
For I:=2 to N Do
Begin
T[I]:=ALPHA*DH*DH/CV[I];
If T[I] < TM Then
Begin
TM:“T[I] ;
J: “I
End;
End;
IF SURCH > 0 {Max. TM is 3.E+5 when SURCH is not zero}
THEN
BEGIN
If TM >= 3.E+5 Then TM:=3.E+5;
If TM >= 3.E+5 Then ALPHA:=TM*CV[J]/(DH*DH);
If (TM >= 3.E + 5) and (ALPHA >= 0.5) THEN TM:=0.A9*DH*DH/CV[J];

312
A:=A + TM;
ATD:=A/86400.;
ATY:=ATD/365.;
{New time step in seconds}
{ in days }
{ in years }
END
ELSE
BEGIN
OLDA:=A;
A:=OLDA+TM;
ATD:=A/86400 . ;
ATY:=ATD/365.;
IF ATY >= AINC THEN
BEGIN
ATY:=AINC;
ATD:=ATY*365.;
A:=ATD*864 00.;
TM:=A-OLDA;
ALPHA:=TM*CV[J]/(DH*DH);
END;
END;
{*** Find av for each node ***}
For I:=1 to NP Do
BEGIN
For J:=l to NDP Do
If DEV[J] < E[I] Then Goto 14;
14:COEF:=log(DSP[J]/DSP[J-l])/(DEV[J]-DEV[J-1]);
AV[I]:=Power(10,(-log(DSP[J-1])-COEF*(E[I]-DEV[J-1])))/(2.303*COEF);
END;
{*** Compute Excess Pore Pressure ***}
For I:=1 to NP Do
Begin
UE[I]:=SSUW[I]-SP[I];
End;
If NZZZ > 1 Then Goto 15;
Writeln(Outl,’*** Initial conditions ***’);
For I:—1 to NP Do
Begin
UEI[I]:=UE[I] ;
HIH[I]:—H[I] ;
Eli[I]:-E[I] ;
SPim : =SP [ I ] ;
End;
Writeln(Outl,’ Elev. Void Eff.Stress Buoyant Excess Pore’);
Writeln(Outl,’ (ft) Ratio (psf) Str.(psf) Press, (psf)’);
Writeln (Outl, ’ ' );
For I:-l to NP Do
Writeln(Outl.HIH[I]:10:2,Eli[I]:10;2,SPI[I]:10:2,SSUWtI]:10:2,UEI[I]:10:2);
Flush(Outl);
{*** Compute new pore pressure distribution ***}
15:UET[1}:=0.;

313
DELUíl]:=0.;
DELUtNP]:=2*(1+E[NP])*TM*TK[N]*(UE[NP]-UE[N])/(62.A*AV[NP]*DH*DH);
For I:=2 to N Do
DELUtl]: = (1+E[I])*TM*(TK[I-1]*(UE[I]-UE[I-1])-TK(I]*(UE[1+1]-UE[I]))/(62.4*AV[I]*DH*DH);
For I:=2 to NP Do
Begin
{ If abs(DELU[I]) <= l.E-7 Then DELU[I]:=0.0 ; }
IF DELU[I] > 0. THEN DELU11]:=0.0 ;
UET[I]:=DELU[I]+UE[I];
If UET[I] <= l.E-5 Then UET[I]:=0.0;
End;
For I:=1 to NP Do
UE[I]:=UET[I] ;
{*** Compute new Eff. Stress ***}
SPF[1]:=SL0AD;
For I:=2 to NP Do
Begin
SPF[I]:=SP[I]-DELUtl];
If SPF[I] < l.E-6 Then SPF[I]:=1.E-6;
{WRITELN(I,SP[I],DELU[I],SPF[I]);}
End;
{*** Compute new Void Ratio ***}
For I:=1 to NP Do
BEGIN
For J:=l to NDP Do
If (DSPtJ] > SPF[I]) Then Goto 16;
Writelnt’New value of Eff. Stress is out of range of e-p data’);
GOTO 22;
16:EF[I]:=DEV[J-l]+((DEV[J]-DEV[J-1])*log(SPF[I]/DSP[J-1])/log(DSP[J]/DSP[J-1]));
{WRITELN(J,DSP[J-1],SPF[I],DSP[J]); }
SCFF[I]:=100*G2/(G2+EFtI]); {New solids content}
END;
{*** Compute the new thickness of each layer ***}
For I:=l to N Do
HZ[I]:=DH*(1. + (((EF[I]+EF[I+1])-(E[I]+E[1+1]))/(2+E[I]+E[1 + 1] )));
{*** Compute the new elevation of each layer ***}
HH[NP]:=0.0;
For I:=1 to N Do
Begin
J:-NP-I;
HH[J]:=HH[J+l]+HZ[J];
End;
HT:=HH[1]; {New height of pond}
{*** Calculate the Average Degree of Consolidation ***}
DegreeofConsol;
{*** Print Control ***}

314
IF ATY >= AINC THEN GOTO 17;
IF U >= 99.9 THEN GOTO 17;
IF ATY >= UMAX THEN GOTO 17;
GOTO 18;
17:PrintResults;
NoPRINTS:=NoPRINTS+l;
{*** Compute Avg. Solids Content and assign values for Summary of Results ***}
FISC:=SCFF[1] ;
FOR I:—1 TO NP DO
FISC:=FISC+SCFF[I] ;
AFISC[NoPRINTS]:=FISC/NP;
TIME[NoPRINTS]:=ATD;
HEIGHT[NoPRINTS]:=HT;
DEGCONS[NoPRINTS]:=U;
{*** Increment time for next outputting of results and iteration number ***}
AINC:=AINC*2.0;
18:NZZZ:=NZZZ+1;
{*** Reassignation of new values to different variables ***}
For I:—1 to NP Do
EEV[I]:=EF[I];
NE:=NP;
DH:=HT/N;
UNTIL (ATY >= UMAX) OR (U >= 99.9);
{*** Print Summary of Results ***}
Writeln(Out 1, ’ ’ );
Writeln(Outl,’**************** SUMMARY OF RESULTS *******************'); Writeln(Outl,
Writeln(Out1,* Time Height Ave.Degree Ave. Sol.*);
Writeln(Outl,’ (days) (ft) of Consol(%) Content (%)’);
Write In (Outl, ’ ’);
For I:=1 to NoPRINTS Do
WriteIn(Outl,TIME[I]:10:2,HEIGHT[I]:10:2,DEGCONS[I]:13:2,AFISC[I]:15:2);
22:WRITELN(’EXECUTION TERMINATED’);
Close(Outl);
END.

315
Prediction of Pond KC80-6/0
Prediction using Exp. Data Points (e-p-k) from Test CRD-1
Summary of Data
1) Initial Pond height (ft) = 16.00
2) Initial Solids Content (%) = 16.00
3) Maximum Simulation Time (yrs) = 30.00
4) Pond Surcharge (psf) = 0.00
5) Number of layers = 10
6) Specific Gravity of Clay = 2.71
7) Number of points defining the e-p-k curves = 10
Experimental Data Points
Sol .
Cont.(%)
Eff. Stress (psf)
Permeability(ft/day)
15
. 30
0 ,
. 50
0 ,
. 700
15
. 75
2 ,
. 00
0 ,
. 150
16
. 12
4 ,
. 00
0 .
.070
17
.03
8 .
. 00
0 .
.032
19
. 21
24 ,
. 00
0 .
. 010
20
. 51
42 .
. 00
0 .
. 006
22
. 01
55 ,
. 00
0 ,
. 004
23
. 75
70 .
. 00
0 ,
. 003
25
. 78
100 .
. 00
0 ,
. 002
28
. 20
174 ,
. 00
0 ,
. 001
*** Initial conditions ***
Elev. Void Eff.Stress
(ft) Ratio (psf)
Buoyant
Str.(psf)
Exc e s s
Press .
Pore
(psf)
16
. 00
14 .
. 23
3 ,
. 21
3 .
.21
0
. 00
14
. 40
14 ,
. 23
3 .
. 21
14 .
.42
11
. 21
12
. 80
14 .
. 23
3 ,
.21
25 ,
. 63
22
. 42
11
. 20
14 .
. 23
3 ,
, 21
36 .
. 84
33 ,
. 64
9
.60
14 .
, 23
3 .
, 21
48 .
. 05
44
.85
8
. 00
14 .
. 23
3 .
. 21
59 .
. 26
56 ,
. 06
6
. 40
14 .
, 23
3 .
. 21
70 .
.48
67 ,
. 27
4
.80
14 .
. 23
3 .
. 21
81 .
.69
78 .
.48
3
.20
14 .
. 23
3 .
. 21
92 .
, 90
89 ,
. 69
1
. 60
14 .
. 23
3 .
, 21
104 .
, 11
100 ,
. 91
0 ,
. 00
14 .
23
3 .
, 21
115 .
. 32
112 .
. 12

316
Time = 45.63 days = 0.125 years
Elevation
Void Ratio
Eff. Stress
Exc. Pore
Press.
15.54
14.23
3 .21
0.00
13.98
14.20
3 . 34
10.77
12.43
14.17
3.53
21.49
10.87
14.13
3.81
32 . 17
9.32
14.09
4.03
42.92
7.76
14.06
4.12
53.83
6.21
13 . 99
4.37
64.61
4.66
13.81
5.01
75.11
3 . 10
13.49
6.43
84.99
1.55
12.96
9.26
93.80
0.00
11.97
16.95
98.41
New Height
of Pond =15
.536
Ave. Degree
of Consolidation = 9.58%
Time - 91.25 days = 0.
250 years
Elevation
Void Rat io
Eff. Stress
Exc. Pore
Press .
15.16
14.23
3.21
0.00
13.64
14.05
4.15
9 . 75
12.12
14.05
4.15
20.51
10.61
13.99
4.37
31.07
9.09
13.88
4.74
41.53
7.57
13.73
5 . 34
51.86
6.06
13.52
6.25
62.00
4.54
13.27
7 . 62
71.87
3.03
12.91
9 . 56
81.40
1.51
12 . 30
13.83
89.00
0.00
11.46
23.07
92 . 31
New Height
of Pond =15
.158
Ave. Degree
of Consolidation = 17.43%
Time = 182.
50 days = 0
.500 years
Elevation
Void Rat io
Eff. Stress
Exc. Pore
Press .
14.54
14.23
3.21
0.00
13.09
13.70
5.44
8 . 14
11.63
13 . 55
6 .12
18.07
10.18
13.42
6.78
28.13
8.72
13.28
7.57
38.15
7.27
13 . 12
8.43
48.22
5.81
12 . 88
9.72
58.01
4.36
12 . 55
11 . 90
67.14
2.91
12.12
15.46
75.21
1.45
11 . 58
21.44
81.30
0.00
10.95
31.69
83.69
New Height
of Pond =14
. 541
Ave. Degree
of Consolidation = 30.56%
30.56%

317
Time = 365.
00
days = 1 .
000 years
Elevation
Void Ratio
Eff. Stress
Exc. Pore
Press .
13.79
14.23
3.21
0.00
12.41
13 . 24
7 .79
5.42
11.03
12 . 94
9.41
14.24
9.65
12.72
10.70
23.60
8.27
12.51
12.18
32.92
6.89
12.27
14.13
41.96
5 . 52
11.99
16.76
50.53
4.14
11.66
20.43
58 . 34
2.76
11.29
25.62
64.94
1 . 38
10.88
33.14
69.60
0.00
10.39
43.42
71.96
New Height
o f
Pond =13.
792
Ave. Degree
o f
Consolidation = 46.62%
Time = 730.
00
days = 2 .
000 years
Elevation
Void Ratio
Eff. Stress
Exc. Pore
Press .
12.98
14.23
3.21
0.00
11.69
12.85
9.92
2 . 82
10.39
12.22
14.59
8 . 39
9.09
11.85
18.17
15.44
7.79
11 . 58
21.42
23.08
6.49
11.34
24.81
30.81
5.19
11.11
28.80
38 . 15
3.89
10.85
33.72
44.80
2 . 60
10.59
39.75
50.59
1 . 30
10.13
46.90
55.62
0.00
9.43
57 . 57
57.80
New Height
o f
Pond =12.
984
Ave. Degree
o f
Consolidation = 63.95%
Time = 1460
. 00
days = 4
.000 years
Elevation
Void Rat io
Eff. Stress
Exc. Pore
Press .
12.28
14.23
3 .21
0.00
11.05
12.68
11.03
1 . 25
9.82
11 . 86
18 . 14
4.01
8.59
11.37
24.47
8.07
7 . 37
11.02
30.35
12.93
6 . 14
10.74
36.13
18.18
4.91
10.50
41.99
23.59
3.68
10.06
47.91
29.28
2.46
9.61
54.88
34.40
1.23
9.05
63.72
38.24
0.00
8.49
75.99
39.37
New Height of Pond =12.277
Ave. Degree of Consolidation =
78.87%

318
Time = 2920
.0 0 days -
8.000 years
Elevation
Void Rat io
Eff. Stress
Exc. Pore
Press.
11.65
14.23
3.21
0.00
10.49
12.63
11.36
0.46
9 . 32
11.72
19.73
1 . 54
8 . 16
11.15
28.05
3 . 22
6.99
10.73
36.39
5.29
5.83
10.29
44.79
7 . 70
4.66
9 . 70
53.42
10.38
3 . 50
9 . 12
62.60
13.14
2.33
8.59
73.03
15 . 34
1.17
8.22
84.60
16 . 98
0.00
7.86
97.70
17.63
New Height
of Pond =11
.655
Ave. Degree
of Consolidation = 91.89%
Time = 5840
.00 days =
16.000 years
Elevation
Void Ratio
Eff. Stress
Exc. Pore
Press.
11 . 30
14.23
3.21
0.00
10.17
12 . 60
11.53
0.04
9.04
11.65
20.62
0.14
7.91
11.03
30.23
0.31
6.78
10.57
40.24
0.51
5.65
9 . 87
50.72
0.77
4.52
9 . 16
61.88
1.08
3.39
8 . 57
73.81
1 .37
2 .26
8 .17
86.41
1 . 64
1 . 13
7 .81
99 . 64
1 .82
0.00
7 . 60
113.45
1.87
New Height
of Pond =11
. 300
Ave. Degree
of Consolidation = 99.27%
Time = 6890
.45 days =
18.878 years
Elevation
Void Ratio
Eff. Stress
Exc. Pore
Press.
11.27
14.23
3.21
0.00
10.14
12 . 60
11 . 54
0.00
9.02
11 . 64
20.70
0.02
7.89
11.02
30.43
0.04
6.76
10.56
40.60
0.07
5.63
9.83
51.30
0.11
4.51
9.11
62.74
0.15
3.38
8.53
74.95
0.19
2.25
8.13
87.81
0.22
1.13
7.78
101.22
0.23
0.00
7.57
115.08
0.24
New Height
of Pond =11
.270
Ave. Degree of Consolidation =
99.90%

**************** SUMMARY OF RESULTS *******************
Time
(days)
Height
(ft)
Ave.Degree
of Consol(%)
Ave . S
Content
45 ,
.63
15 .
. 54
9 .
.58
17 .
. 96
91 .
.25
15 .
, 16
17 .
.43
18 .
. 32
182 .
. 50
14 .
, 54
30 ,
.56
18 .
.93
365 ,
. 00
13 .
, 79
46 ,
. 62
19 .
.73
730 .
. 00
12 .
. 98
63 .
. 95
20 .
.71
1460 ,
. 00
12 .
. 28
78 ,
. 87
21 .
, 66
2920 .
. 00
11 .
65
91 .
. 89
22 .
, 56
5840 .
. 00
11 .
30
99 .
. 27
23 .
, 10
6890 .
.45
11 .
27
99 .
. 90
23 .
, 14

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BIOGRAPHICAL SKETCH
Ramon E. Martinez was born in Panama City, Panama, on
November 24, 1951. He is the second of four children of
Damaso and Catalina Martinez. After completing elementary
and secondary schools, he decided that civil engineering was
his career and entered the College of Engineering at the
University of Panama in 1970. He graduated with a 214-
credit bachelor's degree in March of 1975.
During his senior year, Ramon worked part-time for a
major design and construction firm in Panama City. After
graduation, he continued to work with this company for one
year. It was then that he was offered the opportunity of
working for the Instituto Politécnico (former College of
Engineering of the University of Panama). Between 1976 and
1979, he worked as an instructor in the civil engineering
department, and was also involved in very important adminis¬
trative duties. While working for the Instituto Politéc¬
nico, Ramon completed a two-year graduate degree in system
analysis at the Universidad Santa Maria La Antigua in
Panama.
In August of 1979, Ramon married a wonderful girl,
Virginia Núñez. Immediately after getting married, they
moved to Ohio where Ramon attended The Ohio State Univer¬
sity. During his entire stay at OSU he worked as a research
assistant in the soil mechanics area under Dr. T.H. Wu.
326

327
Ramon received his M.S. degree in civil engineering in
April, 1981.
After receiving his M.S., Ramon returned to work for
the Instituto Politécnico, which soon became the Universidad
Tecnológica de Panama (UTP). In October of 1981 Ramon and
Virginia had a handsome son, Juan Ramon.
In 1983 Ramon won a tenure position in soils mechanics
and engineering sciences at the UTP. Always looking for
professional growth, he decided to continue graduate
studies. In January, 1985, he went to the University of
Florida to pursue a doctorate degree. At UF Ramon worked as
a reasearch assistant; he also taught a soils lab class.
During his studies at UF, Ramon became a member of Tau
Beta Pi, the National Engineering Honor Society. He is also
a charter member of the Pi Chapter of Phi Beta Delta, an
International Honor Society, and a student member of the
American Society of Civil Engineers.
As part of his doctoral work, Ramon wrote several
papers, including one presented at the VIII Panamerican
Conference on Soils Mechanics and Foundation Engineering, in
Cartagena, Colombia, in August, 1987.
In December, 1987, Ramon will receive his Ph. D . degree.
He and his wife are also expecting his second child in
December. Ramon and his family plan to return to Panama
where he will continue working for the UTP.

I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presenta¬
tion and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Frank C. Townsend, Chairman
Professor of Civil Engineering
I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presenta¬
tion and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presenta¬
tion and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Michael C. McVay
Associate Professor of Civil
Engineering
I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presenta¬
tion and is fully adequate, in scope and quality, as a^
dissertation for the degree of Doctor of Philosophy
David Bloom^ijist/
Assistant Engineer of Civil
Engineering

I certify that I have read this study and that in my opinion
it conforms to acceptable standards of scholarly presenta¬
tion and is fully adequate, i ’ ’ ' "
dissertation for the degree of Doclfo
/ Gustavo Antonini
Professor of Latin American
Studies
This dissertation was submitted to the Graduate Faculty of
the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
December 1987
Dean, College of Engineering
Dean, Graduate School

UNIVERSITY OF FUOR'p;
3 1262 08554 0333



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