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
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xiv, 327 leaves : ill. ; 28 cm.
Language:
English
Creator:
Martinez, Ramon E., 1951-
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Subjects

Subjects / Keywords:
Slurry   ( lcsh )
Soil consolidation test   ( lcsh )
Sedimentation analysis   ( lcsh )
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

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

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University of Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001081027
notis - AFG6004
oclc - 19109802
System ID:
AA00003375:00001

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 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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