CONSOLIDATION PROPERTIES OF PHOSPHATIC CLAYS
FROM AUTOMATED SLURRY CONSOLIDOMETER
AND CENTRIFUGAL MODEL TESTS
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
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
GOD BLESS THEM ALL.
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
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
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
ACKNOWLEDGMENTS ...................... ..................... iii
LIST OF TABLES ......................... ................... viii
LIST OF FIGURES ......................................... ix
A BSTRA CT ................................................ x iii
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
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...........
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
LIST OF TABLES
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
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 ........
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
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. ...................
- 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 .............
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..
.......... 24 5
. .. .. 2 52
.. .. .. 28 3
... ....... 285
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
RAMON E. MARTINEZ
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
An automated slurry consolidometer, which is fully
controlled by a computer-data acquisition system that
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.
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
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
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
Alternative tests are being developed. These include
settling column tests, constant rate of deformation consoli-
dation tests, and others. Chapter II will discuss the
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
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).
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
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.
BACKGROUND AND LITERATURE REVIEW
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
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
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)
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
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;
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;
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
k cy av Yw (2.1)
1 + ef
with cv T h(2.2)
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
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
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
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
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
the right approach it can provide both, the compressibility
and permeability relationships, over a wide range of void
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.
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)
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
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
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
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
acceptable deformation rate should produce a maximum excess
pore pressure of up to 30%-50% of the applied stress
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
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
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
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-
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,
obtained from the equation of fluid continuity (Poindexter,
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
of the material at relatively low void ratios (e < 7)
(Ardaman and Assoc., 1984).
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
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.
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.
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
e A.(a')B (2.8)
Likewise, the permeability relationship was expressed by the
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 parameters A,B,C,D obtained by several studies for
Kingsford phosphatic clay are presented in Table 2-1.
Table 2-1. Kingsford Clay Parameters
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,
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
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,
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
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,
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
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.
AUTOMATED SLURRY CONSOLIDOMETER--
EQUIPMENT AND TEST PROCEDURE
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
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
Power Supply Manual Control
Figure 3.1 Schematic of Automated Slurry Consolidometer
Power Connection T
Suppl Box T
I I ., LVDT
Su0y suPPLY J SI
to t I- IF= =
DIMENSIONS IN INCHES
Figure 3.2 Schematic of Slurry Consolidometer Chamber
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
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
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,
POROUS ELECTRICAL CONNECTION
DISC RED: SUPPLY POSITIVE
BLUE: SUPPLY NEGATIVE
YELLOW: OUTPUT POSITIVE
GREEN: OUTPUT NEGATIVE
Figure 3.3 Pore Pressure Transducer PDCR81. a) Photograph;
b) Sketch Showing Dimensions
model GCD-121-1000 and manufactured by Schaevitz, has a
nominal range of 1 inch and linearity of 0.25% at full
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
00 Lt) 14-4
PL|CL A AL
00 C\ r-4
04 40 1
-4 0-0 1=
r--( CN M
:L4 P64 C4 a
:3: 1-- :: ::
P14 rW a4 OL4
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
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
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
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
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
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
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
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
and to leave the HP-6940B exclusively to control the
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
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
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
Subroutine CALIBRATIONS reads the calibration factors
for all the devices from a file on disk; it allows changing
or adding new devices to the file, after displaying the
current configuration on the monitor. Subroutine INITIALI-
ZATION takes the initial readings of the transducers and
LVDT; it also prints the general test information and
headings of the results table.
Subroutine STEPPING activates the motor as requested
by either the CRD or CHG routines. Subroutine RUNTIME
evaluates the elapsed time of the test at any moment.
Subroutines READLOWVOLT and READHIGHVOLT read consecutively
all the devices.
Subroutine CONVERTDATA uses the readings of the
transducers and LVDT, and their calibrations, to compute all
the pressures, load, and specimen deformation; these
parameters are stored on disk for future data reduction.
Subroutine TESTEND decides whether any of the conditions to
finish the test has been reached. Appendix D presents a
flowchart of the main routine of SLURRY1, and a listing of
the full program.
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-
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
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-
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
Figure 3.9 Vacuum System
Fill with 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
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
The following is a list of the steps followed in the
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
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
5. Set the height of water to the height to be used in the
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
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
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
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
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
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
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
(0.014 psi) is taken as the approximate sensitivity of these
AUTOMATED SLURRY CONSOLIDOMETER--
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
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
i^_ ^ ^ ^^ ^ ^ ^ ^
_______ ^ / /
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
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)
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)
-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
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.
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
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
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)
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
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
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)
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)
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)
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.
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
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
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
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
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
log axes, according to the user's choice. A listing of
SLURRY2 is included in Appendix E.
AUTOMATED SLURRY CONSOLIDOMETER--
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.
Table 5-1. Conditions of Eight Tests Conducted
Test hi (cm) Si (%) Rate (mm/min) Gradient
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-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.
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
ca U') mr CT) C'a -) oo rl- co
V" V" W" V"-4 -4
" o'01408 PI0A
+_ %_o __ 4
+ E___ ~4- Q
to in cm 0 C'D m- r- t~ o
6 'OT-40 PTOA
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-
When the data of test CRD-2, with a dilute specimen,
was first reduced, the average effective stress showed
negative values up to a solids content of about 13.5%. The
data reduction program was later modified to make zero any
negative effective stress computed at the location of the
pore pressure transducers. This result seems to indicate
that below this solids content the slurry has no effective
stresses, or these are two low to be detected with the
equipment used. Once the program was modified to eliminate
negative values, it was observed that the average effective
stress increased above 0.01 psi (the estimated sensitivity
of the transducers) when the solids content was again about
13.4%. Figure 5.2 shows the compressibility and permeabi-
lity curves of test CRD-2 as plotted by SLURRY2. The
initial portion of the compressibility plot (Figure 5.2a)
shows clear evidence of pseudo-static piston friction.
Another interesting aspect of the plot is the step-like
shape. This effect may be attributed to a discontinuity in
the computed effective stress when the piston passes by
transducer No. 3 (at h 11.235 cm.), as a result of the
analytical approach used. However, this irregular effect is
not observed with the same magnitude in all the tests. The
permeability plot, on the other hand, exhibits a well
defined trend with almost no scatter.
The new chamber described in Chapter III was used for
the rest of the tests. It was found that the 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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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
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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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
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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
Table 5-2 summarizes the conditions of the specimens at
the end of the four CRD tests, and shows the duration of
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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