New Structure-Based Model for Estimating Undrained

Shear Strength
Ozer Cinicioglu1; Dobroslav Znidarcic, M.ASCE2; and Hon-Yim Ko, M.ASCE3

Abstract: This paper presents an experimental study of the strength in anisotropic clays by means of centrifuge model, cone penetration,
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and vane shear tests. To understand the effects of void ratio, overconsolidation ratio, and testing rate on the undrained shear strength 共Su兲
of anisotropic Speswhite clay, a new centrifugal testing technique is designed to obtain constant overconsolidation ratio 共OCR兲 profiles
with varying void ratios 共e兲, called the “descending gravity test.” The parameters controlling the generation of peak shear strength are
quantified. As a result of this function, a new material and rate-dependent surface is defined in the e-OCR-Su space, which is identified as
a “structural state capacity surface” since it relates the anisotropic structure to structure inherent capacity and properties. A new function
for the estimation of excess pore pressure 共uex兲 generated by cone penetration is found. By combining the strength and pore pressure
functions a new model is proposed, called the “CU model.” The CU model is a structure-based model that provides reliable estimates of
shear strength for in situ saturated clays using the knowledge of void and overconsolidation ratios. Finally, by combining Su-e-OCR and
uex-e-OCR relationships, it estimates the void ratio and OCR profiles of anisotropic clays from piezocone penetration test results.
DOI: 10.1061/共ASCE兲1090-0241共2007兲133:10共1290兲
CE Database subject headings: Clays; Centrifuge; Void ratio; Cone penetration tests; Shear strength; Overconsolidated soils; Pore
water pressure; Vanes.

Introduction transforms into a new formation which is controlled by the void

ratio, granular shape, and size. But this concept presents a differ-
Shear strength is an important parameter for describing the resis- ent structural behavior than the one that is observed during the
tance of soil masses against shear stresses, but it is not a funda- peak failure of naturally deposited clays. Strength varies with the
mental soil property. It is dependent on various variables such as orientation of clay particles as the forces acting between them are
the orientation of the respective shear planes, type of testing, and completely different in the cases of parallel and random orienta-
tion. In the case of one-dimensionally anisotropic kaolin, the par-
the rate of shearing. Therefore, to be able to correctly estimate
ticles are flat plates, arranged mostly face to face in subparallel
shear strength under any condition, it is essential to link it to
groups called “domains.” These domains retain their identity, ori-
measurable and calculable soil properties. This paper presents a
entation, and relative positions during prepeak shearing. The gen-
new empirical model that is developed with the aim of relating
erated strain is accommodated by small changes in their sizes due
the shear strength of saturated cohesive soils to various measur- to particle packing as they slip over one another 共Bai and Smart
able and calculable soil properties. 1997兲. Therefore, since stress history is a parameter controlling
According to critical state soil mechanics theory, undrained the formation of these domains, peak undrained strength of one-
strength depends only on the void ratio. However, strength here is dimensionally anisotropic kaolin is dependent on stress history.
defined as the deviator stress at critical state. At critical state, The dependence of peak strength on stress history has been ob-
shear deformations can continue at constant effective stresses and served at the Massachusetts Institute of Technology on a wide
constant volume. The soil is being continuously churned up or variety of clays. It has been reported that the results of various
remolded 共Wood 1990兲. As a result, the effects of stress history laboratory tests on clay samples with the same overconsolidation
are obliterated. Under constant deformation, the granular structure ratio 共OCR兲, but different consolidation stresses, exhibit very
similar strength and stress–strain characteristics when normalized
1
Assistant Professor, Dept. of Civil Engineering, Bogazici Univ., with respect to the consolidation stress. Ladd and Foott 共1974兲
Bebek, Istanbul, Turkey, 34342 共corresponding author兲. E-mail: have adopted this observation to come up with a new design
ozer.cinicioglu@boun.edu.tr procedure for stability of soft clays from the normalized soil pa-
2
Professor, Dept. of Civil, Environmental and Architectural Engineer- rameter 共NSP兲 concept, called “stress history and normalized soil
ing, Univ. of Colorado, Boulder, CO 80309.
3
engineering properties” 共SHANSEP兲. The most frequently used
Professor, Dept. of Civil, Environmental and Architectural Engineer- NSP is Su/␴⬘v; in which ␴⬘v⫽in situ vertical effective stress. Ac-
ing, Univ. of Colorado, Boulder, CO 80309.
cording to SHANSEP
Note. Discussion open until March 1, 2008. Separate discussions must

冉 冊 冉 冊
be submitted for individual papers. To extend the closing date by one
month, a written request must be filed with the ASCE Managing Editor. Su Su
= OCRm 共1兲
The manuscript for this paper was submitted for review and possible ␴⬘v oc ␴⬘v nc
publication on March 30, 2006; approved on March 15, 2007. This paper
is part of the Journal of Geotechnical and Geoenvironmental Engineer- where m⫽soil parameter defining the relationship between nor-
ing, Vol. 133, No. 10, October 1, 2007. ©ASCE, ISSN 1090-0241/2007/ malized undrained shear strength values at different OCR levels.
10-1290–1301/$25.00. The validity of Eq. 共1兲 is dependent on the assumption that the

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 normalized strength parameter is a constant for each OCR. As a
result, the shear response is assumed to be completely frictional.
This may be correct for residual or ultimate strengths of reconsti-
tuted clays where the shear surface has already been created or
the stress history has been obliterated. But for peak strength the
outcome should depend on the combined effects of interlocking
and friction 共Schofield 1998兲.
Other than void ratio and stress history, rate dependency of
shear strength of cohesive soils has long been recognized by
many researchers. It was pointed out that the rate effect is caused
by the change in the excess pore pressure generated during the
shearing process. New techniques have been proposed to model
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the rate dependency of strength 共Lefebvre and Leboeuf 1987;

Sheahan et al. 1996; Zhu and Yin 2000; Katti et al. 2003兲.
As a result, it is found that void ratio, stress history, and rate
are the parameters that control the generation of undrained shear
strength in reconstituted cohesive soils. In this research a new Fig. 1. Container
centrifugal testing method is used to observe the uncoupled ef-
fects of void ratio, stress history, and testing rate on the genera-
testing equipment, materials, and testing procedure are described.
tion of undrained shear strength and accompanying excess pore
In the second part, the test results are presented. And in the final
pressure in reconstituted Speswhite clay. This new method is
part, the CU model is presented and discussed.
named the descending gravity test 共DGT兲 共Cinicioglu et al.
2006a兲.
Testing Equipment, Material, and Procedure
Descending Gravity Test
Testing Equipment
The descending gravity test is a new centrifuge test that combines The centrifuge employed in this research is located in the Depart-
in situ shear strength tests with a new material preparation tech- ment of Civil Engineering at the University of Colorado at Boul-
nique. By using this new material preparation technique, within a der. In the fully extended position, the top of the swing platform
one-dimensionally anisotropic sample it is possible to create a is at a radius of 5.5 m. This centrifuge has a payload capacity of
section where the OCR does not change as the void ratio changes 1,800 kg and it is capable of accelerating to a maximum of 200g.
with depth. This section of the clay model is called the constant The configuration of the container that houses the clay model
OCR section 共COS兲. As explained in detail in Appendix I, the is shown in Fig. 1. Prior to the test, the container containing the
OCR of the COS is found as 共Cinicioglu et al. 2006a兲 clay cake is placed inside a specifically designed testing frame
that is located on the centrifuge arm. The testing frame 共Fig. 2兲 is
␻2max designed to conduct CPT and vane shear tests, and to rotate the
OCR = 共2兲 container in-flight. There are four motors on the frame that are
␻2u
used to operate the turntable which is used to rotate the container
where ␻max⫽maximum angular rotational speed; and ␻u⫽angular in-flight to reach virgin testing sites on the clay model, to facili-
rotational speed of the centrifuge during the unloading stage. tate cone and vane penetration, and to apply torque to the vane
When this new material preparation technique is combined with rod.
in situ shear strength tests, such as the cone penetration test 共CPT兲 The piezocone used in this research is approximately 175 mm
and the vane shear test that has been used for this research, and in length with a tip area of 1 cm2. The piezofilter is located on the
repeated for a series of successively lower g levels—which cor- shoulder of the cone tip 共u2兲. The vane is 12.7 mm in height and
respond to a series of successively greater OCRs within the 12.7 mm in width. Moreover, six miniature pore pressure trans-
COS—this new test is called the descending gravity test. DGT ducers are used to monitor the consolidation process.
provides the void ratio–shear strength relationships for various
OCRs. Therefore, it renders the observation of the uncoupled ef-
Material
fects of void ratio and OCR on the generation of shear strength
feasible. The soil that has been used as a testing material is reconstituted
Obtained data from the DGTs conducted during this research Speswhite clay. Speswhite clay is almost 100% kaolinite and clas-
are used to construct an empirical model named the CU model. sified as CH. Its plastic limit is 32% and plasticity index is 21%.
The reason for calling this model CU is that the tests were con- The specific gravity is 2.66. Basic physical properties of Sp-
ducted in the centrifuge by successively unloading the model eswhite clay are presented in detail by Peric et al. 共1988兲. From
under consolidated-undrained conditions. Also, the tests were the results of oedometer tests, the average coefficient of consoli-
conducted at the University of Colorado at Boulder. CU model dation 共cv兲 is found as 15.3 m2/year for the loading history and
estimates the test specific undrained shear strength and the ac- stress ranges of the centrifuge tests.
companying excess pore pressure generated in one-dimensionally
consolidated cohesive soil using the knowledge of void ratio and
Defining the e-␴v⬘ Relationship for Speswhite Clay
OCR profiles. Also, it allows the engineer to back-calculate the
void ratio and OCR profiles by using the undrained shear strength Since the goal of this study is to obtain the void ratio–shear
and excess pore pressure data. In the first part of this paper, the strength relationships for various OCRs, it is imperative to track

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Fig. 2. Configuration of the frame: 共a兲 side view; 共b兲 plan view; and 共c兲 photograph

the changes in the void ratio profile during the DGT. This is e = 共␣A ln ␴⬘vo + ␤A兲 . 关␴⬘v + Z兴共␣B ln ␴⬘vo+␤B兲 共4兲
achieved by obtaining e-␴⬘v data from a step loading test in an
oedometer, and constructing representative functions of the load- where ␣A, ␤A, ␣B, ␤B⫽parameters defining the semilogarithmic
ing and unloading processes. The extended power function relationship between parameters A, B and preconsolidation stress
proposed by Liu and Znidarcic 共1991兲 has been selected for math- 共␴⬘vo兲 共Cinicioglu et al. 2006a兲.
ematically defining the e-␴⬘v relationship of Speswhite clay:
Preparation for the Test
e = A共␴⬘v + Z兲B 共3兲
The model is prepared by consolidating clay slurry. During this
where A, B, and Z⫽empirical consolidation constitutive param- research, water content of 1.36 has been chosen for the prepara-
eters specific for the normal consolidation or unloading–reloading tion of the slurry since this value corresponds to the empirically
lines 共url兲 they are obtained for. The methods for obtaining and found appropriate water content at which the Speswhite clay
calculating these parameters have been explained in detail by Liu
and Znidarcic 共1991兲. However, in its original form, this extended
power function Eq. 共3兲 has to be defined exclusively for each url.
This is a drawback since in the case of DGT, there are an infinite
number of urls. Undoubtedly, it is impossible to obtain the param-
eters for all urls by testing. But given that the urls have the same
shape 共which means parameter Z is the same for all urls兲 and are
parallel in the e-log ␴⬘ graph, it has been found that it is possible
to find a trend between the parameters A, B, and the preconsoli-
dation stresses 共␴⬘vo兲. When the A and B parameters calculated
from experimentally obtained urls are plotted against respective
preconsolidation stresses, semilogarithmic relationships are ob-
tained 共Fig. 3兲. Using these semilogarithmic relationships, the
path followed by soil of known preconsolidation stress on the e-
␴⬘v graph can be mathematically defined without resorting to ex-
clusive step-loading tests. Accordingly, modifying Eq. 共3兲 to in- Fig. 3. Variation of A and B parameters with respect to preconsoli-
clude A and B as functions of ␴⬘vo we get dation pressure

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 slurry can be prepared and poured without entrapping air in. The
slurry is preconsolidated in the model container by surcharge
loading. After the completion of consolidation under the selected
preconsolidation pressure, the surcharge load is released and the
sample rebounded. Then, pore pressure transducers are inserted at
predetermined positions. Finally, the sample is placed in the test-
ing frame on the centrifuge arm for the initiation of the test.

Selection of Testing Rates

Since undrained strength is investigated, selection of an appropri-
ate testing rate is critical. The selected cone penetration rate
Fig. 4. Comparative CPTs at subsequent g levels: 共a兲 loading from
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should provide undrained conditions during all stages of the test.

20 to 60g; 共b兲 loading from 1 to 20g
For an undrained cone penetration test in clay, the recommended
constant rate of penetration is 20 mm/ s 共Lunne et al. 1997兲 for
standard size cones 共35.7 mm diameter兲 under earth’s gravity.
Bolton et al. 共1993兲 used miniature cone penetrometer 共10 mm boundaries. Therefore, the total degrees of rotation sum up to
diameter兲 during centrifuge tests on kaolin clay. They have used 2,000°, which would require an excessive amount of time with
undrained penetration rates ranging from 3.6 to 26 mm/ s. A non- the recommended field testing rates. Matsui and Abe 共1981兲 sug-
dimensional velocity for assessing the degree of consolidation gested that the undrained testing of kaolin can be achieved at rates
during penetration is proposed by Finnie and Randolph 共1994兲 greater than 1°/s. Bolton et al. 共1993兲 reported that increasing the
rate from 1.2 to 6°/s resulted in a 6–10% increase in shear
vd strength. This is an indication of possible drainage since 6°/s
V= 共5兲
cv corresponds to less than 10% drainage according to the time fac-
tor suggested by Blight 共1968兲 and with the vane and clay used by
where v⫽cone velocity; and d⫽cone diameter. Using this nondi- Bolton et al. 共1993兲. Therefore, rotational speed of the vane was
mensional velocity, Randolph and Hope 共2004兲 present a back- selected to be 50°/s as a result of time constraints and to assure
bone curve for kaolin clay obtained by cone penetration tests in that shearing is completely undrained.
centrifuge. From the investigation of the data, it is observed that
the penetration resistances drop up to a V value of 400. This
suggests that there is no viscous rate effect up to this point. Un- Testing Method
fortunately, there are no reported test results for V values greater Centrifuge is used to obtain various e-OCR profiles within the
than 400. Because this value is reported as a result of tests on clay model. This is achieved by varying the angular swept veloc-
kaolin clay, an average V value of 400 is adopted for this work. ity, therefore, changing the self-weight stresses in the clay. When
This corresponds approximately to 20 mm/ s rate with the avail- a desired soil profile is obtained in-flight 共calculated from the e-
able cone penetrometer and within the stress ranges experienced ␴⬘v relationship of the soil, and verified through pore pressure
by Speswhite clay. Therefore, cone penetration rates ranging from monitoring兲 then in situ tests are conducted on virgin testing sites.
5 to 30 mm/ s have been used in this study to create undrained This is accomplished by rotating the model container, located
conditions. inside the testing frame, around its axis via rotating the turntable
The presence of viscous rate effects during CPT has been in- 共Fig. 2兲. When the stationary minipiezocone and vane shear de-
vestigated for the model scale changes due to the centrifugal vices are above previously determined testing sites, they are in-
forces. Employed method was to conduct comparative CPT tests serted into the model to obtain the shear strength profiles. To
on the same soil with the same penetration rate, but at different g minimize the disturbance from the neighboring tests, the relative
levels. This was achieved by performing subsequent CPTs, one positions of the testing sites on the model surface are determined
being at the end of the consolidation process at one g level, and by taking into account the in situ testing device dimensions and
the other immediately at the next g level. As a result the soil did the size of the container.
not have sufficient time to consolidate or to rebound, hence, the A reference penetration rate for CPT is used for all e-OCR
void ratios and effective stresses were almost identical 共there may profiles. However, to examine the effects of penetration rate on
be minor differences as a result of the duration of centrifuge the shear strength and generated pore pressure, CPTs can be re-
speeding up or slowing down兲. But the g levels were significantly peated occasionally with different rates. Results from the simul-
different. Any viscous effect as a result of model scale change taneous vane shear tests are used as a reference to obtain the
would have been noticed from the comparison of the cone resis- necessary cone factor Nkt. The cone factor is defined as the em-
tances. Fig. 4 shows some results obtained from such comparative pirical parameter that is used to relate the CPT tip resistance
CPT tests. Clearly, there are no viscous rate effects as a result of measurements to undrained shear strength. By using a total stress
model scale change. Therefore the selected penetration rates for approach the cone factor is obtained as 共Lunne et al. 1997兲
CPT are suitable at any g level to be used as the undrained pen-
etration rate. qt − ␴v
The vane rotation rate has to be chosen considering the testing Nkt = 共6兲
Su−R
time limitations. The total rotation angle was selected as 400° to
be able to observe the residual drop of strength. Additionally, for where qt⫽corrected cone tip resistance; ␴v⫽total overburden
obtaining the shear strength profile, five vane shear tests were pressure at the level of the cone tip; and Su-R⫽reference und-
conducted during each penetration event. The vertical locations of rained shear strength obtained by the reference shear strength
these tests were selected such that they are one vane diameter test—vane shear test. Accordingly, the rotation rate of the vane
away from the neighboring tests and from the top and bottom shear device is kept constant throughout each centrifuge test.

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 Table 1. Summary of the Tests
Test

Measurement 1 2 3
␴⬘vo 共kPa兲 360 100 70
Model thickness 共mm兲 164 157 157
g levels 1-20-60-150-60-20 1-20-60-150-60-20 1-150-50-30-15-1
DGT — 3 3
COS OCRS — 1-2.5-7.5 1-3-5-10-150
COS thickness 共mm兲 — 50 75
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Tests context, it is useful to investigate the shear strength–void ratio

relationship for constant OCR values. The void ratio profiles, cal-
In the course of this project, three different centrifuge tests were culated using the constitutive relations in Eqs. 共3兲 and 共4兲 are later
conducted 共Table 1兲. The final two of these tests were descending verified by obtaining samples from the model after the completion
gravity tests. The main differences of these three tests were the of the DGT test. Void ratio profiles measured by testing the ob-
chosen initial preconsolidation pressures and the g levels. As tained samples are compared with the calculated profiles to con-
shown in Table 1, the preconsolidation pressure of the model firm the accuracy of predictions. Figs. 6 and 7 show the void
during Test 1 was 360 kPa. The basis for the selection of such a ratio–shear strength relationships obtained from the COS of Tests
high stress level is obtaining compatibility with some previous 2 and 3, respectively. The void ratio values are calculated by
centrifuge model tests. As a result, the combination of the sample using Eq. 共4兲 and constant OCR values are calculated by using
thickness and the centrifuge capabilities was not sufficient to cre- Eq. 共2兲. From these results shown in Figs. 6 and 7, it is possible to
ate a constant OCR section 共COS兲 within the clay model. But the claim that void ratio-shear strength relationship is linear for a
different OCR and void ratio profiles of Test 1 were very valuable constant OCR value, and this linear relationship is dependent on
for the evaluation of the constructed model. A single penetration the value of the OCR. This phenomenon will be further investi-
rate of 10 mm/ s was used for all CPTs of Test 1. gated and quantified in the CU Model section of this paper.
Both during Tests 2 and 3, COS were created within the clay As previously pointed out, in situ tests were carried out by a
model. The initial preconsolidation stresses of the models as a piezocone penetrometer which, in addition to cone tip measure-
result of surcharge loading–unloading outside the centrifuge were ments, simultaneously measures the pore pressure. Evidently,
100 and 70 kPa, respectively. Test 3 was solely designed as a variation of pore pressure with depth is similar to the variation of
DGT, and Test 2 was designed as a transition test with a first undrained shear strength with depth. This similarity of response
half—before 150g—similar to Test 1 and a second half—after the should be anticipated since excess pore pressure generated by
generation of a COS at 150g—similar to Test 3 共Table 1兲. The cone penetration is a product of the disturbance to the soil struc-
OCRs of the COS during Tests 2 and 3 are given in Table 1. ture, as tip resistance measurements are. This parallel behavior
A single penetration rate 共10 mm/ s兲 for all CPTs and a single can be appreciated by examining the void ratio–excess pore pres-
rotation rate 共50°/s兲 for all vane shear tests were used during Test sure relationships obtained from the COS of Test 3 共Fig. 8兲. With-
2. However during Test 3, three different CPT rates were used. out a doubt, the void ratio and CPT-generated excess pore
CPTs for the evaluation of the effects of void ratio and OCR on pressure relationship is linear for constant OCR. When the OCR
undrained shear strength were conducted at 20 mm/ s, and from changes, the slope and zero intercept of this linear relationship
time to time these tests are repeated both with 50 mm/ s and also changes. However, it should be noted that pore pressures
30 mm/ s rates to observe the changes in the measured shear
strength profiles and generated excess pore pressures.

Test Results

Cone factors 共Nkt兲 obtained from the comparison of all simulta-

neous CPT and vane shear tests has been found to vary around 8.
Therefore, this value is found to be suitable for calculating the
shear strength from the cone tip resistance measurements.
The most noteworthy observation obtained from the analysis
of the shear strength-depth profiles is the different trends of re-
sponse obtained from the varying OCR and COS. Fig. 5 shows
the shear strength–depth profiles obtained from some of the CPTs
conducted on samples with COS. Visibly, the soil in the COS
共below 100 mm depth兲 responds differently. The possible expla-
nation to this observable fact is the absence of the OCR effect. In
a naturally deposited overconsolidated clay layer, OCR varies
with the stresses as void ratio does. As a result, shear strength
varies with depth similar to the shear strength–depth profiles ob- Fig. 5. Su depth profiles obtained from samples with constant OCR
tained from the varying OCR section 共VOS兲 of the model. In this sections

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Fig. 8. e-uex relationships obtained from the constant OCR section of

Fig. 6. Void ratio–shear strength relationships obtained from the
Test 3
constant OCR section of Test 2

CU Model

The linear void ratio–shear strength relationships, obtained during

measured via u2 piezocone during DGT should be corrected for the DGT of Test 3 for different OCRs 共Fig. 7兲 have been quanti-
time lag in order to be able to compare pore pressure measure- fied by simple mathematical expressions. As a result of the lin-
ments at different g levels. The u2 pore pressure measurement earity, the void ratio–shear strength relationship for a single OCR
correction is explained in Appendix II. can be written as follows 共Cinicioglu 2005兲:
The undrained shear strength and excess pore pressure values
obtained at different CPT rates are very close, suggesting und- Su = Te + R 共7兲
rained conditions for the range of penetration rates that have been where T and R⫽empirical parameters defining the slope and the
used. However, even though not sufficient for quantification, the zero intercept, respectively. These parameters are dependent on
results also suggest that there is a slight dependence on penetra- the stress history of the soil and the rate of testing. Their units are
tion rate for both Su and uex, which increases with increasing the same as Su. Su⫽undrained shear strength calculated from the
OCR. The results of this rate comparison, even though not con- cone tip measurements by using the appropriate cone factor 共Nkt兲.
clusive, have been reported by Cinicioglu et al. 共2006a兲. This calculation method does not alter the e-Su relationship since
Nkt is a function of OCR and the plasticity index, which are con-
stants within the COS 共Francescon 1983; Almeida and Parry
1985; Aas et al. 1986; Powell and Quarterman 1988兲.
To quantify the dependency of the T and R parameters on
OCR, the values obtained from different g levels corresponding to
different OCRs are plotted in Fig. 9. Consequently, the T共OCR兲
and R共OCR兲 functions are found to be in the form of a power
function. These power functions can be quantified as follows:
T = bTOCRkT 共8兲

R = bROCRkR 共9兲
where bT, bR, kT, and kR⫽rate-dependent empirical parameters
that can be obtained for a specific clay by conducting DGT tests.
The parameters bT and bR have the units of stress, and the param-
eters kT and kR are unitless. Finally, we obtain the equation for
undrained shear strength as shown
Su = Te + R = 共bTOCRkT兲e + 共bROCRkR兲 共10兲
This equation is rate dependent since the e-Su relationship is rate
dependent 共Cinicioglu et al. 2006a兲. The validity of Eq. 共10兲 has
been investigated by comparing the obtained Su profiles of Tests
1, 2, and 3 with the estimations of Eq. 共10兲. The differences in
rate are not considered here, since the penetration has been shown
to be completely undrained for the range of 5–30 mm/ s. Some of
the results are shown in Fig. 10. Clearly, the estimations closely
captured the trends of the experimentally obtained Su-depth
profiles.
Fig. 7. e-Su relationships obtained from the constant OCR section of Eq. 共10兲 defines a special surface in the e-OCR-Su space 共Fig.
Test 3 11兲. The shape and location of this surface is material and shear-

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Fig. 10. Comparisons of the experimentally obtained and estimated

Su depth profiles

range of void ratios. For void ratios greater than this range, the
Fig. 9. Variation of T and R parameters with OCR and the obtained peak failure is obtained on the Hvorslev surface. This transition
functions void ratio range is expected to depend on the grain size and shape.
The effect of this transition void ratio on the shear strength is
more plainly observed in Fig. 12共b兲. Each line in Fig. 12共b兲 rep-
ing rate dependent. It yields the peak undrained shear strength resents the OCR-Su relationship at a different void ratio.
values for any combination of void ratio and OCR for the refer- Visibly, undrained shear strength increases with OCR for soils
ence testing rate. This surface is not a state boundary surface, with a greater void ratio than the transition void ratio range, and
because even though the void ratio and OCR define the preshear decreases with OCR for soils with a lower void ratio than the
state of the soil, Su represents the capacity of this state to with- transition void ratio range. This is a consequence of the response
stand shear stresses. Therefore, a new terminology is necessary. of the clay domains to shear. The domains and the force chains
The surface defined by Eq. 共10兲 is a “structural state capacity formed by domains 共Wood 2004兲 as a result of one-dimensional
surface.” It relates the structure to the structure inherent capacity anisotropy 共Bai and Smart 1997兲 form a strong structure against
and properties. There are some advantages of using this surface, prepeak shearing. However, since these domains are formed by
such as: particles of flat plates, as the OCR of the clay increases the do-
• The surface is dependent on the measured preshear soil prop-
erties, not soil properties at the time of failure.
• The surface is a result of one-dimensionally anisotropic soil
behavior; therefore, it is suitable for field conditions.
• It covers all possible combinations of void ratios and OCRs
for reconstituted clays that are inside the scope of soil mechan-
ics problems, which also include the highly overconsolidated
clays with low void ratios and soils that fail on the Hvorslev
surface 共Fig. 11兲. The only exception is clays with very high
void ratios, which require further investigation with more sen-
sitive equipment.
• The surface is defined by parameters that can be obtained by
conducting a single DGT.
For better perception, Figs. 12共a and b兲 present the projections
of the surface on the e-Su and OCR-Su planes, respectively. In Fig.
12共a兲, each line represents the e-Su relationship for a single OCR
value. Clearly, as the OCR increases the slopes of the linear rela- Fig. 11. Surface defined by the Su共e,OCR兲 function in the e-OCR-Su
tionships decrease. Consequently, the lines intersect at a small space

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Fig. 13. Variation of F and C parameters with OCR and the obtained
Fig. 12. Projection of the Su共e,OCR兲 function on the e-Su plane functions

main buckling and force chain buckling as a result of preferred The breadth of the deformed soil surrounding the cone is depen-
orientation increases. Even though this interlocking behavior at dent on the cone diameter and the rate of penetration. As a result,
high void ratios results in high shear strength, at small void ratios unlike the T and R parameters of shear strength, parameters F and
it leads to a more unstable structure due to the stored buckling C of excess pore pressure are cone diameter dependent. F and C
energy. Therefore, under shear stresses, highly overconsolidated vary with OCR in the form of an extended power function, as
clays at low void ratios fail sooner as a result of a repressed shown in Fig. 13. Therefore, the uex共e,OCR兲 function for a spe-
buckling mechanism. Since the energy stored within a domain cific penetration rate and certain cone diameter can be written as
as a result of overconsolidation is dependent on particle shape
uex = eF + C = e关bF共OCR + jFC兲kF兴 + 关bC共OCR + jFC兲kC兴
and size, the transition void ratio is a function of the particle
characteristics. 共13兲
Similar behavior is observed from the results of the void ratio– where bF, bC, kF, kC, and jFC⫽rate- and cone diameter-dependent
excess pore pressure relationship. This is expected since excess empirical parameters that can be obtained for a specific clay by
pore pressure generated as a result of cone penetration is a con- conducting DGT with a certain cone penetrometer. The param-
sequence of the deformation of the same structure. The linear e-u2 eters bF and bC have the units of stress, and the parameters kF, kC,
relationships for different OCRs 共Fig. 8兲 can be represented by a and j FC are unitless. The validity of Eq. 共13兲 has been investigated
function as by comparing the obtained uex profiles of Tests 1, 2, and 3 with
uex = eF + C 共11兲 the estimations of Eq. 共13兲. The differences in rate are not con-
sidered here. Some of the results are shown in Fig. 14. Clearly,
where F and C⫽empirical parameters defining the slope and the the uex estimations were close to the experimentally obtained uex
zero intercept of the linear relationship, respectively. uex⫽excess profiles.
pore pressure, which is obtained as The combination of Su-e-OCR and uex-e-OCR relationships
constitutes a structure-based model. This model is called the CU
uex = u2 − uo 共12兲
model. The Su and uex functions as given by Eqs. 共10兲 and 共13兲,
where u2⫽pore pressure measured at the shoulder of the cone tip, respectively, have the same variables; e and OCR. As a result of
and uo⫽hydrostatic pore pressure. Hydrostatic pore pressure is their different parameters, they link the same structural properties
used since the data in Fig. 8 were obtained at the completion of to different outcomes as shear strength and excess pore pressure.
consolidation and swelling processes. It should be noted here that Since these two relationships form two equations with two un-
the calculated uex values were corrected for the time difference knowns, by using both of them it is possible to predict the void
between the instants of initial generation and measurement as ratio and OCR profiles of clay from the knowledge of the Su and
explained in Appendix II. uex profiles, which are measured by piezocone penetration tests.
The generated pore pressure during CPT is a consequence of This method requires knowledge of the presence of possible ex-
the instantaneous compression of the clay surrounding the cone. cess pore pressures in the soil, which should be investigated by

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 Table 3. Measured Values of CU Model Parameters for Excess Pore
Pressure
Excess pore pressure parameters Values
bF 共kPa兲 −972.50
bC 共kPa兲 1,742.30
kF −0.41
kC −0.40
jFC −0.98

Discussion
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One of the interesting features of the CU model is the power

function form of the shear strength and excess pore pressure func-
tions, shown by Eqs. 共10兲 and 共13兲, respectively. Both of these
functions have OCR as a variable. As a result of its definition,
OCR is a power function itself 关OCR= f共␴⬘v兲 = ␴⬘vo共␴⬘v兲−1兴. There-
fore, any function with OCR as a variable yields a power function
as in the cases of Eqs. 共10兲 and 共13兲.
Fig. 15 represents the Su共e,OCR兲 function defined by the CU
model on the preshear ␴⬘v-Su plane. It is clear that the behavior is
not frictional. Solely frictional behavior can only occur between
well-defined surfaces sliding with respect to each other. Since
saturated-reconstituted clay is a continuum, to have a completely
frictional failure, first the continuum has to be broken. The con-
tinuum of clay is formed by particles that interlock. When the
initial deformations occur due to shearing, the particles move
around each other, getting rearranged in the direction of the shear
band. The process requires shear stresses to overcome the combi-
Fig. 14. Comparisons of the experimentally obtained and estimated nation of interlocking and friction. Therefore, the peak shear
uex depth profiles strength is a function of both interlocking and friction. Here, one
should not confuse peak strength with critical state or residual
strength. It is clear from Fig. 15 that according to the CU model,
the ␴⬘v-Su relationship is dependent on the OCR. As the vertical
stopping the cone several times and allowing the CPT-generated effective stress 共␴⬘v兲 increases, in other words as the void ratio
excess pore pressure to dissipate. Tables 2 and 3 present the mea- decreases, the interlocking mechanism dominates the peak shear
sured values of CU model parameters for Speswhite clay. These strength. Therefore, both the interlocking and friction mecha-
values were obtained at a CPT rate of 20 mm/ s and by using vane nisms are functions of preshear void ratio and OCR. To obtain the
shear as the reference test. It should be noted that the rate depen- magnitudes for interlocking 共c兲 and friction angle 共␾⬘兲, the tan-
dency of the parameters should be investigated. Additionally, the gent to the surface for the specific OCR should be found, as
reference strength test should be chosen by considering the pos-
sible failure mechanism investigated. Consequently, the CU
model serves several purposes:
• It provides reliable estimates of shear strength for one-
dimensionally anisotropic saturated clays, using the knowl-
edge of void ratio and OCR.
• It provides estimates of excess pore pressure generated as a
result of cone penetration.
• By combining Su-e-OCR and uex-e-OCR relationships, it esti-
mates the e and OCR profiles of anisotropic clays from CPTU
measurements.

Table 2. Measured Values of CU Model Parameters for Shear Strength

Shear strength parameters Values
bT 共kPa兲 −230.90
bR 共kPa兲 390.40
kT −0.22
kR −0.21 Fig. 15. Depiction of the Su共e,OCR兲 function on the ␴⬘v-Su plane

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J. Geotech. Geoenviron. Eng. 2007.133:1290-1301.

 shown in Fig. 15. Consequently, structural properties such as fric- ␻ 2r
tion and interlocking have physical meanings within the CU N= 共15兲
g
model.
There are some limitations to the applicability of CU model. where ␻⫽angular rotational velocity of the centrifuge; and
For clays with very high void ratios, which do not form interlock- r⫽radius to any element in the soil model. Radius r is assumed to
ing structures, the strength is a consequence of a mechanism that be constant since the deformations are miniscule compared to the
combines both internal friction and rolling of particles without radius of the centrifuge. N is called the g level. Clearly, N is a
volume change. Because of the inadequacy of Eq. 共10兲 to capture controlled factor and it is dependent on the angular rotational
the transition to this different mechanism, the estimated shear velocity of the centrifuge. As a result, N is the only variable in Eq.
strength values at high void ratios reach zero even though there 共14兲. To be able to track the changes in the void ratio profile, it is
are effective stresses present. Another limitation of CU model is necessary to prepare the clay slurry uniformly at a predetermined
the shear strength of extremely stiff clays for which interlocking void ratio. As a result, the initial void ratio 共ei兲, and the initial
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totally dominates the behavior therefore failure occurs by the undeformed depth of the clay slurry are known to the researcher.
breaking of clay particles. This phenomenon may be regarded as Subsequently, the equivalent thicknesses of solids above any hori-
a rock mechanics problem out of the context of soil behavior. zontal slurry layer can be calculated by using the following
equation:

Conclusion Dsa = Dia/ei 共16兲

where Dia⫽depth of a horizontal layer in the slurry. Since all the
A series of centrifuge tests have been designed and carried out to parameters other than the g level in Eq. 共14兲 are constants after
understand the uncoupled effects of void ratio and OCR on the the preparation of the slurry, the effective stress can be calculated
undrained shear strength of one-dimensionally anisotropic Sp- at any instant by using the appropriate g level. This gives the
eswhite clay. The centrifugal testing method, solely designed for researcher the flexibility to monitor the changes in the void ratio
this purpose, is called the Descending Gravity Test 共Cinicioglu et by using the previously obtained parameters of Eqs. 共3兲 and 共4兲.
al. 2006a兲. Obtained results have revealed that the undrained This can be achieved even by a simple worksheet function. Then,
shear strength varies linearly with void ratio for constant OCR the thickness of the model can be back-calculated from the cal-
profiles and these linear relationships are dependent on the OCR. culated void ratios. The obtained values can be verified through
A similar pattern of behavior has been observed from the mea- measurements and sampling.
surements of excess pore pressure generated by cone penetration. The model preparation technique is composed of two distinct
The Su and uex functions have been quantified to construct a struc- phases. The first phase is the preconsolidation of the clay slurry
ture based model called the CU model. Shear strength function of by surcharge loading and unloading outside the centrifuge, and
CU model defines a surface in the e-OCR-Su space which yields the second phase is the formation of the desired testing conditions
the peak shear strength values for any combination of void ratio in the centrifuge by increasing the body forces within the precon-
and OCR including soils that fail on the Hvorslev surface. In solidated clay cake to obtain stresses that are dependent on the
other words, it relates the structure to structure inherent capacity relative positions of soil layers. The initial preconsolidation pres-
and properties. Therefore it is defined as a “structural state capac- sure, obtained by the step loading and unloading process outside
ity surface,” because it is dependent on the measured preshear soil the centrifuge, is a constant for the entire soil profile. However,
properties, not soil properties at the time of failure. Additionally, during centrifuge spinning at sufficiently high g levels, soil below
it is a result of anisotropic behavior, thus it is suitable for field a certain depth may consolidate under a vertical stress equal to the
conditions. From the perspective of the CU model, the peak sample’s initial preconsolidation pressure. If that is the case, the
strength of soil is a consequence of combined effects of interlock- stress state of the sample at that certain depth and deeper reaches
ing and internal friction mechanisms. And finally, by combining the normal consolidation line. Due to the nature of centrifuge
Su-e-OCR and uex-e-OCR relationships, CU model estimates the testing, the vertical stresses increase significantly with depth.
void ratio and OCR profiles of anisotropic clays from CPTU data. Therefore, for a clay model that is consolidated normally in the
centrifuge, the stress state of any layer in the normally consoli-
dated region represents a unique point on the normal consolida-
Appendix I. Descending Gravity Test tion line in the e-␴⬘v graph. Consequently, when the consolidation
is complete under these stress conditions, the preconsolidation
The details of the theory and material preparation for DGT have stress of each layer becomes a function of soil depth for the
been given by Cinicioglu et al. 共2006a兲. It is a well-based assump- portion of soil that is normally consolidated. This section of the
tion that during one-dimensional consolidation, no clay particle sample is called the COS. When this sample is unloaded, we
can pass other particles. Therefore, the amount of solids 共not soil, obtain a different unloading–reloading line for each unique pre-
solids without any voids兲 above any horizontal layer within the consolidation stress. Unloading of the clay layer in the centrifuge
model remains constant, and the end of consolidation vertical corresponds to decreasing the angular rotational speed of the cen-
effective stress 共␴⬘v兲 at any point can be calculated by using the trifuge. Therefore, the OCR of the COS is found as 共Cinicioglu
buoyant unit weight of solids—soil particles without any voids— et al. 2006b兲
⬘ 兲
共␥solid
␴⬘v = NDsa␥solid
⬘ = NDsa␳w共Gs − 1兲g 共14兲 ␴⬘vo NmaxDsa␳w共Gs − 1兲g Nmax ␻2max
OCR = = = = 2 共17兲
␴⬘v NuDsa␳w共Gs − 1兲g Nu ␻u
where Dsa⫽equivalent thickness of the solids above the corre-
sponding horizontal soil layer; g⫽earth’s gravitational accelera- where Nmax⫽g level during the normally consolidated state of the
tion; ␳w⫽mass density of water; Gs⫽specific gravity of solid COS; and Nu⫽g level at the unloaded state. Since the g level is
particles; and N⫽gravity ratio as defined in Eq. 共15兲 the only variable in Eq. 共17兲, the equation simplifies to the form

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / OCTOBER 2007 / 1299

J. Geotech. Geoenviron. Eng. 2007.133:1290-1301.

 Notation

The following symbols are used in this paper:

A , B , Z ⫽ consolidation constitutive parameters;
C , F ⫽ empirical excess pore pressure parameters;
Dsa ⫽ thickness of solids above a certain layer;
Gs ⫽ specific gravity;
H , Y ⫽ empirical parameters defining the effect of
gravity on u2;
K ⫽ absolute permeability;
N ⫽ gravity ratio;
Nkt ⫽ empirical cone factor;
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Nmax ⫽ maximum gravity ratio;

Nu ⫽ gravity ratio at the unloaded state;
R , T ⫽ empirical shear strength parameters;
Fig. 16. Obtained uex-1g/uex-Ng ratios from Test 2
Su ⫽ undrained shear strength;
Su-r ⫽ reference undrained shear strength for Nkt;
V ⫽ nondimensional velocity;
of Eq. 共2兲. Consequently, even though all layers within the COS bC, kC, jFC ⫽ empirical parameters defining C;
unload on different unloading lines, their OCRs are a function of bF, kF, jFC ⫽ empirical parameters defining N;
the angular rotational speed of the centrifuge. Since the ratios of bR, kR ⫽ empirical parameters defining R;
the angular rotational velocities are equal to each other for all bT, kT ⫽ empirical parameters defining T;
points in the clay model, all the layers within the COS have the cv ⫽ coefficient of consolidation;
same OCR after unloading. Even if the OCR is the same for all d ⫽ cone diameter;
the layers within the COS, the effective stresses they are experi- e ⫽ void ratio;
encing and unloading lines they are following are different. g ⫽ earth’s gravitational acceleration;
Therefore, their void ratios are different. kNg ⫽ coefficient of permeability of water at Ng;
qt ⫽ corrected cone tip resistance;
r ⫽ radius;
u ⫽ pore pressure;
Appendix II. Correction of uex for the g Level u2 ⫽ pore pressure measured at the cone
shoulder;
The excess pore pressure generated as a result of cone penetration uex ⫽ excess pore pressure;
共uex兲 is measured at the back of the cone 共u2兲 after a time lag that uo ⫽ hydrostatic pore pressure;
is dependent on the speed of penetration. During this interval v ⫽ cone penetration velocity;
some amount of excess pore pressure dissipates into the perim- ␣A, ␣B, ␤A, ␤B ⫽ empirical consolidation parameters;
eter. The amount of dissipation is a function of the penetration ⬘ ⫽ buoyant unit weight of solids;
␥solid
rate and the hydraulic conductivity. Unfortunately, during centri- ␮ ⫽ absolute viscosity;
fuge testing hydraulic conductivity is dependent on the g level of ␳w ⫽ mass density of water;
the test ␴⬘v ⫽ vertical effective stress;
␴⬘vo ⫽ preconsolidation stress;
N␥w ␻max ⫽ maximum angular rotational speed; and
kNg = K 共18兲
␮ ␻u ⫽ angular rotational speed at the unloaded
state.
where kNg⫽hydraulic conductivity when the g level of the centri-
fuge is equal to N; K⫽absolute permeability; and ␮⫽absolute
viscosity of the pore fluid. References
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