Upload
others
View
19
Download
0
Embed Size (px)
Citation preview
Beesley, M. E. W., & Vardanega, P. J. (2019). Parameter variability ofundrained shear strength and strain using a database of reconstituted soiltests. Canadian Geotechnical Journal. https://doi.org/10.1139/cgj-2019-0424
Peer reviewed version
Link to published version (if available):10.1139/cgj-2019-0424
Link to publication record in Explore Bristol ResearchPDF-document
This is the author accepted manuscript (AAM). The final published version (version of record) is available onlinevia NRC Research Press, Canadian Science Publishing at https://doi.org/10.1139/cgj-2019-0424 . Please referto any applicable terms of use of the publisher.
University of Bristol - Explore Bristol ResearchGeneral rights
This document is made available in accordance with publisher policies. Please cite only the publishedversion using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/user-guides/explore-bristol-research/ebr-terms/
Page 1
Parameter variability of undrained shear strength and strain using a database of reconstituted soil tests
Mair E. W. Beesley, MEng (Brist.)
PhD student,
University of Bristol,
Department of Civil Engineering,
Bristol, BS8 1TR, UK,
Email: [email protected],
ORCID: 0000-0002-7495-2368
Paul J. Vardanega, BE MEngSc (QldUT) PhD (Cantab) GMICE MASCE MIEAust FHEA
Senior Lecturer in Civil Engineering,
University of Bristol,
Department of Civil Engineering,
University of Bristol,
Bristol, BS8 1TR, UK,
Email: [email protected],
OCRID: 0000-0001-7177-7851
No. words in main text: ≈ 2,700
No. figures: 3
No. tables: 3
Page 1 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 1
Parameter variability of undrained shear strength and strain using a database of reconstituted soil tests
M. E. W. Beesley and P. J. Vardanega
ABSTRACT
During construction, the mobilisation of undrained shear strength must be limited to avoid soil failure.
Soil strains must be controlled to avoid compromising structural serviceability. To assess foundation
performance by strength mobilisation, an understanding of soil strains at various levels of strength
mobilisation is required. In practice, ground investigation data is often limited, and assessment of the
expected variation of stress-strain and undrained shear strength is improved with empirical correlations
calibrated with a database. The new database RFG/TXCU-278 contains data of 278 consolidated-
undrained triaxial tests on reconstituted fine-grained soil samples compiled from the literature. Analysis
of the database to evaluate the variability of undrained strength ratio (cu /'v0) and a reference shear
strain with shear mode is undertaken in this paper. The new database provides evidence that shear strain
(like undrained shear strength) is sensitive to the consolidation (isotropic or K0) and shear mode (triaxial
compression or extension) applied in the test. For the materials included in the database, the strength
mobilisation parameters obtained from a triaxial compression test can be used to predict the
corresponding triaxial extension parameters to a reasonable accuracy.
Keywords: Databases, Stress-strain, Fine-grained soils
INTRODUCTION
Prediction of soil strains at increments of stress ratio or mobilisation level cf. BSI, 1994) allows
engineers to better evaluate foundation performance. For this purpose, the Mobilisation Strain
Framework (MSF) is a convenient model for characterising nonlinear stress-strain from undrained shear
test data (Vardanega and Bolton 2011; Vardanega et al. 2012). Whether a simple hand calculation or a
more advanced numerical model is used, checking the possible range of ground movements at any
mobilisation level requires the selection of representative design parameters which are often determined
by experiment. If a test is representative of the site, ref (a reference strain parameter) controls undrained
foundation settlement at 50% mobilisation. This important question of whether the soil test is
Page 2 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 2
representative can only be answered if the possible variation of ref within the displacement mechanism
is known.
Understanding parameter variability by database analysis
Variability of a soil test parameter arises from an incomplete knowledge of its variation with different
test conditions together with the contribution of natural geological variation. Database analysis is an
essential tool for characterising geotechnical variability (e.g., Kulhawy and Mayne 1990; Mayne 1980;
Phoon and Kulhawy 1999a,b; Ching and Phoon 2013, 2014a) and many empirical correlations between
measured parameters are available in the literature. A decision to use general parameter trends for
design depends largely upon the availability of data from the ground investigation. For example, to
measure the anisotropy of undrained shear strength (cu) at a ground investigation site advanced testing
apparatus such as the hollow cylinder could be used to shear soil specimens to peak failure following
different complex stress paths (e.g. Brosse et al. 2017). Alternatively, a variety of soil tests can be
employed to assess the effect of shear mode on cu variation (e.g., Low et al. 2011; Ratananikom et al.
2015). In practice, projects often have limited scope for detailed ground investigation and advanced
experimental work. When project test data is scarce, predicting the variation in cu /'v0 or must
necessarily be estimated from any available test information. Databases such as RFG/TXCU-278 can
also be used to establish prior estimates of relevant statistical parameters for subsequent Bayesian
analysis as has been done for standard geotechnical parameters in the works of Cao and Wang (2014),
Cao et al. (2016) and Wang et al. (2016).
Variation of Undrained Strength Ratio
It is well established that cu is sensitive to its method of measurement. For example, differences have
been observed from comparisons of test specimens that were either unconsolidated or reconsolidated
(Chen and Kulhawy 1993), isotropically or anisotropically consolidated (Mayne 1985), sheared in
different directions (Mayne and Holtz 1985) and at various strain rates (Sheahan et al. 1996; Kulhawy
and Mayne 1990). Undrained shear strength is also known to vary with stress history (Ladd et al. 1977;
Mayne 1980; Jamiolkowski et al. 1985; Chandler 1988; Ladd 1991). Ladd et al. (1977) proposed a
Page 3 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 3
framework for clays exhibiting ‘normalized behaviour’ that enables the prediction of cu if in-situ
effective vertical stress and OCR are known (Equation 1):
( 𝑐𝑢 𝜎ˈ𝑣0)
𝑂𝐶
( 𝑐𝑢 𝜎ˈ𝑣0)
𝑁𝐶
= 𝑂𝐶𝑅𝛬 (1)
Where, Λ = fitted exponent; σ'v0 = present vertical effective consolidation stress; (cu /σ'v0)OC = normalised
strength of an overconsolidated material; (cu /σ'v0)NC = normalised strength of a normally consolidated
material; and OCR = ratio of maximum past vertical effective consolidation stress to present vertical
effective consolidation stress.
Using large databases of soil tests, Mayne (1988) and Ching and Phoon (2014b) showed that
the fitted regression coefficient Λ was sensitive to the consolidation type (isotropic or anisotropic) and
mode of shear (triaxial compression or extension). Following the framework proposed by Kulhawy and
Mayne (1990), Ching and Phoon (2013) developed a data-driven method to standardise cu /σ'v0 using
modification factors to capture the effects of different test mode, OCR, strain rate and plasticity index.
Variation of Mobilised Strain
While much research effort has focussed on understanding cu variability, less information is available
to quantify the variability of shear strains. The Mobilisation Strain Framework (MSF) has been
developed to incorporate undrained strength mobilisation parameters in a framework suitable for
reliability-based design style approaches (Vardanega and Bolton 2016a) by employing a simple power-
law model. Equation (2) can be fitted to shear stress-strain data if the peak failure stress is known
(Vardanega and Bolton 2011) and can be expressed as:
0.2 ≤ mob/cu ≤ 0.8 (2)1𝑀 =
𝜏𝑚𝑜𝑏
𝑐𝑢= 0.5( 𝛾
𝛾50 𝐶𝐼𝑈)𝑏𝐶𝐼𝑈
Where, M = mobilisation factor (which is akin to a reduction factor on undrained shear strength);
τmob = the mobilised shear strength; = shear strain; 50 CIU = shear strain to mobilise 0.5cu under
isotropically-consolidated undrained conditions (denoted in previous works as M=2 and for compression
and extension tests the notation 50 CIUC and 50 CIUE is respectively used in this paper); and bCIU is an
Page 4 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 4
exponent to describe non-linearity (ductility): for compression and extension tests the notation bCIUC and
bCIUE is respectively used in this paper.
Equation (2) is similar to models used in classic p-y curve work for offshore structures which
often assume a set ‘b’ value and thus imply a constant soil ductility (Matlock 1970; Zhang and Anderson
2017). A variant of Equation (2) has been incorporated in the AUS constitutive model recently presented
in Krabbenhøft et al. (2019).
Vardanega and Bolton (2016b) when discussing the work of Casey et al. (2016) did
acknowledge that a modification of Equation (2) is needed when considering K0-tests (shown here in
the form of Equation 3) making use of the B parameter which was proposed in Casey et al. (2016) and
Vardanega (2012). Equation 3 reduces to Equation 2 if 0 = 0 (isotropic stress conditions).
(3)𝜏𝑚𝑜𝑏 ― 𝜏0
𝑐𝑢 ― 𝜏0= 𝐵 = 0.5( 𝛾
𝛾50 𝐶𝐾𝑈)𝑏𝐶𝐾𝑈 0.2 ≤
𝜏𝑚𝑜𝑏 ― 𝜏0
𝑐𝑢 ― 𝜏0≤ 0.8
Where, τ0 = initial shear stress; γ50 CKU = shear strain to mobilise 0.5(cu – τ0) (denoted in previous works
as ref and for compression and extension tests the notation 50 CKUC and 50 CKUE is used in this paper);
and bCKU is an exponent that describes soil non-linearity (ductility): for compression and extension tests
the notation bCKUC and bCKUE is respectively used in this paper.
The importance of shear mode was highlighted by P. W. Mayne when discussing Vardanega et
al. (2012) (Vardanega et al. 2013): ‘[one] must take care in the mixing and matching of different
strength modes’. Klar and Klein (2014) also pointed out that the experimental stress-strain function
used in a model prediction should be based on tests simulating the appropriate stress path (for instance,
triaxial extension was selected for their study of volume losses with tunnel advancement). Casey (2016)
observed that a large difference in reference strain measured in triaxial compression may occur as a
result of using an isotropic or K0 consolidation stress path and recommended Equation 4 to describe
the variation of reference strain with OCR for CKUC tests:
(4)𝛾50 𝐶𝐾𝑈𝐶 = 0.0004(𝑂𝐶𝑅)1.57
By extending the application of the MSF framework to different triaxial stress paths, the key
contribution of this paper is in demonstrating the likely variation in stress-strain response with
consolidation type (CIU or CKU) and shear mode (triaxial compression or extension).
Page 5 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 5
Comparing shear modes to estimate parameter variation
The mobilisation strain parameters can be used in any serviceability design method that requires a
characteristic nonlinear stress-strain curve in the moderate to high strain range (e.g., Lam and Bolton
2011, McMahon et al. 2014). Procedures of settlement prediction which rely upon the assumption of
similarity between the load-settlement relationship and the experimental stress-strain curve (e.g.,
Skempton 1951; Bolton et al. 1990; Osman and Bolton 2005; Klar and Klein 2014) require the selection
of an ‘average’ characteristic curve. When ground investigations are limited, a method to quantify the
variation of deformation parameters due to changing shear modes is valuable when evaluating the
sensitivity of such parameters. As a first step we examine the effect of shear mode and stress history
(OCR) on the MSF parameters in absence of the effects of soil structure. To this end a large database
of reconstituted soils tests was compiled.
DATABASE: RFG/TXCU-278
The new database RFG/TXCU-278 is analysed of to examine the influence of applied shear mode on
cu /σ'v0, 50 CIU, 50 CKU, bCIU and bCKU for reconstituted soils. Two shear modes are investigated: triaxial
compression and triaxial extension. Table 1 lists the sources of data in the database compiled from
experiments on 23 fine-grained soils from 21 publications. Shear stress-strain data from 278
consolidated undrained triaxial tests were digitised or acquired from the authors’ tabulated data where
available. The selection criteria for the database were:
(i) Multiple experiments using reconstituted samples of natural fine-grained soil,
(ii) consolidated at different overconsolidation ratios (OCR), under isotropic or K0 conditions,
(iii) and subsequently sheared in triaxial compression or extension up to peak failure to examine the
effect of applied shear mode. (Several datasets included samples sheared in compression only,
to increase the range of soil types studied – see Table 1).
Strain rate corrections were not applied to the digitised test data as a universal modification factor for
strain measurements was not available. Previous studies have shown that cu increases by 10 to 20% per
log cycle of increased strain rate (Kulhawy and Mayne 1990). The number of digitised data-points for
each triaxial test ranged from 3 to around 200 with a mean of 24. Therefore, for consistency the model
Page 6 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 6
parameters were derived by applying either Equation 2 or 3 as appropriate to the digitised test data and
then using the fitted equation to calculate them (e.g., 50 CIUC and bCIUC).
Classification of database samples
Classification of the 23 experimental soils indicate a wide range of plasticity (Figure S1), with about
70% of materials classified as inorganic and medium-high plasticity. Materials classified outside of this
range include the processed kaolin clays, which cluster close to the A-line, and a low plasticity glacial
till investigated by Gens (1982). With exception of the kaolin materials, all soils included in
RFG/TXCU-278 were sampled from natural deposits.
ANALYSIS
The power-law model (Equation 2 or 3) was fitted to the data points of 271 tests with a range of 0.779
≤R2≤0.9999 and 0.0017≤S.E.≤0.0925. Seven tests provided only peak stress data. The collected
test database is presented in sub-databases of specimen consolidation type (isotropic or K0) and shear
mode (triaxial compression or triaxial extension) which are identified by test mode i.e. CIUC, CIUE,
CKUC and CKUE. Undrained strength data from a triaxial test database (number of tests = 70) of
natural clays, digitised from Mayne and Holtz (1985), are also presented for comparison: about 75% of
each sub-database consists of normally consolidated specimens, with OCR ranging from 1 to 25 for
CIU tests and 1 to 20 for CKU tests.
Empirical correlations (or transformation models) of the test parameters were investigated
using linear regression analysis and standard errors were calculated to describe scatter in the data. An
alternative description of parameter variability using predicted vs. measured plots and bandwidths of
prediction error is valuable (Koutsoftas et al. 2017; Kootahi and Mayne 2017), particularly when
evaluating the variability of different parameters (or the uncertainty of different transformation models).
All factor errors quoted in this paper refer to a region that encompasses 80% of the data points and may
be viewed in graphical form in the Online Supplement.
Page 7 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 7
Correlation between triaxial extension and compression parameters
The undrained strength (Figure 1) and strain parameters obtained for each digitised test are presented
by comparing extension and compression modes. Pairs of tests (i.e. extension and compression) on the
same material with identical OCR (±0.1) and strain rate were selected from each published series of
experiments. Linear regression analysis indicates that a significant relationship exists between cu/σ'v0
measured in compression and in extension for samples consolidated under either isotropic or K0
stresses, with a high coefficient of determination and p<0.001 (see Figure 1). K0-consolidated specimens
appear to have greater strength anisotropy and less scatter (standard error). The intact soils show similar
ranges in cu/σ'v0 to the reconstituted soils and produce close best-fit lines between normalised
compression and extension strengths. On average, intact soils demonstrate to some extent greater
strength anisotropy and more variability than reconstituted soils. A comparison of predicted vs.
measured reconstituted soil data shows the factor error of the regression to be 1.3 to 1.4 depending on
consolidation type (Figure S2).
Significant correlations also exist between the reference strains measured in triaxial extension
and compression, although only reconstituted soil data are available. Figure 2 shows that the reference
strains are less sensitive to shear mode if tested from an isotropic stress state: the slope regression
coefficient for CKU tests is five times the slope for CIU tests. Reference strains mobilised in CKUE, in
some cases, are one order of magnitude greater than the strains mobilised in CKUC; considerable scatter
of the strain anisotropy (Figure S3) warrants further investigation. No correlation to describe the shear
mode effect was found for bCKU or bCIU (see Table 2 for average means and standard deviations) although
the CKU tests analysed here show more disparity between compression and extension (see Figure S4).
Using the framework presented in this paper, a designer could possibly justify the likely variation of
reference strain from a single triaxial compression test with no prior information about the material or
in-situ conditions. From this database, the prediction of triaxial extension reference strain includes a
factor error of 1.7 to 2.2 (dependent on CIU or CKU test conditions), which can be incorporated into
sensitivity analyses.
Page 8 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 8
Estimation of OCR
Using only 2 measurements of cu/σ'v0, at different depths, the SHANSEP framework (Ladd et al. 1977;
Mayne 1988) can be adopted to assess OCR of the soil using Equation (1). Table 3 shows the values of
(cu/σ'v0)NC and Λ by shear mode for the sub-databases presented here and in other studies (see also Mayne
et al. 2009 for values of (cu/σ'v0)NC by test mode). The reference strain data in Figure 3 suggest that a
similar approach can be used with measurements of The new transformation models given by
Equations 5 to 8 identify positive correlations between the reference strain and OCR in all four test
modes. Hence, with knowledge of a reference strain from a triaxial test OCR may be estimated (using
an analogous approach to that shown in Mayne 1988 with cu).
Using Equations 5 to 8 (Figure 3), OCR can be approximated with a factor error of 1.5 to 2.7
for the selected consolidation-shear mode. Adopting the SHANSEP framework (Equations 9 to 12,
given in Table 3) to estimate OCR produces a factor error of 1.3 to 1.8. Perhaps as expected soil
mobilisation strains are a poorer predictor of OCR than undrained shear strength (i.e. the correlations
have lower R2 values). Figures S7 and S8 show that for Equations 5 to 8 around 80% of the data plots
within a bandwidth of 1.7 to 2.1 factor error (about the predicted = measured line). Equation 6 is of
similar form to Equation 4 and this may be partly explained by some shared data from Abdulhadi
(2009).
[n = 114, R2 = 0.51, S.E. = 0.0051, p<0.001] (5)𝛾50 𝐶𝐼𝑈𝐶 = 0.0010(𝑂𝐶𝑅) +0.0074
[n = 55, R2 = 0.65, S.E. = 0.0033, p<0.001] (6)𝛾50 𝐶𝐼𝑈𝐸 = 0.0013(𝑂𝐶𝑅) +0.0042
[n = 67, R2 = 0.79, S.E. = 0.234, p<0.001] (7a)𝑙𝑜𝑔10(𝛾50 𝐶𝐾𝑈𝐶) = 1.35𝑙𝑜𝑔10(𝑂𝐶𝑅) ―3.31
which can be rearranged as:
(7b)𝛾50 𝐶𝐾𝑈𝐶 = 0.00049(𝑂𝐶𝑅)1.35
[n = 30, R2 = 0.45, S.E. = 0.0086, p<0.001] (8)𝛾50 𝐶𝐾𝑈𝐸 = 0.0038(𝑂𝐶𝑅)
Page 9 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 9
SUMMARY
RFG/TXCU-278 is a large database of triaxial tests on reconstituted soil samples that has been analysed
by consolidation mode (isotropic or K0) and shear mode (compression or extension) to quantify the
variability of shear strength and strain. Undrained strength ratio (cu/σ'v0) and MSF parameters 50 CIU,
50 CKU, bCIU and bCKU were chosen to study the influences of shear-mode anisotropy and OCR on
parameter variability. The correlations presented for quantifying the variability of the undrained
strength and strain parameters in this study may not be representative of intact materials, but the general
trends are useful for those wishing to assess the effects of OCR (less reported for studies on intact soils)
and shear mode. Factor errors of the new transformation models provide a useful indication of parameter
variability related to the uncertain effects of different experimental procedures and the material
variability of reconstituted soils.
ACKNOWLEDGEMENTS
The first author gratefully acknowledges the financial support which has been provided through the
Engineering and Physical Sciences Research Council (EPRSC) Studentship Award Reference:
1514817.
DATA AVAILABILITY STATEMENT
This research has not generated new experimental data.
NOTATION
The following notation is used in this paper:
bCIU = fitted exponent (Equation 2) in power-law regression of normalised shear strain ( 50 CIU) and
stress ratio (τmob /cu);
bCKU = fitted exponent (Equation 3) in power-law regression of normalised shear strain ( 50 CKU) and
stress ratio (τmob – τ0)/(cu – τ0);
B = stress ratio for tests sheared from anisotropic conditions (with initial shear stress)
cu = undrained shear strength;
cu /σ'v0 = normalised undrained strength, or undrained strength ratio;
(cu /σ'v0)NC = normalised strength of a normally consolidated material;
Page 10 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 10
(cu /σ'v0)OC = normalised strength of an overconsolidated material;
IP = Plasticity index;
K0 = ratio of horizontal to vertical stress with zero lateral strain;
M = mobilisation factor (which is akin to a reduction factor on undrained shear strength);
n = number of data points;
OCR = overconsolidation ratio (maximum past consolidation stress to present consolidation stress);
p = calculated probability of finding the observed value to be at least as extreme as the test statistic
when the null hypothesis H0 is true;
R2 = coefficient of correlation;
S.E. = standard error;
wL = liquid limit;
wP = plastic limit;
= shear strain;
50 CIU = reference shear strain to mobilise 0.5cu in a consolidated undrained isotropic test;
50 CKU = reference shear strain to mobilise 0.5(cu – τ0) in a consolidated undrained K0 test;
ref = a reference shear strain;
Λ = fitted exponent in power-law regression of normalised undrained strength and OCR;
σ'v0 = current vertical consolidation stress;
τ = shear stress
τmob = increment of mobilised shear strength;
τ0 = initial shear stress;
CAU = Anisotropically-consolidated undrained test of any shear mode;
CIU = Isotropically-consolidated undrained test of any shear mode;
CKU = K0-consolidated undrained test of any shear mode;
CAUC = Anisotropically-consolidated undrained triaxial compression;
CAUE = Anisotropically-consolidated undrained triaxial extension;
CIUC = Isotropically-consolidated undrained triaxial compression
Page 11 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 11
CIUE = Isotropically-consolidated undrained triaxial extension;
CKUC = K0-consolidated undrained triaxial compression;
CKUE = K0-consolidated undrained triaxial extension;
MSF = Mobilisation Strain Framework;
SHANSEP = Stress History and Normalized Soil Engineering Properties.
REFERENCES
Abdulhadi N. 2004. “Triaxial testing on reconstituted London clay”. MSc thesis. Imperial College,
London, UK.
Abdulhadi N. 2009. “An Experimental Investigation into the Stress-Dependent Mechanical Behavior
of Cohesive Soil with Application to Wellbore Instability”. PhD thesis. Massachusetts Institute of
Technology, Cambridge, Massachusetts, USA.
Atkinson, J. H., and Little, J. A. 1988. “Undrained triaxial strength and stress–strain characteristics of
a glacial till soil”. Canadian Geotechnical Journal, 25(3): 428-439. https://doi.org/10.1139/t88-
048
Bolton M. D., Springman S. M., and Sun H. W. 1990. “The behaviour of bridge abutments on clay”.
A.S.C.E. Conference on the Design and Performance of Retaining Structures, P.C. Lambe and L.
A. Hansen (Eds). ASCE, Reston, VA, USA, pp. 292-306.
Braathen, N. 1966. “Investigation of effects of disturbance on undrained shear strength of Boston
Blue Clay”. PhD thesis. Massachusetts Institute Of Technology, Cambridge, Massachusetts.
Brosse, A. M., Jardine, R. J., and Nishimura, S. 2017. “The undrained shear strength anisotropy of
four Jurassic to Eocene stiff clays”. Géotechnique, 67(8): 653-671.
https://doi.org/10.1680/jgeot.15.P.227
BSI. 1994. Code of practice for earth retaining structures. British standard BS8002. British Standards
Institution (BSI), London, UK.
Cao, Z., and Wang, Y. 2014. “Bayesian Model Comparison and Characterization of Undrained Shear
Strength”. Journal of Geotechnical and Geoenvironmetnal Engineering, 140(6): [04014018].
https://doi.org/10.1061/(ASCE)GT.1943-5606.0001108
Page 12 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 12
Cao, Z., Wang, Y., and Li, D. 2016. “Quantification of prior knowledge in geotechnical site
characterization”. Engineering Geology, 203: 107-116.
https://doi.org/10.1016/j.enggeo.2015.08.018
Casey, B., Germaine, J. T., Abdulhadi, N. O., Kontopoulos, N. S., and Jones, C. A. 2016. “Undrained
Young’s Modulus of fine-grained soils”. Journal of Geotechnical and Geoenvironmental
Engineering, 142(2): [04015070]. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001382
Casey, B. 2016. “Closure to ‘Undrained Young’s Modulus of fine-grained soils’ ”. Journal of
Geotechnical and Geoenvironmental Engineering, 142(10): [07016024].
https://doi.org/10.1061/(ASCE)GT.1943-5606.0001570
Chandler, R. J. 1988. “The in-situ measurement of the undrained shear strength of clays using the
field vane”. Vane Shear Strength Testing in Soils: Field and Laboratory Studies. ASTM STP
1014, (A. F. Richards, Ed.), American Society for Testing and Materials, Philadelphia, 1988: 13-
44.
Chen, Y., and Kulhawy, F. H. 1993. “Undrained strength interrelationships among CIUC, UU, and
UC tests”. Journal of Geotechnical Engineering, 119(11): 1732-1750.
https://doi.org/10.1061/(ASCE)0733-9410(1993)119:11(1732)
Ching, J., and Phoon, K. -K. 2013. “Multivariate distribution for undrained shear strengths under
various test procedures”. Canadian Geotechnical Journal, 50(3): 907-923.
https://doi.org/10.1139/cgj-2013-0002
Ching, J., and Phoon, K. -K. 2014a. “Transformations and correlations among some clay parameters –
the global database”. Canadian Geotechnical Journal, 51(6): 663-685. https://doi.org/10.1139/cgj-
2013-0262
Ching, J., and Phoon, K. -K. 2014b. “Reply to the discussion by Mesri on ‘Multivariate distribution
for undrained shear strengths under various test procedures’ ”. Canadian Geotechnical Journal,
51(3): 348-351. https://doi.org/10.1139/cgj-2013-0400
Conn, G. M. 1988. “The two-way repeated loading of a silty clay”. PhD thesis. Loughborough
University of Technology, Loughborough, UK.
Page 13 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 13
Fayad, P. H. 1986. “Aspects of the volumetric and undrained behavior of Boston Blue Clay”. PhD
thesis. Massachusetts Institute of Technology, Cambridge, MA, USA.
Gasparre, A. 2005. “Advanced laboratory characterisation of London Clay”. PhD thesis. Imperial
College, London, UK.
Gens, A. 1982. “Stress-strain and strength characteristics of a low plasticity clay”. PhD thesis.
Imperial College, London, UK.
Hight, D. W., Gens, A., and Jardine, R. J. 1985. “Evaluation of geotechnical parameters from triaxial
tests on offshore clay”. In: Offshore Site Investigation: Advances in Underwater Technology and
Offshore Engineering, Springer, Dordrecht, Netherlands. vol 3, pp. 253-268.
https://doi.org/10.1007/978-94-011-7358-2_16
Jamiolkowski, M., Ladd, C. C., Germaine, J. T., and Lancellotta, R. 1985. “New developments in
field and laboratory testing of soils”. In: Proceedings of the 11th International Conference on Soil
Mechanics and Foundation Engineering, San Francisco/ 12-16 August 1985, (Publications
Committee of XI ICSMFE, Eds.) A.A. Balkema, Rotterdam, Netherlands, vol. 1, pp. 57-153.
Kamal, R. H. 2012. “Experimental study of the geotechnical properties of UK mudrocks”. PhD thesis.
Imperial College, London, UK.
Kamei, T. and Nakase, A. 1989. “Undrained shear strength anisotropy of K0-overconsolidated
cohesive soils”. Soils and Foundations, 29(3): 145-151.
https://doi.org/10.3208/sandf1972.29.3_145
Klar, A., and Klein, B. 2014. “Energy-based volume loss prediction for tunnel face advancement in
clays”. Géotechnique, 64(10): 776-786. https://doi.org/10.1680/geot.14.P.024
Kootahi, K., and Mayne, P. W. 2017. “Closure to ‘Index Test Method for Estimating the Effective
Preconsolidation Stress in Clay Deposits’ by Karim Kootahi and Paul W. Mayne”. Journal of
Geotechnical and Geoenvironmental Engineering, 143(10): [07017031].
https://doi.org/10.1061/(ASCE)GT.1943-5606.0001765
Page 14 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 14
Koutsoftas, D. C., Karina, K., and Hashash, Y. M. A. 2017. “Discussion of ‘Index Test Method for
Estimating the Effective Preconsolidation Stress in Clay Deposits’ by Karim Kootahi and Paul W.
Mayne”. Journal of Geotechnical and Geoenvironmental Engineering, 143(10): [07017031].
https://doi.org/10.1061/(ASCE)GT.1943-5606.0001764
Krabbenhøft, K., Galindo-Torres, S. A., Zhang, X., and Krabbenhøft, J. 2019. AUS: Anisotopic
undrained shear strength model for clays. International Journal for Numerical and Analytical
Methods in Geotechnics. https://doi.org/10.1002/nag.2990 (ahead of print).
Kulhawy, F. H., and Mayne, P. W. 1990. “Manual on estimating soil properties for foundation
design”. EL-6800 Research Project 1493-6, Final Report, August 1990.
Ladd, C. C. 1991. “Stability evaluation during staged construction (The Twenty-Second Karl
Terzaghi Lecture)”. Journal of Geotechnical Engineering, 117 (4), 540-615.
https://doi.org/10.1061/(ASCE)0733-9410(1991)117:4(540)
Ladd, C.C., Foott, R., Ishihara, K., Schlosser, F., and Poulos, H. 1977. “Stress-deformation and
strength characteristics”. In: Proceedings of the 9th International Conference on Soil Mechanics
and Foundation Engineering, (Publications Sub-Committee of the Organizing Committee for the
Ninth International Conference on Soil Mechanics and Foundation Engineering, Eds.) Japanese
Society of Soil Mechanics and Foundation Engineering, Tokyo, Japan. vol. 2, pp. 421–494.
Lam, S. Y., and Bolton, M. D. 2011. “Energy conservation as a principle underlying mobilizable
strength design for deep excavations”. Journal of Geotechnical and Geoenvironmental
Engineering, 137(11): 1062-1074. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000510
Liu, Y. 2004. “The stress-strain behavior of kaolinite clay in triaxial compression and extension tests
at elevated pressures”. PhD thesis, University of Delaware, Newark, Delaware, USA.
Loudon, P. A. 1967. “Some deformation characteristics of kaolin”. PhD thesis, University of
Cambridge, Cambridge, UK.
Low, H. E., Landon Maynard, M., Randolph, M F., and DeGroot, D. J. 2011. “Geotechnical
characterisation and engineering properties of Burswood clay”. Géotechnique, 61(7): 575-591.
https://doi.org/10.1680/geot.9.P.035
Page 15 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 15
Matlock, H. 1970. “Correlations for design of laterally loaded piles in soft clay”. In: Offshore
Technology Conference, Houston, Texas, USA. OTC 1204.
Mayne, P. W. 1980. “Cam-Clay predictions of undrained strength”. Journal Geotechical Engineering
Division, 106(11): 1219-1242.
Mayne, P. W. 1985. “Stress anisotropy effects on clay strength”. Journal Geotechical Engineering
Division, 111(3): 356-366. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:3(356)
Mayne, P. W. 1988. “Determining OCR in clays from laboratory strength”. Journal of Geotechnical
Engineering, 114(1): 76-92. https://doi.org/10.1061/(ASCE)0733-9410(1988)114:1(76)
Mayne, P. W. and Holtz, R. D. 1985. “Effect of principal stress rotation on clay strength”. In:
Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering,
San Francisco/ 12-16 August 1985, (Publications Committee of XI ICSMFE, Eds.) A.A. Balkema,
Rotterdam, Netherlands, vol. 2, pp. 579-582.
Mayne, P. W., Coop, M. R., Springman, S., Huang, A-B., and Zornberg, J. 2009. State-of-the-Art
Paper (SOA-1): “GeoMaterial Behavior and Testing”. Proceedings of the 17th International
Conference on Soil Mechanics and Geotechnical Engineering, (Hamza, M, Shahien, M. and El-
Mossallamy, Y., Eds.), Millpress/IOS Press Rotterdam, Netherlands, vol. 4, pp. 2777-2872.
McMahon, B. T., Haigh, S. K., and Bolton, M. D. 2014. “Bearing capacity and settlement of circular
shallow foundations using a nonlinear constitutive relationship”. Canadian Geotechnical Journal,
51(9): 995-1003. https://doi.org/10.1139/cgj-2013-0275
Osman, A. S., and Bolton, M. D. 2005. “Simple plasticity-based prediction of the undrained
settlement of shallow circular foundations on clay”. Géotechnique, 55(6): 435-447.
https://doi.org/10.1680/geot.2005.55.6.435
Parry, R. H. G. 1956. “Strength and deformation of clay”. PhD thesis. Imperial College, London, UK.
Parry, R. H. G. 1960. “Triaxial compression and extension tests on remoulded saturated clay”.
Géotechnique, 10(4): 166-180. https://doi.org/10.1680/geot.1960.10.4.166
Parry, R. H. G., and Nadarajah, V. 1974. “Observations on laboratory prepared, lightly
overconsolidated specimens of kaolin”. Géotechnique, 24(3): 345-357.
https://doi.org/10.1680/geot.1974.24.3.345
Page 16 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 16
Phoon, K-K., and Kulhawy, F. H. 1999a. “Characterization of geotechnical variability”. Canadian
Geotechnical Journal, 36(4): 612-624, https://doi.org/10.1139/t99-038
Phoon, K-K., and Kulhawy, F. H. 1999b. “Evaluation of geotechnical property variability”. Canadian
Geotechnical Journal, 36(4): 625-639, https://doi.org/10.1139/t99-039
Ratananikom, W., Yimsiri, S., and Likitlersuang, S. 2015. “Undrained shear strength of very soft to
medium stiff Bangkok clay from various laboratory tests”. Geotechnical Engineering: Journal of
the SEAGS & AGSSEA, 46(1): 64-74.
Sachan, A., and Penumadu, D. 2007. “Effect of microfabric on shear behavior of kaolin clay”.
Journal of Geotechnical and Geoenvironmental Engineering, 133(3): 306-318.
https://doi.org/10.1061/(ASCE)1090-0241(2007)133:3(306)
Sheahan, T. C. 1991. “An experimental study of the time-dependent undrained shear behavior of
resedimented clay using automated stress path triaxial equipment”. PhD thesis. Massachusetts
Institute of Technology, Cambridge, Massachusetts, USA.
Sheahan, T. C., Ladd, C. C., and Germaine, J. T. 1996. “Rate-dependent undrained shear behavior of
saturated clay”. Journal of Geotechnical Engineering, 122(2): 99-108.
https://doi.org/10.1061/(ASCE)0733-9410(1996)122:2(99)
Skempton, A. W. 1951. “The bearing capacity of clays”. Building Research Congress, London, 1:
180-189.
Valls-Marquez, M. 2009. “Evaluating the capabilities of some constitutive models in reproducing the
experimental behaviour of stiff clay subjected to tunnelling stress paths”. PhD thesis. University of
Birmingham, Birmingham, UK.
Vardanega, P. J. 2012. “Strength Mobilisation for Geotechnical Design & its Application to Bored
Piles”. PhD thesis. University of Cambridge, Cambridge, UK.
Vardanega, P. J., and Bolton, M. D. 2011. “Strength mobilization in clays and silts”. Canadian
Geotechnical Journal, 48(10): 1485–1503, https://doi.org/10.1139/t11-052 and Corrigendum,
49(5), 631. https://doi.org/10.1139/t2012-023
Page 17 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Page 17
Vardanega, P. J., and Bolton, M. 2016a. “Design of Geostructural Systems”. ASCE-ASME Journal of
Risk and Uncertainty in Engineering Systems. Part A: Civil Engineering, 2(1): [04015017].
https://doi.org/10.1061/AJRUA6.0000849
Vardanega, P. J., and Bolton, M. 2016b. “Discussion of ‘Undrained Young’s Modulus of fine-grained
soils’ by B. Casey, J. T. Germaine, N. O. Abdulhadi, N. S. Kontopoulos, and C. A. Jones”. Journal
of Geotechnical and Geoenvironmental Engineering, 142(10): [07016023].
https://doi.org/10.1061/(ASCE)GT.1943-5606.0001571
Vardanega, P. J., Lau, B. H., Lam, S. Y., Haigh, S. K., Madabhushi, S. P. G., and Bolton, M. D. 2012.
“Laboratory measurement of strength mobilisation in kaolin: link to stress history”. Géotechnique
Letters, 2(1): 9–15. https://doi.org/10.1680/geolett.12.00003
Vardanega, P. J., Lau, B. H., Lam, S. Y., Haigh, S. K., Madabhushi, S. P. G., Bolton, M. D., and
Mayne, P. W. 2013. “Discussion to ‘Laboratory measurement of strength mobilisation in kaolin:
link to stress history’ ”. Géotechnique Letters, 3: 16–17. https://doi.org/10.1680/geolett.13.00005
Wang, Y., Akeju, O. V., and Cao, Z. 2016. "Bayesian Equivalent Sample Toolkit (BEST): an Excel
VBA program for probabilistic characterisation of geotechnical properties from limited
observation data". Georisk: Assessment and Management of Risk for Engineered Systems and
Geohazards, 10(4): 251-268. https://doi.org/10.1080/17499518.2016.1180399
Zhang, Y., and Anderson, K. H. 2017. “Scaling of lateral pile p-y response in clay from laboratory
stress-strain curves”. Marine Structures, 53: 124-135.
https://doi.org/10.1016/j.marstruc.2017.02.002
Zhu, J.-G., and Yin, J.-H. 2000. “Strain-rate-dependent stress-strain behavior of overconsolidated
Hong Kong marine clay”. Canadian Geotechnical Journal, 37(6): 1272-1282.
https://doi.org/10.1139/t00-054
Page 18 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Table 1: Sources of experimental data in RFG/TXCU-278
Reference Test Material wL(%)
IP a
(%)Test modes b OCR Range Excluded test data
Isotropically-consolidated undrained triaxial shear testsParry (1956, 1960) Weald Clay (n=8) 43 25 CIUC (n=6) CIUE (n=2) 1-12 8 undrained tests available for digitisation (drained tests excluded)
Gasparre (2005)- 6 of 7 tests from Abdulhadi (2004)
London Clay (n=7) 63-67 35-41 CIUC (n=7) 1-12 6 tests excluded from digitisation due to poor resolution
Gens (1982) Lower Cromer Till (n=10) 25 12 CIUC (n=5) CIUE (n=5) 1-10 All undrained tests included (drained tests excluded)Loudon (1967) Kaolin (n=8) 74 32 CIUC (n=8) 1-8.1Liu (2004) Kaolin (n=22) 56 24 CIUC (n=11) CIUE (n=11) 1-8 3 tests excluded from digitisation due to poor resolutionSachan & Penumadu (2007)
Kaolin (n=12) 62 30 CIUC (n=6) CIUE (n=6) 1-10 6 tests on ‘Flocculated’ samples included; 6 tests on ‘Dispersed’ samples excluded
Conn (1988) Keuper Marl (n=20) 36 17 CIUC (n=9) CIUE (n=11) 1-10Valls-Marquez (2009) Kaolin (n=11) 65 32 CIUC (n=7) CIUE (n=4) 1-5.1Braathen (1966) Boston Blue Clay (n=3) 45.5 22.3 CIUC (n=3) 1-8.1 4 cyclic tests and 7 anisotropically consolidated tests excluded from digitisation as
per selection criteria; 1 CIUC test (OCR=2) excluded due to possible seating/bedding error
Fayad (1986) Boston Blue Clay (n=1) 42 21 CIUC (n=1) 7.5Zhu and Yin (2000) Hong Kong Marine Clay
(n=24)60 32 CIUC (n=12) CIUE (n=12) 1-8
Atkinson & Little (1988) Ware Lodgement Till (n=7)
40 22 CIUC (n=7) 1-32 10 ‘tubed’ (intact) samples excluded
Kamal (2012) Oxford Clay (n=5) 66 32 CIUC (n=5) 1-10Kamal (2012) Gault Clay (n=3) 74 46 CIUC (n=3) 1-5Kamal (2012) Kimmeridge Clay (n=3) 49 26 CIUC (n=3) 1-5Vardanega et al. (2012) c Kaolin (n=18) 62.6 33 CIUC (n=18) 1-20Parry & Nadarajah (1974) Kaolin (n=8) 72 32 CIUC (n=4) CIUE (n=4) 1-2.3K0-consolidated undrained triaxial shear testsFayad (1986) Boston Blue Clay (n=7) 42 21 CKUC (n=4) CKUE (n=3) 1-8.2 1 cyclic test excludedGens (1982) Lower Cromer Till (n=10) CKUC (n=6)
CKUE (n=4)1-101-7
All undrained tests included (drained tests excluded)
Valls-Marquez (2009) Kaolin (n=2) 65 32 CKUC (n=1) CKUE (n=1) 1Abdulhadi (2009) Boston Blue Clay (n=22) 46.5 22.7 CKUC (n=19)
CKUE (n=3)1-4.21
1 CKUE test excluded from digitisation due to poor resolution
Kamei & Nakase (1989) Kawasaki Clay (n=8) 55.3 29.4 CKUC (n=4) CKUE (n=4) 1-9.6Hight et al. (1985) London Clay (n=7) 75 47 CKUC (n=4) CKUE (n=3) 1-7Hight et al. (1985) North Sea Clay (n=8) 32 17 CKUC (n=5)
CKUE (n=3)2-81-17
Sheahan (1991) Boston Blue Clay (n=37) 45.1-45.8
23-25.5
CKUC (n=28) CKUE (n=9)
1-81-4
Parry & Nadarajah (1974) Kaolin (n=7) 72 32 CKUC (n=3) CKUE (n=4) 1-2.6 1 CKUC test excluded from digitisation due to poor resolution
Notes: Digitised peak deviator stress and shear strain = 1.5 times axial strain have been used to develop all the correlations in this paper. a Liquid limit (wL) and plastic limit (wP) were measured using the standard methods (BSI 1990) of fall cone penetrometer and thread-rolling. In two studies (Gasparre 2005 and Sheahan 1991) the authors identify wL and wP values for the block sample associated with each reconstituted specimen, while the other studies indicate a single ‘best estimate’ value for the set of specimens.b n = number of tests.c Experimental data of the triaxial tests published by Vardanega et al. (2012) were reanalysed and re-filtered from the original data source for this paper.
Page 19 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Table 2: Distribution of non-linearity parameter from undrained triaxial compression and extension tests sorted by test mode
Sample type OCR Test mode mean standard deviation
n Reference
Reconstituted 1-32 bCIUC 0.459 0.143 114Reconstituted 1-12 bCIUE 0.399 0.082 55Reconstituted 1-10 bCKUC 0.581 0.167 68Reconstituted 1-17 bCKUE 0.350 0.100 34
This study
Intact Unknown bCIU 0.608 0.158 92 Vardanega & Bolton (2011)
Page 20 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Table 3: Correlations between OCR and (cu/σ'v0) from undrained triaxial compression and extension tests sorted by test mode
Sample type Database Reference
OCR Test mode
(cu/'v0)NC Λ (slope regression coefficient)
(Equation number)/Equation
n R2 S.E. p-value Data within error bounds
Factor Error
Figure in Online Supplement
Reconstituted This study 1-32 CIUC 0.288 0.653 (9) log10(cu/'v0)=0.653log10(OCR)-0.541 115 0.86 0.114 <0.001 80% 1.45 S5Intact Mayne 1988
Upper Bound1-20 CIUC 0.25 0.7
Intact Mayne 1988 Lower Bound
1-20 CIUC 0.55 0.7
Intact Ching & Phoon 2014b
1-6 CIUC 0.397 0.71 127
Reconstituted This study 1-12 CIUE 0.267 0.729 (10) log10(cu/'v0)=0.729log10(OCR)-0.574 55 0.92 0.083 <0.001 80% 1.30 S5Intact Mayne 1988
Upper Bound1-20 CIUE 0.20 0.58
Intact Mayne 1988 Lower Bound
1-20 CIUE 0.60 0.58
Reconstituted This study 1-10 CKUC 0.300 0.790 (11) log10(cu/'v0)=0.790 log10(OCR)-0.522 74 0.94 0.066 <0.001 80% 1.2 S6Intact Mayne 1988
Upper Bound1-20 CAUC 0.20 0.78
Intact Mayne 1988 Lower Bound
1-20 CAUC 0.45 0.78
Intact Ching & Phoon 2014b
1-6 CKUC 0.328 0.736 143
Reconstituted This study 1-10 CKUE 0.165 0.952 (12) log10(cu/'v0)=0.952 log10(OCR)-0.782 34 0.94 0.087 <0.001 79% 1.30 S6Intact Mayne 1988
Upper Bound1-20 CAUE 0.12 0.85
Intact Mayne 1988 Lower Bound
1-20 CAUE 0.25 0.85
Intact Ching & Phoon 2014b
1-6 CKUE 0.146 1.009 83
Page 21 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Figure 1. Comparison of cu/'v0 CIU and cu/'v0 CKU from triaxial extension and compression tests on two similarly reconstituted specimens (a) for CIU tests and (b) for CKU tests
Mayne & Holtz (1985) CIUcu /v0 CIUE = 0.774 cu /v0 CIUC
n=14 (28 tests in total)R² = 0.96 S.E. = 0.117 p<0.001
Reconstituted CIUcu /v0 CIUE = 0.835 cu /v0 CIUC
n=50 (100 tests in total) R² = 0.94 S.E. = 0.110 p<0.001
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
c u/
' v0
CIU
E
cu/'v0 CIUC
Mayne & Holtz (1985) CIUReconstituted CIU1:1
Mayne & Holtz (1985) CKUcu /v0 CKUE = 0.619cu /v0 CKUC
n=56 (112 tests in total)R² = 0.84 S.E. = 0.112 p<0.001
Reconstituted CKUcu /v0 CKUE = 0.649cu /v0 CKUC
n=29 (58 tests in total)R² = 0.92 S.E. = 0.080 p<0.001
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0
c u/
' v0
CKU
E
cu/'v0 CKUC
Mayne & Holtz (1985) CKUReconstituted CKU1:1
(a)
(b)
Page 22 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Figure 2. Comparison of 50 CIU and 50 CKU from triaxial extension and compression tests on two similarly reconstituted specimens (a) for CIU tests and (b) for CKU tests
50 CIUE = 0.74950 CIUCn=50 (100 tests in total)
R² = 0.71 S.E. = 0.0031 p<0.001
0.00
0.01
0.02
0.03
0.04
0.00 0.01 0.02 0.03 0.04
50
CIU
E
50 CIUC
Reconstituted CIU1:1
50 CKUE = 3.7650 CKUC + 0.0054n=25 (50 tests in total)
R² = 0.46 S.E. = 0.0099 p<0.001
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.00 0.01 0.02
50
CKU
E
50 CKUC
Reconstituted CKU1:1
(a)
(b)
Page 23 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.
Figure 3 (a) Variation of 50 CIU with OCR for all CIUC and CIUE tests in the database and 3 (b) Variation of 50 CKU with OCR for all CKUC and CKUE tests in the database. Previously
reported trend 50 CKUC = 0.0004OCR1.57 (Casey 2016) (Equation 4) is shown for comparison.
50 CIUC = 0.0010OCR + 0.0074n=114 R² = 0.51 S.E. = 0.0051 p<0.001
50 CIUE = 0.0013OCR + 0.0042n=55 R² = 0.65 S.E. = 0.0033 p<0.001
0.00
0.01
0.02
0.03
0.04
0.05
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
50
CIU
OCR
Reconstituted CIUCReconstituted CIUE
(a)
50 CKUC = 0.00049OCR1.35
n=67 R² = 0.79 S.E. = 0.234 p<0.001
50 CKUE = 0.0038OCRn=30 R² = 0.45 S.E. = 0.0086 p<0.001
Equation (4)
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
1 2 3 4 5 6 7 8 9 10
50
CKU
OCR
Reconstituted CKUCReconstituted CKUEOutlier CKUCOutliers CKUE(b)
Page 24 of 24C
an. G
eote
ch. J
. Dow
nloa
ded
from
ww
w.n
rcre
sear
chpr
ess.
com
by
UN
IVE
RSI
TY
OF
BR
IST
OL
on
11/1
2/19
For
pers
onal
use
onl
y. T
his
Just
-IN
man
uscr
ipt i
s th
e ac
cept
ed m
anus
crip
t pri
or to
cop
y ed
iting
and
pag
e co
mpo
sitio
n. I
t may
dif
fer
from
the
fina
l off
icia
l ver
sion
of
reco
rd.