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

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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: mb0126@bristol.ac.uk,

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: p.j.vardanega@bristol.ac.uk,

OCRID: 0000-0001-7177-7851

No. words in main text: ≈ 2,700

No. figures: 3

No. tables: 3

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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

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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

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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

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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).

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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

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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.

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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.

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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)

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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;

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(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

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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.

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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.

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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)

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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

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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)

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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)

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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)

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