Parameter variability of undrained shear strength and strain using a database of reconstituted soil tests

During construction, the mobilization 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 mobilization, an understanding of soil strains at various levels of strength mobilization is required. In practice, ground investigation data are 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/[Formula: see text]) 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 mobilization parameters obtained from a triaxial compression test can be used to predict the corresponding triaxial extension parameters to a reasonable accuracy.


INTRODUCTION
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;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 (c u ) 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 c u 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 c u /' 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 c u 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 framework for clays exhibiting 'normalized behaviour' that enables the prediction of c u if in-situ effective vertical stress and OCR are known (Equation 1): Where, Λ = fitted exponent; σ' v0 = present vertical effective consolidation stress; (c u /σ' v0 ) OC = normalised strength of an overconsolidated material; (c u /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 c u /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 c u 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 powerlaw 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: Where, M = mobilisation factor (which is akin to a reduction factor on undrained shear strength); τ mob = the mobilised shear strength;  = shear strain;  50 CIU = shear strain to mobilise 0.5c u 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 b CIU is an exponent to describe non-linearity (ductility): for compression and extension tests the notation b CIUC and b CIUE 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)  (3) Where, τ 0 = initial shear stress; γ 50 CKU = shear strain to mobilise 0.5(c u -τ 0 ) (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 b CKU is an exponent that describes soil non-linearity (ductility): for compression and extension tests the notation b CKUC and b CKUE 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 K 0 consolidation stress path and recommended Equation 4 to describe the variation of reference strain with OCR for CKUC tests: (4) 50 = 0.0004( ) 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).

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., 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 c u /σ' v0 ,  50 CIU,  50 CKU, b CIU and b CKU for reconstituted soils. Two shear modes are investigated: triaxial compression and triaxial extension. Table 1  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 c u 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 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 b CIUC ).

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 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 24
Can. Geotech. J. Downloaded from www.nrcresearchpress.com by UNIVERSITY OF BRISTOL on 11/12/19 For personal use only. This Just-IN manuscript is the accepted manuscript prior to copy editing and page composition. It may differ from the final official version of record.

Correlation between triaxial extension and compression parameters
The undrained strength ( Figure 1)  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 b CKU or b CIU (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 24
Can. Geotech. J. Downloaded from www.nrcresearchpress.com by UNIVERSITY OF BRISTOL on 11/12/19 For personal use only. This Just-IN manuscript is the accepted manuscript prior to copy editing and page composition. It may differ from the final official version of record.

Estimation of OCR
Using only 2 measurements of c u /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 (c u /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 (c u /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 c u ).
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)

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.

Isotropically-consolidated undrained triaxial shear tests
a Liquid limit (w L ) and plastic limit (w P ) were measured using the standard methods (BSI 1990) of fall cone penetrometer and thread-rolling. In two studies (Gasparre 2005 andSheahan 1991) the authors identify w L and w P 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.