Modeling critical-state shear strength behavior of compacted silty sand via suction-controlled triaxial testing

Accepted Manuscript Modeling critical-state shear strength behavior of compacted silty sand via suction-controlled triaxial testing

Ujwalkumar D. Patil, Anand J. Puppala, Laureano R. Hoyos, Aravind Pedarla PII: DOI: Reference:

S0013-7952(16)30409-4 doi:10.1016/j.enggeo.2017.10.011 ENGEO 4676

To appear in:

Engineering Geology

Received date: Revised date: Accepted date:

28 September 2016 10 October 2017 11 October 2017

Please cite this article as: Ujwalkumar D. Patil, Anand J. Puppala, Laureano R. Hoyos, Aravind Pedarla , Modeling critical-state shear strength behavior of compacted silty sand via suction-controlled triaxial testing. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Engeo(2017), doi:10.1016/j.enggeo.2017.10.011

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ACCEPTED MANUSCRIPT Modeling critical-state shear strength behavior of compacted silty sand via suction-controlled triaxial testing Ujwalkumar D. Patil1, Anand J. Puppala 2, Laureano R. Hoyos3, and Aravind Pedarla 4

Assistant Professor (Corresponding Author), University of Guam, School of Engineering, Mangilao, Guam 96923. E-mail: [email protected]

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Professor, Department of Civil Engineering, University of Texas at Arlington, Arlington, Texas 76019. Email: [email protected]

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Professor, Department of Civil Engineering, University of Texas at Arlington, Arlington, Texas 76019. Email: [email protected]

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Post-Doctoral Research Associate, University of Texas at Arlington, TX 76019. E-mail: [email protected]

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ACCEPTED MANUSCRIPT ABSTRACT Most of the recently postulated unsaturated shear strength models have been calibrated only for a short variety of soils. In addition, these models are yet to be extended and calibrated over a wider range of matric and total suction states. The present work focuses on further refinements of

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previously proposed shear strength equations in light of newly obtained experimental evidence of

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shear strength behavior of compacted silty sand at a critical state from suction-controlled triaxial tests

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conducted between 0.05 MPa to 300 MPa suction range. A refined and rather simple equation comprising two independent functions, is introduced and validated, including a thorough parametric

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investigation, to predict the unsaturated shear strength of compacted silty sand at a critical state for a wide range of matric and total suction states. The experimental program included a total of 21

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consolidated drained (CD) triaxial tests conducted on statically-compacted specimens of silty sand

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under strain- and suction-controlled conditions. Experimental results show that the angle of internal friction (ϕʹ) remained virtually constant over the entire range of induced suction states; however, the

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shear strength increased while the angle of internal friction with respect to suction (ϕb) decreased

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with increasing suction, with both varying non-linearly. Finally, a gradual increase in brittleness of the test soil at peak-failure condition, as well as an increasingly marked strain-softening post-failure,

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Keywords

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was observed with increasing suction.

Soil suction, Suction-controlled triaxial testing, Axis-translation, Vapor-pressure, Shear strength modeling.

ACCEPTED MANUSCRIPT 1. Background and scope The pioneering frameworks postulated by Bishop (1959) and Fredlund and Morgenstern (1977) require expensive, time consuming experimental studies to determine the shear strength parameters and properties of unsaturated soils. In an effort to make the process more cost-effective,

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several researchers have attempted to use the soil-water retention curve (SWRC) as an interpretative

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tool, along with the saturated shear strength parameters, cʹ and ϕʹ, and thus develop relatively simple

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and readily available shear strength equations or models for unsaturated soils (for e.g., Vanapalli et al., 1996; Fredlund et al., 1996; Oberg and Sallfors, 1997; Khalili and Khabbaz, 1998; Vilar, 2006;

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Houston et al., 2008; Alonso et al., 2010; Sedano and Vanapalli, 2011; Han and Vanapalli, 2016). Rassam and Cook (2002) presented a new model by adopting a power additive function to

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predict shear strength of unsaturated soils based on the assumption of ϕb = 0 at residual suction, and

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with knowledge of shear strength of soil at residual suction. Although they could predict shear strength for different soils with residual suction ψr varying between 0.1 MPa to 10 MPa, the method

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appears to be most suitable for coarse- to medium-grained soils with relatively low residual suction

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that can be easily attained in laboratory. The procedure is limited to soils whose increase in shear strength varies mostly between air entry and residual suction, while remaining constant beyond

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residual suction, which may not necessarily be the case, as manifested in experimental test results

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from present research.

Nishimura and Fredlund (2003) used vapor equilibrium technique to perform triaxial tests on silty soil at total suction ψ = 39 MPa and five different net normal stresses; however, to the authors’ best knowledge, the results were not used to verify any of the shear strength prediction models available in the literature. Blatz et al. (2002) performed triaxial tests on compacted sand-bentonite specimens that were meant to be used as buffer for nuclear waste by using salt solutions of different concentrations to induce high suction between 5.0 MPa to 42.4 MPa at high net confining cell

ACCEPTED MANUSCRIPT pressures (0.5, 1.0, 2.0, and 3.0 MPa). They could best-fit three-dimensional surface that predicted peak shear strength as a function of mean stress and suction. More recently, Han and Vanapalli (2016) proposed a new methodology to predict the nonlinear stiffness-suction and shear strength-suction relationship of unsaturated soils, within the lower

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suction range, using a normalized function formulated with ‘suction times exponential degree of

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saturation. In addition, they could account for various influencing factors including external stress,

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soil structure, anisotropy, hydraulic hysteresis, and testing techniques. Likewise, the effective degree of saturation has been used in past to interpret and predict stiffness-suction and shear strength-suction

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relationships for unsaturated soils (Fredlund at al., 1996; Vanapalli et al., 1996; Alonso et al, 2010). Recently, a novel suction-controlled triaxial system that can accommodate both axis-

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translation and relative-humidity techniques has been implemented at the University of Texas at

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Arlington. The operational functionality of this equipment and its capability to replicate test results using both axis-translation and relative-humidity techniques have been thoroughly verified through a

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short series of tests conducted over a wide range of controlled suction states, between 0.05 to 300

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MPa (Patil, 2014; Patil et al., 2016a; Patil et al., 2016b). Test specimen preparation, preconditioning, suction equalization, and unsaturated triaxial testing procedures via both the axis-translation and

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relative-humidity technique has been thoroughly described by Patil et al. (2016b).

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The chief objectives of the present work can be summarized as follows: (1) To present a comprehensive set of experimental data from densely compacted (overconsolidated) silty sand using the newly implemented triaxial system, which is suitable for testing unsaturated soils well beyond residual suction state; (2) To analyze these results to test the efficacy of previously postulated equations for unsaturated shear strength over a wide range of suction states; and (3) To refine the existing equations in light of new experimental evidence from pertinent soil. All the models analyzed in the present work were tested and parametrically investigated by using experimental data at critical state failure.

ACCEPTED MANUSCRIPT Six different proposed models in their original form (i.e., Vanapalli et al., 1996; Fredlund et al., 1996; Khalili and Khabbaz, 1998; Vilar, 2006; Houston et al., 2008; and Sedano and Vanapalli, 2011) were first evaluated in the matric suction range (ψm = 0 to 1500 kPa) by plotting soil suction on natural scale, and then further extended to assess their validity in the high total suction range (ψt =

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20 and 300 MPa) by plotting soil suction on logarithmic scale. Mainly, two unsaturated soil shear

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strength parameters are analyzed: first, increase in cohesion intercept (c″) i.e. suction-induced

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increase in shear strength with increase in suction; and second, decrease in angle of internal friction with respect to suction (i.e. ϕb).

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In lieu of costly setups and time-consuming experimental procedures, the availability of verified predictive models, with reasonable acceptability over wider suction states and soil types,

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could provide practicing engineers with a quick preliminary estimate of the shear strength of

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unsaturated soil: a practically viable tool that is much needed in implementing the said subject in

2.1. Soil properties

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2. Test material and variables

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actual practice (Vilar, 2006; Houston et al., 2008).

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The test material used in this work consisted of 45:55 mixtures by dry mass of fines (37% silt and 8%

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non-plastic clay) and coarse material (fine sand), classifying as silty sand (SM) according to the Unified Soil Classification System (USCS). Standard Proctor compaction tests indicated a maximum dry density of 1.87 g/cm3, at an optimum water content of 12.2%. 2.2. Specimen preparation for SWRC and triaxial tests Dry test soil was hand mixed with distilled water at a water content of 14.2% (+2% of optimum), sealed in airtight zip lock bags and kept in a 100% humidity chamber for at least 24 hours to attain moisture equilibrium prior to static compaction. Specimens were statically compacted in nine equal lifts via stress-based approach by using a 50 kN load frame, at a constant rate of 1

ACCEPTED MANUSCRIPT mm/min, to a

final vertical stress of 1600 kPa, producing homogenous specimens with

overconsolidation stress history (Patil, 2014). The initial voids ratio for all specimen varied between 0.46-0.49. Likewise, Identical SWRC specimens (2 cm diam. and 1 cm ht.) were prepared using the

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same stress-based approach but compacted in a single lift. Each specimen was compacted to a dry

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unit weight of 1.80 g/cm3 (112.4 lb/ft3) with negative pore water pressure, and hence matric suction,

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between 8-10 kPa at water content of 14.2%.

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2.3. Soil water retention curve (SWRC)

Tempe Cell device was used to assess the soil-water retention curve (SWRC) of the silty sand up to

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matric suction values of 500 kPa. A custom-designed relative humidity (RH) chamber, along with an in-house fabricated Plexiglas chamber, was used to obtain remainder of SWRC data in the higher

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suction range (“Residual Zone”), beyond 10,000 kPa suction (Patil, 2014). A new specimen was

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prepared with identical initial conditions and then used to determine water retention capacity at each matric suction or total suction level by drying it; thus, each point on the SWRC represents one test.

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SWRC models by Fredlund and Xing (1994) and van Genuchten (1980) were used to best fit

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the experimental points along drying path in order to complete the characteristic curve over the entire range of soil suction, from 0-10,000 Mpa, as shown in Fig. 1. The best fitting parameters are

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summarized in Table 1. As has been extensively documented, an increase in matric suction causes the wetted area of contact between soil particles to decrease and vice versa; hence, there exists a nonlinear relationship between the soil-water retention curves and the shear strength of soil as it changes from saturated to unsaturated state (Vanapalli et al., 1996). In the present work, target values of matric suction, varying from 50 to 750 kPa, and target values of total suction, at 20,000 and 300,000 kPa, were induced on identically prepared specimens of compacted silty sand prior to monotonic shearing.

ACCEPTED MANUSCRIPT 2.4. Experimental variables Unsaturated soil testing typically involves three essential tests. First, SWRC tests that establish the relationship between water holding capacity of soil with change in suction, i.e. explaining hydraulic behavior; second, suction-controlled one dimensional or isotropic consolidation tests that explain

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suction-controlled volumetric response; and thirdly, shear strength tests, such as direct shear test or

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triaxial shear test modified to impose and maintain suction within the specimen, that are used to

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quantify strength-deformation variation, i.e. explaining mechanical behavior.

In the present work, and as previously stated, tests were conducted using a fully-automated,

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double-walled triaxial test equipment that accommodates the essential modifications for unsaturated soil testing, including high-air-entry (HAE) ceramics in the bottom pedestal; pore-water pressure

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control; pore-air pressure supply via the top cap; and diffused-air flushing assembly (Patil, 2014).

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With the operational apparatus, a comprehensive series of saturated and unsaturated consolidated drained (CD) triaxial tests on statically compacted silty sand specimens was performed.

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The axis-translation technique was used to impose and control matric suction in the range of

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0 to 750 kPa. Three confining pressures were used: 100, 200 and 300 kPa. The same RH chamber used for SWRC testing was integrated into the new triaxial testing system and a second series of CD

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tests, at higher values of total suction (20 MPa and 300 MPa), were performed under three different

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confining pressures: 100, 200 and 300 kPa. The convention adopted to designate specimens for matric suction-controlled triaxial testing is “CDx-y” while specimens for total suction-controlled testing using relative humidity technique were designated as “CDRHx-y. ” Here, “CD” denotes the consolidated drained test, “x” represents the net confining pressure (σ3 – ua), while “y” represents the imposed constant matric suction (ψm) or total suction (ψt). Furthermore, the terms “matric” or “total” suction essentially refer to the particular “technique” that was used to impose such suction, i.e., “axis-translation” or “relative humidity” based technique, respectively. It is also worth noting that chemical analyses conducted on the silty sand soil

ACCEPTED MANUSCRIPT showed no presence of salts, hence the osmotic component of suction can be expected to be negligible.

3. Unsaturated test results

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3.1. General shear strength response for 0-300 MPa suction range

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Nuth et al. (2008) presented a detail review of the historical developments of the effective

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stresses with the objective of determining a proper stress framework for constitutive modelling of unsaturated soils. Gallipoli et al. (2008) introduced the term capillary bonding which is uniquely

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related to the voids ratio of unsaturated soil to that of saturated soil. They demonstrated that capillary

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bonding can be taken as a measure of openness of unsaturated soil fabric and influence the critical deviator stress the unsaturated soil can sustain at a given mean average skeleton stress.

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Alonso et al. (2010) linked the relationship between effective stress and soil microstructure in

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unsaturated soils via effective degree of saturation, by conceptually differentiating between the volume of water existing in the soil for a given suction into two parts: the free water, partially filling

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the macro-pores, and the ‘immobile’ water, closely attached to the clay minerals. They were

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successful in interpreting experimental data on the strength and stiffness changes with suction for a variety of soils including granular and high-plasticity clays. More recently, Alonso et al. (2013)

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incorporated microstructural information within the conceptual framework to reproduce the compression behavior of compacted soils. Fredlund and Morgenstern (1977) treated net normal stress (σ – ua) and matric suction (ua – uw) as two independent stress state variables in the assessment of their role in the mechanical response of unsaturated soil. Such an approach separates the effect due to changes in net normal stress from those due to change in pore-water pressure, and enables the independent assessment of

ACCEPTED MANUSCRIPT the effect of suction and normal stress on volume change. Shear strength is hence expressed as given in Eq. (1). τf = c ′ + (σ − ua ) f tanϕ′ + (ua − uw )f tanϕb

(1)

Where τf = shear strength at failure; c′ = effective cohesion; ϕ′ = effective friction angle

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associated with net normal stress (σ – ua)f on the failure plane at failure; and ϕb = friction angle that

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captures the contribution of matric suction to shear strength. Equation 1 can further be modified as

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Eq. (2). τf = c ′ + c” + (σ − ua ) tanϕ′

(2)

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Where c″ = τus is defined as the capillary cohesion describing shearing resistance arising from capillarity effects given by Eq. (3).

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τus = c ” = (ua − uw )f tanϕb

(3)

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Figures 2-4 shows all the Mohr circles obtained at critical state under net confining pressures of 100, 200 and 300 kPa, and constant matric suctions of 50, 250, 500 and 750 kPa, as well as high

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total suctions of 20 and 300 MPa. Clearly, the angle of internal friction (ϕʹ), that is slope of failure

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line, remains constant, irrespective of the applied suction and confining pressure. However, there is an upward shift in failure lines at critical state, with increasing suction and at same confining

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pressure, resulting an increase in apparent cohesion (Figs. 2-4). The values of average apparent

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cohesion (c″), and the corresponding average values of the angle of internal friction with respect to soil suction (ϕb), as interpreted from these Figures 2-4 using Eq. 3, are summarized in Table 2, and will be used henceforth in all further analysis to relate the rate of change in shear strength with respect to change in matric suction. Although, not shown here (and not used in further analysis), Mohr circles were also drawn at critical state under different matric suctions of 50, 250, 500, and 750 kPa as well as high total suctions of 20 and 300 MPa and under each of the constant net confining pressures 100, 200, and 300

ACCEPTED MANUSCRIPT kPa. The values of apparent cohesion (c″), and the corresponding values of the angle of internal friction with respect to soil suction (ϕb), as interpreted from these figures using Eq. 3, are summarized in Table 3. It should be noted that the values of apparent cohesion and “average apparent cohesion” are not exactly same, because the former has effect of net confining pressure which is not

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similar while the latter is obtained by neutralizing this effect. Nonetheless, it can be observed that the

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non-linear decrease in ϕb with increasing suction is in accordance with previous findings (i.e., Escario

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and Saez, 1986; Gan et al., 1988; and Houston et al., 2008).

Figure 5(a) illustrates the nature of the increase in shear strength of compacted silty sand with

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increasing suction between 50 to 300,000 kPa, and under net confining pressure of 300 kPa. The remaining stress-strain and volume change curves along with detailed discussion can be obtained in

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Patil et al. (2016a and b). It is worth clarifying that most suction-controlled, consolidated-drained

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(CD) triaxial tests performed in this research were extremely time-consuming, with each test taking at least a month to complete, after pore-fluid equalization; hence, critical state was identified as soon

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as the deviator stress reached an “apparent” critical state condition (i.e., further shearing of soil

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sample under virtually constant stress.

Increase in matric suction beyond air-entry suction, introduces air in the pores and forms

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menisci menisci around the solid grains that pulls the particle together. This causes an apparent

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increase in normal forces at grain point contact resulting in an increase in effective stress. Hence, around 100 to 125 kPa of matric suction, there is a remarkable increase in shear strength, irrespective of net confining pressure. However, beyond approximately 2000 kPa suction (which also happens to be residual suction for the test soil), this increase in shear strength becomes only gradual with further increase in suction. In addition, there is an increase in shear strength with increasing net confining pressure at constant suction. The rate of increase in shear strength (i.e. c″) retards as total suction is increased between 20 to 300 MPa and under net confining pressure of 300 kPa, as indicated in Table 2 and 3. Beyond

ACCEPTED MANUSCRIPT residual suction, the specimen has adsorptive water that is mostly associated with micro-pores (Alonso et al. 2013) and hence remains ineffective in relaying suction to soil grains, thereby possibly retarding the rate of increase in shear strength with any further increasing suction.

3.2. Effect of suction on post-peak strain softening and brittleness

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The soil experiences strain softening when there is a reduction of deviator stress from peak to

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critical stress during shearing. Further insight on experimental stress-strain curves from this work

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strongly suggests an increase in magnitude of strain-softening with increasing suction, as shown in

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Fig. 5(a). Irrespective of net confinement applied, an increase in suction is observed to have a more pronounced influence on peak shear stress than on critical shear stress. One way to quantify

qpeak − qr qpeak

(4)

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IB =

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brittleness is to assess the “brittleness index” (IB) as defined by Bishop (1971):

where, qpeak = peak deviatoric stress and qr = residual deviatoric stress.

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Considering, qr as qcs = critical state deviatoric stress for experiments in this paper, we can

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quantify IB and it varies between 0-1. With decrease in value of brittleness index towards zero, the failure behavior becomes increasingly ductile. On the other hand, specimen failure will become

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increasingly brittle with increasing value of I B. For instance, IB = 1 indicates very brittle behavior.

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Figure 5(b) clearly indicate that the brittleness index increases with increasing matric/total suction, irrespective of net confining pressure with maximum brittleness index value at highest total suction applied i.e. 300 MPa.

Under constant net confinement, continuous shearing beyond peak shear stress drastically disturbs and destroys the air-water menisci imposed via axis-translation technique and formed around contact of solid grains. Hence, the contribution of suction towards strength at peak failure is often greater than at critical state; which is clearly illustrated by Figs. 6(a), (b) and (c). Both the peak and

ACCEPTED MANUSCRIPT critical deviator stress increase gradually up to ψm = 500 kPa, with a dramatic increase in both deviator stresses between ψm = 500 to 750 kPa, and thereafter the increase is gradual up to ψt = 300,000 kPa, but at comparatively much higher rate for peak deviator stress than for critical stress; clearly manifesting increase in strain softening response with increase in suction. In addition, the

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increase in net confinement from 100 to 300 kPa causes the difference between two deviator stresses

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to gradually increase at constant suction.

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The analysis of test results in pʹ-q plane, revealed the mobilized stress ratio at peak failure, ηpeak and at critical state, M equal to 1.60 and 1.42, respectively (Patil et al., 2016a and b). The stress

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ratio is useful in identifying volumetric behavior during shearing. For instance, when η peak > M, plastic softening (Fig. 5a) and volumetric dilation occurs on yielding under shear (Patil et al., 2016a

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and b). The partially saturated test soil showed post-peak softening stress-strain response (Fig. 5a)

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and initial compression followed by dilational volumetric response under shear (Patil et al., 2016a and b). Such a response may be attributed to the relatively dense or overconsolidated stress history of

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the specimens (as explained in section 2.2). Furthermore, the observed dilatancy forms the basis of

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additional energy manifested in terms of peak strength (Schofield and Wroth, 1968; Atkinson, 2007). It is observed from Table 2 that there is a gradual, nonlinear (hyperbolic) reduction in ϕb from

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50 kPa to 750 kPa of matric soil suction, while there is a sharp reduction in ϕb over the high suction

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range from 20 MPa to 300 MPa. The shear strength variation is primarily due to the nonlinear change in cohesion intercept with suction. 3.3. Effect of suction on failure mode It is well known that, in addition to the external loading, an increase in suction tends to apply capillary force on the solid grains at their point of contacts, thereby inducing extra bond among them, and thus rendering a stiffer soil structure that manifests brittleness during shearing. The growth of brittleness in specimen with increasing suction is clearly visualized from pictures taken at the end of the tests that indicate gradual transition in failure zones (i.e. ductile failure mode with barrel shape or

ACCEPTED MANUSCRIPT bulging at center under low to medium suctions and no barrel effect under high suction) after shear failure, as illustrated in Figs. 7(a)-7(d). The specimen with highest value of total suction are expected to exhibit maximum brittle failure, which is precisely the case as visually manifest from Figure 7(f). Specimens sheared in the matric suction range ψm = 50-750 kPa show development of

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multiple shear failure planes with barreling effect in the shear zone, while those sheared at total

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suctions ψt = 20,000 and 300,000 kPa developed distinct single shear failure plane. Also, the

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brittleness increased the amplitude of post-peak softening which is evident from increase in difference between magnitude of deviator stress at peak and critical state failure, as manifested from

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Figs. 6(a)-6(c).

4. Verification of shear strength models

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4.1. Vilar (2006) model - approach I

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Vilar (2006) proposed an hyperbolic equation that considers matric suction contribution towards an increase in peak shear strength by an increase in apparent cohesion to best fit experimental data from

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air-dried samples of Brazilian soils. The model was successfully used to predict the increase in shear

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strength/cohesion intercept, based on the following hyperbolic mathematical Eq. (5). cʺ = c(ψ) = c ′ +

ψ

(a + bψ)

(5)

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Where cʺ = c(ψ) = the cohesion intercept function of the soil suction, ψ = ua – uw, cʹ = effective soil cohesion (at ψ = 0). Parameters a and b are curve-fitting parameters obtained from tests using saturated and air-dried specimens. However, in the present work, similar to Reis et al. (2010), the parameters a and b were obtained from a best-fit analysis, by plotting ψ/(c(ψ) – cʹ) versus ψ > 0 and fitting the experimental points with a straight line given by the least square method. Although, Eq. (5) uses matric suction, attempt was made to apply the same equation and procedure to extend the experimental results up to total suction of 300,000 kPa by plotting soil

ACCEPTED MANUSCRIPT suction on logarithmic scale. The average value of apparent increase in shear strength (c″) was obtained by drawing a tangent at approximately ϕʹ = 35 deg. to Mohr’s stress circles at critical state failure at net confinements of (σ3 – ua) = 100, 200 and 300 kPa for each suction imposed (Table 3). The parameters a and b are captioned in Fig. 12, along with reasonably good correlation between the

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predicted and experimental results with R2 = 0.99.

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Vilar (2006) used direct shear test data from Escario and Juca (1989) on Madrid gray clay

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and Guadalix red clay that was extended to suctions of about 11,000 and 8,000 kPa respectively, far above their respective residual suction value, and then compared with these predictions from Eq. (5),

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with reasonable success. Apart from this exception, to the author’s best knowledge, none of the existing models have been tested over a wider range of suction (0.05 MPa to 300 MPa) as such used

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in this research; thus, making the present virtually the first such attempt, especially with specimens

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prepared in an identical way (e.g., similar compaction method, initial water content and initial voids ratio) and validated using unsaturated triaxial test data. It is worth noting that, when results are

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plotted beyond residual suction value, the shape of the curve resembles that of the SWRC.

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4.2. Vilar (2006) model – approach II and proposed modification

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Vilar (2006) also proposed a model that use maximum measured suction and modified the parameter

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b as in equation below

b=

1 (c(ψmax ) −

c′)

−

1 ψmax tan∅′

(6)

Alternatively, the predictions at critical state are made through equations (2), (3), and (6) and shown in Fig. 9. For the sake of brevity, and to compensate the effect of the net confining pressure, only one plot is shown with average c″ value obtained by plotting Mohr’s-stress circles at three net confining pressures, i.e., (σ3 – ua) = 100, 200 and 300 kPa for each suction level (Table 3). It was also cautioned that in granular soils the model could yield conservative results. In agreement to the suggestion, it can be observed that predictions from model were higher as compared to experimental results with

ACCEPTED MANUSCRIPT R2 = 0.69. Therefore, the value of “a” can be modified to a = 2.5/tanϕʹ instead of the one obtained from Eq. (2). As seen in Fig. 9, a good agreement was obtained between the predicted response and measured test response with R2 = 0.96 using modified value of parameter “a” in Vilar (2006), Eq. (6). It is worth mentioning here that by coincidence, the Vilar (2006) approach I and approach II with

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proposed slight modification yields almost similar predictions.

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4.3. Houston et al. (2008) model and proposed modification

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Houston et al. (2008) proposed a hyperbolic function, as given by Eq. (7), to predict the angle of

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friction with respect to suction, ϕb that can be used along with the extended Mohr-Coulomb shear strength equation proposed by Fredlund and Rahardjo (1993) to further predict the increase in

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suction-induced peak shear strength, provided that the air entry value (AEV) is known, along with

critical state. ψ∗ (a + bψ∗

] , where ψ∗ = (ua − uw ) − AEV

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∅b = ∅′ − [

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the saturated effective stress parameters. It should be noted that analysis is performed in this paper at

(7)

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The parameters “a” and “b” are determined by using transformed linear plot of ψ∗ against ψ ∗/(ϕʹ – ϕb). Experimental values of ϕb are first calculated. For instance, for ψ = 50 kPa, and σ3 – ua = 100 kPa

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from Fig. 2; ϕb = arctan (19/50) = 20.8 deg.

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Houston et al. (2008) were able to use this model quite successfully on triaxial shear strength experimental data from unsaturated CL-ML, SM, CL and SP soils, as well as on data from previous researchers (e.g., Gan et al., 1988; Escario and Juca, 1989; Oloo and Fredlund et al., 1996; and Thu et al., 2007). However, the data set was limited to a matric suction range less than 1500 kPa. As such, the model remains to be validated for suction values beyond 1500 kPa. Houston et al. (2008) also explained the physical significance of correlating “b” with ϕʹ using a simple equation, b = 1/ϕʹ. However, since they lacked the data beyond residual suction range, caution

ACCEPTED MANUSCRIPT was suggested while using the Eq. (7) for dry soils or in high suction range. From present work, when the parameter was evaluated using maximum suction as 750 kPa, the value of ϕʹ obtained from reciprocal of b varied between 29 to 40 deg. However, when maximum suction was taken as 300,000 kPa, equation, b = 1/ϕʹ, resulted in a value of ϕʹ = 35 deg. Remarkably, as can be observed from Fig.

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10, irrespective of the confining pressure (σ3 – ua = 100, 200 and 300 kPa), the value of the best

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fitting parameter b, when fitted over the entire suction range (i.e. b = 0.0286) remained virtually

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constant (see Table 4), and is in agreement with 1/b = ϕʹ = 35deg., as postulated by Houston et al. (2008).

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To extend the results in high suction range, i.e. well beyond residual suction, the soil suction was plotted on logarithmic scale to avoid matric suction data points getting concentrated in narrow

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range, thus providing a better visual representation of ϕ b over the entire suction range, as shown in

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Fig. 10. Good correlations are observed between predictions and experimental results with R 2 = 0.98 over the entire suction range of 50 – 300,000 kPa for net confinement of (σ3 – ua) = 300 kPa, as

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shown in Fig. 10.

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Fig. 11 shows the variation of gravimetric water content (w), angle of friction with respect to suction (ϕb), and apparent cohesion with increasing suction based on model predictions as originally

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postulated by Houston et al. (2008) and Vilar (2006). It can be observed that as the suction increases,

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the value of ϕb and water holding capacity of soil decreases non-linearly. Striking reductions in both, ϕb and water holding capacity of soil are observed beyond AEV of soil as expected for sandy soil. However, beyond the residual suction, the further increase in suction has low impact on reduction in ϕb: an indication that soil had attained its maximum strength. In the present work, no reduction in strength was observed even with imposed suction as high as 300,000 kPa (maximum total suction that can be applied and maintained constant throughout testing using relative humidity technique). For better visual comparison purposes, the y-axis scales were adjusted so that, irrespective of their different individual range, all three plots could be

ACCEPTED MANUSCRIPT accommodated within same plot size. Again, the shape of shear strength curves resembles that of the SWRC. 4.4. Fredlund et al. (1996) model – approach I and proposed modification Fredlund et al. (1996) and Vanapalli et al. (1996) proposed a nonlinear function for predicting the

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peak shear strength of unsaturated soil, utilizing the entire soil-water retention curve with suction

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between 0 to 1000,000 kPa, along with saturated shear strength parameters, cʹ and ϕʹ, as shown by

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Eq. (8). They also suggested the use of Fredlund’s and Xing’s (1994) equation to plot the best fitting SWRC through experimental points.

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τf = c ′ + (σ − ua ) tanφ′ + [(ua − uw ) {(Θ κ)(tanϕ′ )}]

(8)

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Where, κ = fitting parameter used for obtaining best-fit between the measured and predicted values. Θ = normalized volumetric water content = θw/θs ; where, θw = volumetric water content

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obtained using Fredlund and Xing (1994) equation. Third term of the Eq. (8) represents the shear

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strength contribution, τus.

τus = [( ua − uw ) {(Θ κ )(tanϕ′ )}]

(9)

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Fredlund et al. (1996) compared the experimental peak shear strength test results on glacial

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till from a series of multistage tests using modified direct shear test apparatus with predictions from Eq. (9). A thorough parametric study yielded good correlations between experimental and predicted

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peak shear strength with ĸ = 2.2. In the present work, a new function is postulated based on previous equations proposed by Fredlund et al. (1996), Vanapalli et al. (1996), and Sedano and Vanapalli (2011), including critical modifications to extend their usefulness into the high suction range. Eq. (9) was used to predict shear strength values at critical state, which were then compared with experimental results from this work. For instance, for ψ = 50 kPa; Θ = θw/θs = 18.5/30.2 = 0.61; τus = [50*(18.5/30.2)1.21*tan (35˚)] = 19.34 kPa. However, using one value of ĸ, over the entire test suction range, did not yield good

ACCEPTED MANUSCRIPT correlations, especially beyond residual suction value. Therefore, function ĸ can be modified to be comprised of two different values when using this model: the first value between the AEV (i.e. ψ = 10 kPa) and up to residual suction (i.e. ψ = 2000 kPa), and the second value beyond residual suction, as follows: (10)

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For ψ ≤ 0 − 2000 kPa, use ĸ = 1.21; and for ψ > 2000 kPa, use ĸ = 1.81

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As shown in Fig. 12, the experimental increase in shear strength was reasonably well predicted with

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R2 = 0.98 for the entire test range, i.e. 0-300,000 kPa. In previous research, “peak” shear strength values were used for comparison. In the present work, however, the increase in “critical state” shear

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strength is used for comparison, thus validating the model at critical state.

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4.5. Sedano and Vanapalli (2011) model – Approach II and proposed modification Sedano and Vanapalli (2011) introduced Eq. (11), very similar to Eq. (9), but using degree of

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saturation, S instead of normalized volumetric water content (θ), and thus were able to correlate, with

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reasonable accuracy, the critical state shear strength of glacial till obtained from modified ring shear apparatus using best-fit parameter, ĸ = 5.0, thus validating the model at critical state failure.

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τus = (ua − uw )[(S)ĸ tanϕ′]

(11)

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Close observations of experimental test results indicate that the critical state shear strength is fairly constant beyond 300 kPa while the target matric suction range was only up to 500 kPa; thus,

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the validation remains to be addressed in the high suction range. In the present work, an attempt is made to extend the critical state shear failure predictions at critical state failure, and far beyond residual suction, thereby attempting to validate this model for high suction range. Good correlations were obtained only up to ψm = 750 kPa. However, much higher and unrealistic predictions were obtained in the high suction range. It is clearly observed from the SWRC of the test soil (Fig.1) that its water retention capacity changes drastically beyond residual suction,

ACCEPTED MANUSCRIPT and hence the value of the fitting parameter ĸ should be adjusted to capture such dramatic change. Hence, a new value of ĸ = 1.85 is suggested for suction states far beyond residual suction. Parametric investigations of the proposed equation with varying values of ĸ, beyond residual suction, clearly indicate its sensitivity, as shown in Fig.

13. Upon using ĸ = 1.2, up to residual

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suction, and ĸ = 1.85, beyond residual suction, strong correlations (R2 = 0.98) were obtained between

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experimental values and predictions for the entire test suction range (i.e. ψ = 0 – 300 MPa), as

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illustrated in Fig. 14. However, the shear strength, particularly beyond residual suction drops with

4.6. Vanapalli et al. (1996) model - approach III

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any further increases in value of ĸ, and vice-versa.

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Vanapalli et al. (1996) proposed another predictive shear strength (at peak failure) model by eliminating the use of a fitting parameter κ, as given by Eq. (12) below:

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τf = c ′ + ( σn − ua ) tanϕ′ + ( ua − uw ) [(

θw − θr θs − θr

) tanϕ′]

(12)

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where, θw = volumetric water content, θw = saturated volumetric water content, and θr =

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residual volumetric water content that can be estimated from the SWRC. Similar results were obtained while using the degree of saturation (S) or gravimetric water content instead of volumetric

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water content in Eq. (12). Both Eq. (11) and (12) are consistent with the stress-state variable

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approach and satisfy the continuum mechanics concept. However, it has limitations in that increase in shear strength drops to zero at residual suction and might even become negative, i.e. decrease beyond residual suction. Vanapalli et al. (1998) tested the equation within matric suction range of 0500 kPa and obtained good correlation between experimental results and predictions. Authors made attempt to check the validity of this model for large suction range, especially beyond residual suction. Present paper explores suitability of applying above equations at critical state failure. As shown in Fig.

15, good correlations were obtained between experimental and predicted results for

range of matric suction up to ψ = 750 kPa. The nature of the Eq. (12) suggests its apt suitability for

ACCEPTED MANUSCRIPT predictions of decreasing shear strength beyond residual suction. Although it was confirmed experimentally in this research that the shear strength continued to increase with increase in suction beyond residual suction, the comparative predictions showed unrealistic decrease in shear strength; thus, making this model inappropriate beyond residual suction for test soil under investigation.

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4.7. Khalili and Khabbaz (1998) model and proposed modification

as expressed in Eq. 13.

(ua − uw )b

−0.55

]

(13)

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χ=[

( ua − uw )f

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Khalili and Khabbaz (1998) extended Bishop (1959) equation by introducing an empirical constant χ

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where, (ua – uw)f = matric suction in the specimen at failure condition, (ua – uw)b = air entry value suction of soil. Previously available data from 13 different soils indicated that the value of -0.55 best

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fits the equation over a wider range of soil type. In addition, the air entry value is needed along with

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saturated strength parameters to predict the peak shear strength using Eq. 14. (ua − uw )f −0.55 } τf = c + ( σ n − ua )tanϕ + (ua − uw ) [{ tanϕ′] (ua − uw )b ′

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′

(14)

ACCEPTED MANUSCRIPT However, when applied to results from present research at critical state, the predictions from original equation, could be improved with slight modification to the power function used in parameter χ as follows: ( ua−uw) f −0.43

χ = [(

ua−uw) b

]

(15)

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The modified equation holds good correlation (R 2 = 0.96) with results from experimental program

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from this research only up to ψm = 750 kPa (0.75 MPa), as illustrated in Fig. 16. Beyond this level of

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suction, however, the predictions are unrealistically high, thereby, limiting its use below residual

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suction.

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5. Summary and conclusions

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Consolidated drained triaxial tests were conducted on identically prepared (i.e., similar initial voids ratio, water content and compaction method (static), unsaturated silty sand specimens over a

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wide suction range between 50 to 300,000 kPa and sheared along the CTC stress path. Shear strength

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of soil increased dramatically with suction between air entry value and residual suction. On the other hand, it increased at dramatically slower rate beyond residual suction. The specimens underwent

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post-peak strain-softening that increased with increase in soil suction.

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Hyperbolic equation proposed by Houston et al. (2008), in its original form was validated for first time for suction range beyond residual suction. Slight modification was suggested to Vilar (2006) equation, and Khalili and Khabbaz (1998) equation to get better predictions that led to validation of former equation for silty sand test soil over selected wide suction range. Although, good correlations were obtained using modified Khalili and Khabbaz (1998) equation up to ψm = 750 kPa, unrealistically high predictions were obtained in high suction range; thus, limiting its use in lowmedium suction (0-750 kPa) range only for the test soil.

ACCEPTED MANUSCRIPT A new function is postulated based on previous equations proposed by Fredlund et al. (1996), Vanapalli et al (1996), and Sedano and Vanapalli (2011) including critical modifications to extend their predictions over high suction range. The modified equation uses two different values of best fitting parameter, ĸ; First, to improve original predictions up to residual suction and second, beyond

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residual suction, thereby extending it to high suction range up to 300 MPa.

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Almost all the models, except the one by Sedano and Vanapalli (2011), were previously

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validated to predict increase in peak shear strength due to increase in suction; however, this research

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focusses on validating them at critical state. Accurate assessments of unsaturated strength parameters are of extreme importance in natural slopes in fissured rocks with unsaturated clayey and silty sand

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fills that can undergo significant shear strength changes upon wetting, or shallow fissured landslides that can also be activated by wetting. Additional experimental evidence of unsaturated soil shear

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strength on variety of soils is needed in future to corroborate greater acceptance of proposed semi-

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empirical equations in their proposed form or in modified form as from this article or for their further

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Acknowledgements

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future enhancement.

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The experimental work described in this paper is part of an ongoing research project funded by the National Science

Foundation under MRI Award No. 1039956. This support is gratefully

acknowledged. Any findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

References Alonso, E. E., Pereira, J-M., Vaunat, J., Olivella, S., 2010. A microstructurally based effective stress for unsaturated soils. Geotechnique. 60 (12), 913-925.

ACCEPTED MANUSCRIPT Atkinson, J., 2007. The mechanics of soils and foundations , second ed. Taylor and Francis, pp. 442. Bishop, A.

W., 1971.

The

influence

of

progressive

failure

on the

choice

of

stability

analysis. Géotechnique, 21(2), 168-172. Bishop, A. W., 1959. The principle of effective stress. Tecknish. Ukebland, 106(39), 859-863. Escario, V., Juca, J. F. T., 1989. Strength and deformation of partly saturated soils. Proc. 12th Int. Conf. on Soil Mech. Found. Eng. Vol. 1, Balkema, Rio de Janeiro, 43-46.

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Escario, V., Saez, J., 1986. The shear strength of partly saturated soils. Geotechnique. 36(3), 453-

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456.

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Fredlund, D. G., Morgenstern, N. R., 1977. Stress strain variables for unsaturated soils. Proc. Amer. Soc. of Civil Eng. Vol. 103, No. GT5, 447-466.

Fredlund, D. G., Rahardjo, H., 1993. Soil mechanics for unsaturated soils. Wiley, New York.

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Fredlund, D. G., Xing, A., 1994. Equations for the soil-water characteristic curve. Can. Geotech. J. 31(4), 521-532.

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Fredlund, D. G., Xing, A., Fredlund, M. D., Barbour, S. L., 1996. The relationship of the unsaturated soil shear strength to the soil-water characteristic curve. Can. Geotech. J. 33(3), 440-448.

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Gallipoli, D., Gens, A., Chen, G., D’Onza, F., 2008. Modelling unsaturated soil behavior during normal consolidation and at critical state. Computers and Geotechnics. 35, 825-834.

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Gan, J. K. M., Fredlund, D. G., Rahardjo, H., 1988. Determination of shear strength parameter for unsaturated soil using direct shear test. Can. Geotech. J. 25(3), 500-510.

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Han, Z., Vanapalli, S. K., 2016. Stiffness and shear strength of unsaturated soils in relation to soilwater characteristic curve. Geotechnique. 66(8), 627-647.

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Houston. S. L., Perez-Garcia, N., Houston, W. N., 2008. Shear strength and shear-induced volume change behaviour of unsaturated soils from a Triaxial test program. J. Geotech. Geoenviron.

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Eng. 134 (11), 1619-1632.

Sedano, J. A., Vanapalli, S. K., 2011. The relationship between the critical state shear strength of unsaturated soils and the soil-water characteristic curve. Unsaturated Soils - Alonso & Gens (Eds), Taylor and Francis Group, London, 253-258, DOI: 10.1201/b10526-31. Khalili, N., Khabbaz, M. H., 1998. A unique relationship for the determination of the shear strength of unsaturated soils. Geotechnique. 48(5), 681-687. Nishimura, T., Fredlund, D. G., 2003. A new triaxial apparatus for high total suction using relative humidity control. 12th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering. Singapore, Leung et al. (eds), Vol. 1, August 4-8, 65-68, World Scientific Publishing, ISSN: 9789812385598.

ACCEPTED MANUSCRIPT Nuth, M., Laloui, L., 2008. Effective stress concept in unsaturated soils: clarification and validation of a unified framework. Int. J. Numer. Anal. Meth. Geomech. 32, 771-801. Oberg, A., Sallfors, G., 1997. Determination of shear strength parameters of unsaturated silts and sands based on the water retention curve. Geotech.Test. J. 20(1), 40-48. Oloo, S. Y., Fredlund, D. G., 1996. A method for determination of ϕb for statically compacted soils. Can. Geotech. J. 33, 272-280.

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Patil, U. D., 2014. Response of unsaturated silty sand over a wider range of suction states using a

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novel double-walled triaxial testing system. Ph.D. dissertation submitted to the department of

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civil engineering, University of Texas at Arlington, TX.

Patil, U. D., Hoyos, L. R., Puppala, A. J., 2015. Suitable shearing rate for triaxial testing of intermediate soils under vapor controlled medium to high suction range. Geotechnical Special

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Publication - ASCE. GSP 256, 2141-2150, http://dx.doi.org/10.1061/9780784479087.198. Patil, U. D., Hoyos, L. R., Puppala, A. J., 2016a. Modeling essential elasto-plastic features of

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compacted silty sand via suction-controlled triaxial testing. Int. J. Geomech. Available online, pp. 22, DOI: 10.1061/(ASCE)GM.1943-5622.0000726.

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Patil, U. D., Hoyos, L. R., Puppala, A. J., 2016b. Characterization of compacted silty sand using a double-walled triaxial cell with fully automated relative-humidity control. Geotech. Test. J.

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39(5), 742-756, http://dx.doi.org/10.1520/GTJ20150156. Rassam, D. W., Cook, F., 2002. Predicting the shear strength envelope of unsaturated soils. Geotech.

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Test. J. Vol. 25, No. 2, 215-220.

Reis, R. M., Azevedo, R. F., Botelho, B. S., Vilar, O. M., 2011. Performance of a cubical triaxial

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apparatus for testing saturated and unsaturated soils. Geotech. Test. J. 34(3), 1-9. Schofield, A., Wroth, C. P., 1968. Critical state soil mechanics. McGraw-Hill, London.

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Thu, T. M., Rahardjo, H., Leong, E. C., 2007. Critical state behavior of a compacted silt specimen. Soils and Foundations. 47(4), 749-755. van Genuchten, M. T., 1980. A closed-form equation for predicting the hydraulic conductivity unsaturated soils. Soil. Sci. Soc. Amer. J. 44, 892-898. Vanapalli, S. K., Fredlund, D. G., Pufahl, D. E., Clifton, A. W., 1996. Model for the prediction of shear strength with respect to soil suction. Can. Geotech. J. 33, 379-392. Vilar, O. M., 2006. A simplified procedure to estimate the shear strength envelope of unsaturated soil. Can. Geotech. J. 43, 1088-1095.

ACCEPTED MANUSCRIPT List of Tables Table 1. Best-fit parameters for selected SWCC functions Table 2. Experimentally obtained average values of apparent cohesion Table 3. Experimental values of unsaturated shear strength parameters

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Table 4. Calibrated parameters for compacted silty sand according to Houston et al. (2008) model

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Fredlund and Xing (1994)

α = 0.036

α = 55

n=1

n = 0.75

m = 0.5

m = 1.9

θr = 0.3

θs = 16.5 Ψr = 2000 kPa

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θs = 16.5

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200 200 200 200 200 200

& 300 & 300 & 300 & 300 & 300 & 300

20 37 64 88 120 150

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Average angle of friction with respect to suction, deg. (ϕb) 21.8 8.4 7.3 6.7 0.3 0.03

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100, 100, 100, 100, 100, 100,

Average apparent cohesion, kPa (c"avg)

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0.05 0.25 0.50 0.75 20 300

Net confining pressure, kPa (σ3 ‒ ua)

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Soil suction, MPa (ψ)

ACCEPTED MANUSCRIPT Table 3. Experimental values of unsaturated shear strength parameters Soil suction, MPa (ψ)

Apparent cohesion, kPa (c″)

100

0.05 0.25 0.5 0.75 20 300 0.05 0.25 0.5 0.75 20 300 0.05 0.25 0.5 0.75 20 300

19 39 59 99 102 140 31 53 80 131 140 208 21 50 73 96 162 180

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200

Angle of friction with respect to suction, deg. (ϕb) 20.8 8.9 6.7 7.5 0.29 0.03 31.8 12 9 9.9 0.4 0.0397 22.8 11.3 8.3 7.3 0.46 0.03

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Net confining pressure, kPa (σ3 ‒ ua)

ACCEPTED MANUSCRIPT Table 4. Calibrated parameters for compacted silty sand according to Houston et al. (2008) model Suction range

ϕʹ = 1/b 29.2 39.7 30

b 0.0342 0.0252 0.0333

Suction range 50 kPa – 300 MPa

b 0.0286 0.0286 0.0286

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50 – 750 kPa

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σ3 – ua 100 200 300

ϕʹ = 1/b 35 35 35

ACCEPTED MANUSCRIPT List of Figures Figure 1. Soil-water retention curve (SWRC) along drying path for compacted silty sand test soil Figure 2. Critical state Mohr circles under net confining pressures, (σ 3 – ua) = 100, 200, and 300 kPa: (a) ψ = 50 kPa; (b) ψ = 250 kPa Figure 3. Critical state Mohr circles under net confining pressures, (σ 3 – ua) = 100, 200, and 300 kPa: (a)

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ψ = 500 kPa; (b) ψ = 750 kPa

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Figure 4. Critical state Mohr circles under net confining pressures, (σ3 – ua) = 100, 200, and 300 kPa: (a) ψ = 20 MPa; (b) ψ = 300 MPa

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Figure 5. (a) Stress-strain response and (b) Variation of brittleness index of SM soil from suctioncontrolled CTC tests at different matric and total suctions

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Figure 6. Effect of suction on peak and critical deviator stress at different net confinements: (a) (σ 3 – ua) = 100 kPa, (b) (σ3 – ua) = 200 kPa, and (c) (σ3 – ua) = 300 kPa

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Figure 7. Typical specimen failure at different suction states: (a) CD300-50, (b) CD300-250, (c) CD300500, (d) CD300-750, (e) CDRH300-20MPa, (f) CDRH300-300MPa

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Figure 8. Variation of cohesion intercept with matric suction (Vilar, 2006; approach I) from average value of c″ at same suction but different confining pressures

approach II: modified

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Figure 9. Variation of cohesion intercept with matric suction using Vilar, 2006: approach II, and

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Figure 10. (a) Calibration of best-fitting parameters, (b) Variation of cohesion intercept with matric

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suction (Houston et al., 2008) from CD100-xx tests Figure 11. Variation of gravimetric water content, angle of friction with respect to suction and increase in

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shear strength for test soil over 00-1000 MPa soil suction Figure 12. Experimental and predicted increase in shear strength with soil suction using Fredlund et al. 1996 model – approach I with modification Figure 13. Parametric performance of proposed equation with varying value of ĸ beyond residual suction using Sedano and Vanapalli (2011) model – approach II with proposed modification Figure 14. Experimental and predicted suction-induced increase in shear strength up to Ψ = 300,000 kPa using Sedano and Vanapalli (2011) model – approach II with proposed modification Figure 15. Experimental and predicted shear strength using Vanapalli et al. (1996) model – approach III Figure 16. Experimental and predicted shear strength (Khallili and Khabbaz, 1998)

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Figure 1. Soil-water retention curve (SWRC) along drying path for compacted silty sand test soil

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Figure 2. Critical state Mohr circles under net confining pressures, (σ3 – ua) = 100, 200, and 300 kPa:

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(a) ψ = 50 kPa; (b) ψ = 250 kPa

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Figure 3. Critical state Mohr circles under net confining pressures, (σ 3 – ua) = 100, 200, and 300 kPa:

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Figure 4. Critical state Mohr circles under net confining pressures, (σ 3 – ua) = 100, 200, and 300 kPa:

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Figure 5. (a) Stress-strain response and (b) Variation of brittleness index of SM soil from suction-

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Figure 6. Effect of suction on peak and critical deviator stress at different net confinements: (a) (σ3 –

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(b)

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Figure 7. Typical specimen failure at different suction states: (a) CD300-50, (b) CD300-250, (c)

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Figure 8. Variation of cohesion intercept with soil suction (Vilar, 2006; approach I) from average value of c″ at same suction but different confining pressures

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Figure 9. Variation of cohesion intercept with matric suction using Vilar, 2006: Approach II, and

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Figure 10. (a) Calibration of best-fitting parameters, (b) Variation of cohesion intercept with soil suction over wide range of soil suction (Houston et al. 2008) from CD300-xx tests

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Figure 11. Variation of gravimetric water content, angle of friction with respect to suction and

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Figure 12. Experimental and predicted increase in average shear strength with soil suction using

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Figure 13. Parametric performance of proposed equation with varying value of ĸ beyond residual suction using Infante Sedano and Vanapalli (2011) model – approach II with proposed modification

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Figure 14. Experimental and predicted suction-induced increase in shear strength up to Ψ = 300,000 kPa using using Infante Sedano and Vanapalli (2011) model – approach II with proposed

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Figure 15. Experimental and predicted shear strength using Vanapalli et al. 1996 model; approach

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Figure 16. Experimental and predicted shear strength (Khallili and Khabbaz, 1998)