Modeling Unsaturated Soil Response under Suction-Controlled True Triaxial Stress Paths

Modeling Unsaturated Soil Response underSuction-Controlled True Triaxial Stress Paths

Laureano R. Hoyos1; Diego D. Pérez-Ruiz2; and Anand J. Puppala3

Abstract: Results from a comprehensive series of suction-controlled hydrostatic compression, conventional triaxial compression, triaxialcompression, triaxial extension, and simple shear tests, conducted on statically compacted specimens of poorly graded sand with clay, arepresented. The experiments were accomplished in a newly developed true triaxial apparatus to test cubical, 7.62 cm (3 in.) side, specimens ofunsaturated soil under controlled-suction states and for a wide range of stress paths that are not readily achievable in a cylindrical cell. The keyfeatures of the apparatus and a thorough performance verification test program have been documented in a first companion paper. Resultsfrom suction-controlled tests performed in the present work were used to calibrate and further validate two of the most popular elastoplasticcritical state-based frameworks postulated to date for unsaturated soils, namely, the Barcelona Basic Model and the Oxford Model. In general,predictions of unsaturated soil response from either model are shown to be reasonably accurate, highlighting their potential for use in com-putational analyses of geotechnical boundary-value problems that involve geosystems made of compacted soil or resting on unsaturatedground. DOI: 10.1061/(ASCE)GM.1943-5622.0000159. © 2012 American Society of Civil Engineers.

CE Database subject headings: Unsaturated soils; Soil suction; Constitutive models; Soil compression.

Author keywords: Unsaturated soil; Matric suction; Suction-controlled testing; Constitutive modeling.

Introduction

It has been all but a perennial wisdom among practicing engineersto assume fully saturated soil conditions as the most conservativeapproach to analyzing and designing a broad variety of geosystems.Persuasive and now copious unsaturated soil research disputes thisparadigm, and geotechnical engineering communities worldwideare increasingly recognizing the importance of a better understand-ing of the engineering behavior of this type of material. The devel-opment of unsaturated soil mechanics proved rather slow primarilybecause of a continuous debate over the appropriate stress vari-ables and the complexities in laboratory testing. Matyas andRadhakrishna (1968), Fredlund and Morgenstern (1977), and sev-eral others, have demonstrated the definitive benefits of adoptingmatric suction, s ¼ ðua � uwÞ, and the excess of total stress overair pressure, that is, net stress, (σ � ua), as the relevant stress statevariables for modeling essential features of unsaturated soil behav-ior through suction-controlled oedometer, triaxial, and direct sheartesting. However, accurate numerical predictions in geotechnicalboundary-value problems that involve unsaturated soil materials re-quire that the soil constitutive relations be valid for all possible mul-tiaxial stress paths likely to be experienced in the field. It is in this

context that a suction-controlled true triaxial apparatus plays afundamental role.

In the present work, results from a comprehensive series ofsuction-controlled hydrostatic compression (HC), conventional tri-axial compression (CTC), triaxial compression (TC), triaxial exten-sion (TE), and simple shear (SS) tests, conducted on severalstatically compacted specimens of poorly graded sand with clay(SP-SC soil), are presented. The experiments were accomplishedin a newly developed true triaxial apparatus that has been madesuitable to test cubical, 7.62 cm (3 in.) side, specimens of unsatu-rated soil under controlled-suction states. The apparatus is a refinedversion of the one previously reported by Hoyos et al. (2008) andits key features and corresponding performance verification testinghave been documented in a first companion paper.

Results from suction-controlled tests are used to calibrate andfurther validate two of the most popular elastoplastic criticalstate-based frameworks postulated to date for unsaturated soils:the Barcelona Basic Model (BBM) by Alonso et al. (1990) andthe Oxford Model (OM) by Wheeler and Sivakumar (1995).In the last two decades, both models have been the subject of con-tinuous enhancement and sophisticated refinement, primarily froma theoretical standpoint. (An exhaustive literature review is beyondthe scope of this work.) Moreover, a few research efforts have al-ready been reported on models validation in sandy soils using truetriaxial test systems, including Matsuoka et al. (2002), Macari et al.(2003), and Hoyos and Arduino (2008). However, additional exper-imental evidence and calibration data, for a wider variety of soils,are still needed to substantiate the validation of both models, andmore experience is to be gained through parametric investigationsof the original formulations in their simplest form. The presentwork is motivated by these research needs.

Experimental Program and Scope

Preliminary testing on SP-SC soil, documented in a first companionpaper, showed that the newly developed true triaxial apparatus is

1Associate Professor, Dept. of Civil Engineering, Univ. of Texas atArlington, Arlington, TX 76019 (corresponding author). E-mail: [email protected]

2Associate Professor, Departamento de Ingeniería Civil e Industrial,Pontificia Universidad Javeriana, Cali, Colombia. E-mail: [email protected]

3Professor, Dept. of Civil Engineering, Univ. of Texas at Arlington,Arlington, TX 76019. E-mail: [email protected]

Note. This manuscript was submitted on November 11, 2010; approvedon July 8, 2011; published online on July 11, 2011. Discussion period openuntil November 1, 2012; separate discussions must be submitted forindividual papers. This paper is part of the International Journal of Geo-mechanics, Vol. 12, No. 3, June 1, 2012. ©ASCE, ISSN 1532-3641/2012/3-292–308/$25.00.

292 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MAY/JUNE 2012

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http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0000159




suitable for testing soils under suction-controlled conditionsthrough the axis-translation technique. Consistent and replicatebehavior was observed from samples prepared by a static com-paction method with initial moisture content from 10% to 11%.Statically compacted samples yield an average specific volume,v ¼ 1þ e ¼ 1:72. The compacted sample is gently slid inthrough one of the lateral cavities of the core frame, as shownin Fig. 1, after which the remaining wall assemblies are set intoplace, as described in a first companion paper. A dry unit weight,γd ¼ 15:34 kN∕m3 (97:6 lb∕ft3), which corresponds to 80% ofProctor γd�max, was found to yield the lowest preconsolidationpressure, which makes it feasible to bring the soil to a full virginstate, with plastic deformations large enough to identify theloading-collapse curve postulated by the BBM. Finally, a stress-controlled testing scheme, with an 8 kPa∕h loading rate (approx-imately 1:15 psi∕h), proved adequate for testing SP-SC soil underconstant-suction states.

In the present work, a comprehensive series of 4 HC, 13 CTC, 6TC, 3 TE, and 3 SS tests, for a total of 29 suction-controlled tests onan equal number of samples, was accomplished in a period of ap-proximately 18 months by following the sample preparation andtesting protocols summarized previously, with each test taking from12 to 15 days to complete, including pore-fluid equalization time.The samples were tested under sustained matric suction states,s ¼ ua ¼ 50, 100, 200, or 350 kPa, and for initial net mean stresses,p ¼ ð1∕3Þðσ1 þ σ2 þ σ3Þ � ua ¼ 50, 100, or 200 kPa. The initialmoisture content (10% to 11%) in the statically compacted soil

corresponds to a suction value reasonably close to 50 kPa, accord-ing to the soil-water characteristic curve reported in a firstcompanion paper, which reduces the time required for pore-fluidequalization before isotropic loading and/or true triaxial shearing.Diffused-air flushing was performed every 12 hours during suction-controlled testing (Pérez-Ruiz 2009).

Soil Response under Suction-Controlled IsotropicLoading

A series of 4 HC tests was conducted on an equal number of stati-cally compacted samples of SP-SC soil at constant-suction states,s ¼ ua ¼ 50, 100, 200, and 350 kPa, as shown schematically inFig. 2. The soil is first hydrostatically compressed to a target meanstress, p ¼ 50 kPa, as represented by path OA in Fig. 2. The pore-air pressure ua is then gradually increased (soil drying process) tothe preestablished suction state whereas the net mean stress is keptconstant at 50 kPa by a simultaneous and equal increase of the ex-ternal stresses in all three principal directions. This process is rep-resented by the Equalization stage I (Fig. 2). The applied pore-airpressure ua is maintained constant until no further change in bothwater volume (less than 0:035 ml∕day) and specific volume (lessthan 0:01∕day) was observed, at which point the pore-fluid equali-zation stage is considered complete. Fig. 3 shows the change inspecific volume with time, after the initiation of the equalizationstage (point A), for different sustained-suction states. From this

Fig. 1. Placing of compacted cubical sample into inner cavity of core frame

50 600

Mat

ric s

uctio

n, s

(kP

a)

Net mean stress, p (kPa)

100

200

350

50

Ramped consolidation ( II )

Equalization ( I )

O A

Fig. 2. Suction-controlled HC stress paths carried out in p∶s plane

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figure, a 120-hour equalization time (five days) was deemedappropriate for all suction states.

A pore-fluid equalization stage is followed by a constant-suction ramped consolidation stage II (Fig. 2) to a final net meanstress ranging from 600 to 700 kPa. In each case, the sample isultimately unloaded to the initial net mean stress of 50 kPa. Fig. 4shows the change in specific volume with net mean stress (onnatural-log scale) from all suction-controlled HC tests. It can bereadily observed the significant influence that matric suction hason the change in specific volume experienced by the soil through-out the equalization process, with a considerable decrease involume for s ¼ 350 kPa before ramped consolidation. In all cases,the soil was brought to a full virgin state, with plastic deforma-tions large enough to identify the corresponding preconsolidation

pressure poðsÞ for each suction state. In addition, the slope ofall the elastic rebound curves is reasonably constant, in accor-dance to the framework postulated by the BBM (Alonsoet al. 1990).

Fig. 5 shows the change in minor, intermediate, and majorprincipal strains with net mean stress for the sample testedunder matric suction, s ¼ 50 kPa. The similar responses of theminor and intermediate principal strains are indicative of a mini-mal degree of soil anisotropy in the horizontal principal directionswhen samples are prepared through static compaction. Moreover,soil stiffness in the vertical direction is expected to be considerablyhigher in the statically compacted samples, which is reflected in thelower values of the major principal strain during rampedconsolidation.

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0 50 100 150 200 250 300Elapsed time, t (hr)

Cha

nge

in s

peci

fic v

olum

e, ∆

vs = 50 kPa

s = 100 kPa

s = 200 kPa

s = 350 kPa

A

Fig. 3. Assessment of appropriate equalization time for different constant-suction states

1.2

1.3

1.4

1.5

1.6

3.5 4.5 5.5 6.5 7.5

Natural log of net mean stress, ln(p)

Spe

cific

vol

ume,

v =

1 +

e

s = 50 kPa

s = 100 kPa

s = 200 kPa

s = 350 kPa

Fig. 4. Response of compacted SP-SC soil from s-controlled HC tests at s ¼ 50, 100, 200, and 350 kPa


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Soil Response under Suction-Controlled TrueTriaxial Shearing

Stress Paths

A series of 13 CTC and 6 TC tests was also accomplished on anequal number of statically compacted samples of SP-SC soil, asshown schematically in the p∶q∶s space of Fig. 6(a). TC tests were

carried out at constant net mean stress. The encircled number nextto each path represents the number of trial tests accomplished foreach test condition. Tests were conducted at constant-suction statesranging from 50 to 200 kPa, and for initial net mean stress values,before shearing, also ranging from 50 to 200 kPa. After completionof pore-fluid equalization in each test, the soil was monotonicallysheared with a deviatoric-stress application rate of 8 kPa∕h until it

0

200

400

600

800

86420

Principal strain (%)

Net

mea

n st

ress

, p (

kPa)

ε1 ε3 ε2

Fig. 5. Assessment of degree of soil anisotropy from s-controlled HC test at s ¼ 50 kPa

TE (b = 1, θ = 60o)

SS (b = 0.5, θ = 30o)TC (b = 0, θ = 0o)

B

σ2 – σ3

σ1 – σ3b =

(σ1 – ua)

(σ2 – ua () σ3 – ua)

θ

p : kPa

q : kPa

s : kPa

50

100

200

50 100 200

31 2

3

2 22

1

2

# Number of trial tests

1

TE (b = 1, θ = 60o)

SS (b = 0.5, θ = 30o)TC (b = 0, θ = 0o)

B

σ2 – σ3

σ1 – σ3b =

(σ1 – ua)

(σ2 – ua () σ3 – ua)

θTE (b = 1, θ = 60o)

SS (b = 0.5, θ = 30o)TC (b = 0, θ = 0o)

B

σ2 – σ3

σ1 – σ3b =

σ2 – σ3

σ1 – σ3b =

(σ1 – ua)

(σ2 – ua () σ3 – ua)

θ

p : kPa

q : kPa

s : kPa

50

100

200

50 100 200

31 2

3

2 22

1

2

# Number of trial testsNumber of trial tests

1

TE (b = 1, θ = 60o)

SS (b = 0.5, θ = 30o)TC (b = 0, θ = 0o)

B

σ2 – σ3

σ1 – σ3b =

(σ1 – ua)

(σ2 – ua () σ3 – ua)

θTE (b = 1, θ = 60o)

SS (b = 0.5, θ = 30o)TC (b = 0, θ = 0o)

B

σ2 – σ3

σ1 – σ3b =

σ2 – σ3

σ1 – σ3b =

(σ1 – ua)

(σ2 – ua () σ3 – ua)

θ

p : kPa

q : kPa

s : kPa

50

100

200

50 100 200

31 2

3

2 22

1

2


1

p : kPa

q : kPa

s : kPa

50

100

200

50 100 200

3311 22

33

22 2222

11

22

# Number of trial testsNumber of trial tests

1

TE (b = 1, θ = 60o)

SS (b = 0.5, θ = 30o)TC (b = 0, θ = 0o)

B

σ2 – σ3

σ1 – σ3b =

(σ1 – ua)

(σ2 – ua () σ3 – ua)

θTE (b = 1, θ = 60o)

SS (b = 0.5, θ = 30o)TC (b = 0, θ = 0o)

B

σ2 – σ3

σ1 – σ3b =

σ2 – σ3

σ1 – σ3b =

(σ1 – ua)

(σ2 – ua () σ3 – ua)

θ

p : kPa

q : kPa

s : kPa

50

100

200

50 100 200

31 2

3

2 22

1

2


1

p : kPa

q : kPa

s : kPa

50

100

200

50 100 200

3311 22

33

22 2222

11

22

#

11

(a)

(b)

Fig. 6. Suction-controlled stress paths carried out in: (a) p∶q∶s space; (b) octahedral plane


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was readily apparent that the soil had reached peak strength.A more detailed description of the test procedures is presentedby Pérez-Ruiz (2009).

Finally, a series of 3 TE and 3 SS tests was conductedon an equal number of statically compacted samples of SP-SC soil,as shown schematically in the octahedral plane of Fig. 6(b). Testswere conducted at constant-suction states, s ¼ ua ¼ 50, 100, or200 kPa, and, in all cases, under an initial net mean stress,p ¼ 100 kPa. After completion of pore-fluid equalization (pointB), the soil was imposed a monotonic shearing corresponding toeither a TE or SS stress path until it was readily apparent thatthe soil had reached peak strength. (The previously describedTC paths can also be represented on the same octahedral plane.)The following summarizes the observed response of SP-SC soilfrom suction-controlled TC, SS, and TE tests, as described

previously. Results from suction-controlled CTC tests will be pre-sented and used for models calibration and validation in a sub-sequent section.

General Soil Response

Results from TC tests conducted at constant-suction states,s ¼ 50 kPa and 200 kPa, are shown in Fig. 7. Results are presentedin terms of deviatoric-stress versus principal strain response, inwhich the former is defined in Eq. (1). Tests were accomplishedunder a constant net mean stress, p ¼ 100 kPa. A significant in-crease in peak strength is observed for s ¼ 200 kPa. The test cellis also capable of reproducing the compressive (+) nature of themajor principal strain, and the expansive (-) nature of both theminor and intermediate principal strains, as dictated by the TCloading scheme.

0

50

100

150

200

250

300


Dev

iato

ric s

tres

s, q

(kP

a)

s = 200 kPaε1ε1

ε2ε2ε3ε3

0

50

100

150

200

250

300

-30 -20 -10 0 10 20 30

-30 -20 -10 0 10 20 30


Dev

iato

ric s

tres

s, q

(kP

a)

s = 50 kPa

ε1ε1

ε2ε2ε3ε3

(a)

(b)

Fig. 7. Response of compacted SP-SC soil from s-controlled TC tests: (a) s ¼ 50 kPa; (b) s ¼ 200 kPa


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q ¼ 1ffiffiffi2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðσ1 � σ2Þ2 þ ðσ2 � σ3Þ2 þ ðσ1 � σ3Þ2

qð1Þ

Results from SS tests conducted at constant-suction states,s ¼ 50 kPa and 200 kPa, are shown in Fig. 8. Tests were alsoaccomplished under a constant net mean stress, p ¼ 100 kPa.Again, a significant increase in peak strength is observed fors ¼ 200 kPa. During SS testing, the major principal stress is mono-tonically increased whereas the minor principal stress is simultane-ously decreased in the same magnitude (Δσ3 ¼ �Δσ1), asdepicted schematically in Fig. 6(b). The intermediate principalstress is kept constant (Δσ2 ¼ 0). Consequently, the major princi-pal strain is found to be compressive (+), the minor principal strain

is expansive (-), and the intermediate principal strain is virtuallynegligible, which corresponds closely to a suction-controlled plainstrain case.

Results from TE tests conducted at constant-suction states, s ¼50 kPa and 200 kPa, are shown in Fig. 9. Tests were accom-plished under a constant net mean stress, p ¼ 100 kPa. As ex-pected, higher peak strength is observed for s ¼ 200 kPa. DuringTE testing, both the major and intermediate principal stresses aremonotonically increased in the same magnitude (Δσ1 ¼ Δσ2)whereas the minor principal stress is simultaneously decreased(Δσ3 ¼ �2Δσ1 ¼ �2Δσ2), as depicted schematically inFig. 6(b). Consequently, the major and intermediate principalstrains are found to be compressive (+) whereas the minor principal

0

50

100

150

200

250

300

-60 -40 -20 0 20 40 60

Major and minor principal strain (%)

Dev

iato

ric s

tres

s, q

(kP

a)

s = 50 kPa

ε1ε1ε3ε3

0

50

100

150

200

250

300

-20 0 20

Intermediate p. s. (%)

ε2ε2

0

50

100

150

200

250

300

-60 -40 -20 0 20 40 60

Major and minor principal strain (%)

Dev

iato

ric s

tres

s, q

(kP

a)

s = 200 kPa

ε1ε1ε3ε3

0

50

100

150

200

250

300

-20 0 20

Intermediate p. s. (%)

ε2ε2

(a)

(b)

Fig. 8. Response of compacted SP-SC soil from s-controlled SS tests: (a) s ¼ 50 kPa; (b) s ¼ 200 kPa


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strain is expansive (-) and significantly higher in magnitude. Sim-ilar behavioral trends were reported for low-plasticity silty sand(SM soil) by Macari and Hoyos (2001).

Barcelona Basic Model: Key Features

The BBM is an elastoplastic critical state-based formulation involv-ing six state variables for the axisymmetric (σ2 ¼ σ3) stress statecondition; namely, the net mean stress, p ¼ ð1∕3Þðσ1 þ 2σ3Þ � ua;deviatoric-stress, q ¼ ðσ1 � σ3Þ; matric suction, s ¼ ðua � uwÞ;specific volume, v ¼ 1þ e; total volumetric strain, εvp ¼ðε1 þ 2ε3Þ; and total shear strain, εq ¼ ð2∕3Þðε1 � ε3Þ. The modelis intended for soils of moderate and low-plasticity, featuring elasticstrains when the soil state lies inside a state boundary hypersurface,and plastic strains once the state boundary hypersurface is reached.Plastic behavior, as the soil state traverses the state boundary

hypersurface, corresponds to an expansion of a yield surface inthe p∶q∶s space, as depicted schematically in Fig. 10. A detaileddescription of the BBM framework, including yield loci, flow rules,hardening laws, and elastic and plastic strain definitions, is given byJosa (1988) and Alonso et al. (1990).

A first distinctive feature of the model is the assumption of amonotonic decrease of the volumetric stiffness parameter λðsÞ withincreasing matric suction, expressed as follows:

λðsÞ ¼ λð0Þ½ð1� rÞ expð�βsÞ þ r� ð2Þ

in which r ¼ λðs → ∞Þ∕λð0Þ; and, β = parameter controlling therate of increase of soil stiffness with matric suction. The previousexpression is then used to define a loading-collapse (LC) yield lo-cus in the p∶s plane, which is shown in Fig. 10 as a full set ofpreconsolidation pressures poðsÞ for each associated value ofmatric suction, expressed as follows:

0

50

100

150

200

250

300

-30 -20 -10 0 10 20 30Principal strain (%)

Dev

iato

ric s

tres

s, q

(kP

a)

s = 200 kPa

ε1ε1

ε2ε2

ε3ε3

0

50

100

150

200

250

300

-30 -20 -10 0 10 20 30Principal strain (%)

Dev

iato

ric s

tres

s, q

(kP

a)

s = 50 kPa

ε1ε1

ε2ε2

ε3ε3

(a)

(b)

Fig. 9. Response of compacted SP-SC soil from s-controlled TE tests: (a) s ¼ 50 kPa; (b) s ¼ 200 kPa


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�poðsÞpc

�¼

�poð0Þpc

�λð0Þ�kλðsÞ�k ð3Þ

in which k = elastic rebound index with respect to net mean stress;and pc = preconsolidation stress under saturated conditions (s ¼ 0)for which the LC yield locus becomes a straight line, i.e., for anygiven value of matric suction, pc ¼ poðsÞ.

A second distinctive feature of the model is the assumption of anonassociative flow rule for the direction of plastic shear strain in-crements dεpq associated with the yield locus in p∶q plane, as shownin Fig. 10, and proposed as follows:

dεpqdεpvp

¼ 2αqM2½2pþ ps � poðsÞ�

ð4Þ

in which dεpvp = plastic volumetric strain increments. The constantα is then defined as follows:

α ¼ MðM � 9ÞðM � 3Þ9ð6�MÞ

�1

1� k∕λð0Þ�

ð5Þ

in whichM = suction-independent slope of critical state line (CSL).A detailed description of the explicit step-by-step integration of allBBM constitutive relations is presented by Hoyos (1998) andPérez-Ruiz (2009).

Oxford Model: Key Features

The OM formulation is similar to that of the original BBM,although it takes a slightly different approach to model calibrationand evaluation of constitutive parameters. The model postulatesthat all the essential constitutive parameters are suction-dependentand ought to be experimentally predetermined for a particular

matric suction state, including the slope of critical state lines inthe p∶q plane and soil stiffness parameters in the v∶p plane, as shownschematically in Fig. 11. A detailed description of the developmentof the OM framework is presented by Sivakumar (1993) andWheeler and Sivakumar (1995).

The model postulates a loading-collapse yield locus in the p∶splane defined as follows:

½λðsÞ � k� ln�poðsÞpat

�¼ ½λð0Þ � k� ln

�poð0Þpat

�þ NðsÞ � Nð0Þ

þ ks ln

�sþ patpat

�ð6Þ

in which pat = atmospheric pressure (101.3 kPa), which is used as areference pressure to make the expression dimensionally consis-tent; NðsÞ = specific volume on normal compression line for netnormal stress equal to atmospheric pressure; and ks = elastic re-bound index with respect to suction. The definitions of modelparameters in Eq. (6) are schematically represented in Fig. 11.

Eq. (6) would reduce to Eq. (3) if there indeed exists a referencepressure pc at which the LC locus becomes a straight line in the p∶splane, as postulated by the BBM. However, in contrast with theBBM formulation, the OM framework adopts an associated flowrule for the assessment of plastic shear strain increments dεpq, asfollows:

dεpqdεpvp

¼ qM2�ðp� pxÞ

ð7Þ

The definitions of these and other model parameters are alsorepresented in Fig. 11. A detailed description of the explicitstep-by-step integration of all OM constitutive relations ispresented by Pérez-Ruiz (2009).

Fig. 10. General critical state-based framework of Barcelona BasicModel (BBM)

Fig. 11.General critical state-based framework of OxfordModel (OM)


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Calibration of Model Parameters under IsotropicLoading

BBM Parameters

Fig. 12 illustrates the graphical determination of preconsolidationpressure poð350Þ from ramped consolidation under constant-suction state, s ¼ 350 kPa. The semilogarithmic plot is essentiallythe same as that shown in Fig. 4. A natural-log value of 4.7, iden-tified by a marked change in slope, corresponds to a preconsolida-tion pressure, poð350Þ ¼ 111 kPa, which is also illustrated inFig. 12 when the horizontal axis for net mean stress is changedto arithmetic scale. Likewise, for ramped consolidation testsconducted under constant-suction states, s ¼ 50, 100, and200 kPa, approximate values for the corresponding precon-solidation pressures, poð50Þ ¼ 75 kPa, poð100Þ ¼ 85 kPa, andpoð200Þ ¼ 100 kPa, were obtained.

This pattern corroborates the existence of an initial LC yieldlocus induced by the static compaction method used to preparethe cubical samples. Fig. 13 shows the initial LC curve experimen-tally assessed in this current work, along with previously reportedLC curves for different soils and compaction methods (i.e.,Wheeler and Sivakumar 1995; Hoyos 1998; Laikram 2007).Although the target densities are different in all cases, it can bereadily observed that the static compaction method used in thispresent work corresponds to a compactive effort considerablyhigher than that induced by tamping or kneading, as clearly man-ifested by the largest values of compaction-induced preconsolida-tion pressure poðsÞ.

Fig. 14 illustrates the graphical determination of volumetricstiffness parameter λð200Þ from ramped consolidation underconstant-suction state, s ¼ 200 kPa, including assessment ofthe elastic rebound index. Best-fit values for the slopes of thesenormal compression lines were found to be λð50Þ ¼ 0:1275,

1.2

1.3

1.4

1.5

1.6

50 150 250 350 450 550 650


Spe

cific

vol

ume,

v =

1 +

e

po(350) = 111 kPa

s = 350 kPa

1.2

1.3

1.4

1.5

1.6

5.65.55.45.3


Spe

cific

vol

ume,

v =

1 +

e

s = 350 kPa

ln(p) = 4.7

Fig. 12. Example determination of preconsolidation pressure poð350Þ for s ¼ 350 kPa


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λð100Þ ¼ 0:1157, λð200Þ ¼ 0:1033, and λð350Þ ¼ 0:0970 for ma-tric suction values s ¼ 50, 100, 200, and 350 kPa, respectively. Thispattern is also consistent with the BBM formulation, which postu-lates a monotonic decrease in λðsÞ with increasing suction. In ad-dition, best-fit values for the elastic rebound index were found to bek ¼ 0:0314, 0.0308, 0.0326, and 0.0307 for matric suction valuess ¼ 50, 100, 200, and 350 kPa, respectively. An average value,k ¼ 0:0314, was adopted.

The least squares method can then be used to solve the over-determined system in Eq. (2), allowing for determination ofconstitutive parameters λð0Þ, r, and β. Using experimental values,

λð50Þ ¼ 0:1275, λð100Þ ¼ 0:1157, λð200Þ ¼ 0:1033, andλð350Þ ¼ 0:0970, best-fit values for these three unknowns werefound to be λð0Þ ¼ 0:146, r ¼ 0:649, and β ¼ 8:952 MPa�1, witha coefficient of determination, R2 ¼ 0:99. The same method canalso be used to solve the overdetermined system in Eq. (3),allowing for the assessment of parameters pc and poð0Þ. Usingexperimental values, poð50Þ ¼ 75 kPa, poð100Þ ¼ 85 kPa,poð200Þ ¼ 100 kPa, and poð350Þ ¼ 111 kPa, best-fit values forthese two unknowns were found to be pc ¼ 31:9 kPa andpoð0Þ ¼ 65:4 kPa, with a coefficient of determination, R2 ¼ 0:98.A parametric performance of the LC yield locus for this partial set

0

200

400

600

0 20 40 60 80 100 120 140


Mat

ric s

uctio

n, s

(kP

a)

Silty sandTamping compaction

γd = 10.59 kN/m3

(Hoyos, 1998)

Silty sandPluviation-tamping compaction

γd = 10.39 kN/m3

(Laikram, 2007)

Poorly-graded sand with clayStatic compaction

γd = 15.34 kN/m3

(Current Work)

KaolinKneading compaction

γd = 11.77 kN/m3

(Wheeler and Sivakumar, 1995)

Fig. 13. Current and previously reported LC curves for different soil compaction conditions

λ(200) = 0.1033

1.25

1.30

1.35

1.40

1.45

1.50

5.65.55.45.3


Spe

cific

vol

ume,

v =

1 +

e

k = 0.0326

k = 0.0326

Fig. 14. Example determination of model parameters k and λð200Þ for s ¼ 200 kPa


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of calibrated parameters is shown in Fig. 15. The experimental datapoints from compacted SP-SC soil show very close agreement withthe LC curve predicted for net mean stress, poð0Þ ¼ 65:4 kPa.

OM Parameters

Using atmospheric pressure, pat ¼ 101:3 kPa, as the referencestress shown in Fig. 11, the corresponding specific volumes onthe normal compression lines were found to be Nð50Þ ¼ 1:550,Nð100Þ ¼ 1:529, Nð200Þ ¼ 1:483, and Nð350Þ ¼ 1:439 for matricsuction values s ¼ 50, 100, 200, and 350 kPa, respectively. Again,the least squares method can be used to solve the overdeterminedsystem in Eq. (6), allowing for determination of constitutive param-eters λð0Þ, poð0Þ, Nð0Þ, and ks. Best-fit values for these fourunknowns were found to be λð0Þ ¼ 0:146, poð0Þ ¼ 63:9 kPa,Nð0Þ ¼ 1:589, and ks ¼ 0:0318, with a coefficient of determina-tion, R2 ¼ 0:98. As expected, the values for parameters λð0Þand poð0Þ are virtually identical to those obtained for the BBM.

Calibration of Model Parameters underAxisymmetric Shearing

BBM Parameters

Results from the series of 13 CTC and 6 TC tests conducted in thiswork, as shown in Fig. 6(a), were used for the calibration of BBMand OM parameters in p∶q∶s∶v space. Fig. 16 shows the best-fittingcritical state lines assessed from all suction-controlled CTC/TCtests and plotted in q∶p and v∶p planes. In all cases, critical statecondition was identified whenever it was readily apparent thatthe soil had reached peak strength or the total induced shear strainwas close to 25%, whichever condition was first achieved. Matricsuction is observed to exert a noticeable influence on the finalposition of the CSL; however, the slope MðsÞ of all critical statelines remains reasonably constant, in clear agreement with theBBM formulation.

Within the range of stresses applied, i.e., matric suction, s ¼ 50to 200 kPa, and initial net mean stress, p ¼ 50 to 200 kPa, the three-dimensional plain-surface plane expressed by Eq. (8) fits all the

experimental values of deviatoric-stress at critical state, with a stan-dard deviation of 6.82%. The plane yields best-fit values,M ¼ 1:103, for the slope of critical state lines; and k ¼ 0:616,for the rate of increase in apparent tensile strength with suction(Fig. 10), with a coefficient of determination, R2 ¼ 0:904.Comparison between experimental and predicted values ofdeviatoric-stress at critical state condition is shown in Fig. 17,which shows a reasonably close agreement for the obtained valuesof parameters M and k, as follows:

q ¼ MpþMks ¼ 1:103 pþ 0:616 s ð8Þ

Finally, as a consequence of the flow rule postulated in Eq. (4),no plastic shear strain is expected to occur during initial shearingwhen the soil is under lightly overconsolidated condition. Hence,the elastic shear modulus can be estimated from the initial portionof the deviatoric-stress versus total shear strain curve. A close in-spection of Fig. 6(a) clearly indicates that only the six CTC testsperformed under initial net mean stress, p ¼ 50 kPa, as shown inFig. 15, fall within the elastic region enclosed by the compaction-induced LC yield locus (Fig. 10). These tests yield an averagevalue of shear modulus for statically compacted SP-SCsoil, G ¼ 5:5 MPa.

OM Parameters

Fig. 16 shows that, even when plotted in a v∶p plane, a uniquecritical state hyperline can be devised for each matric suctionstate, regardless of the test path followed to reach critical statecondition. Again, using atmospheric pressure, pat ¼ 101:3 kPa,as the reference stress shown in Fig. 11, the correspondingbest-fit values for the remaining model parameters were foundto be ψð50Þ ¼ 0:230, Γð50Þ ¼ 1:416, μð50Þ ¼ 79:29 kPa, andMð50Þ ¼ 0:963 for matric suction s ¼ 50 kPa; ψð100Þ ¼ 0:242,Γð100Þ ¼ 1:459, μð100Þ ¼ 105:16 kPa, and Mð100Þ ¼ 0:971for matric suction s ¼ 100 kPa; and ψð200Þ ¼ 0:280,Γð200Þ ¼ 1:530, μð200Þ ¼ 139:41 kPa, and Mð200Þ ¼ 0:975for matric suction s ¼ 200 kPa.

A constant value, M ¼ 0:970, can be assumed, independent ofmatric suction, as shown in Fig. 16. It is also worth noting that the

po(0) = 31.9 kPa

po(0) = 55 kPa

po(0) = 45 kPa po(0) = 65.4 kPa

po(0) = 75 kPa

0

100

200

300

400

06102108040


Mat

ric s

uctio

n, s

(kP

a)

Experimental

BBM (Alonso et al. 1990)

pc = 31.9 kPaλ(0) = 0.146

β = 8.9 MPa-1

r = 0.649

Fig. 15. Parametric performance of LC yield loci for different poð0Þ values


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intercept μðsÞ of the critical state lines increases with suctionin a nonlinear fashion, with a tendency to a constant value forhigher suction states. This is consistent with the observed be-havior of parameter ϕb, particularly beyond the air-entry valueof a given soil, as part of the modified shear strength frameworkpostulated by Fredlund et al. (1978) and corroborated by Escarioand Saez (1986) and Wheeler and Sivakumar (1995), among a fewothers.

The shapes of the critical state lines shown in Fig. 16 are alsoconsistent with the BBM framework, which postulates that all criti-cal state lines in a v∶p plane would be curved, i.e., convex upward,with a slope ψðsÞ that tends to the soil stiffness parameter λðsÞ athigher values of net mean stress. Similar behavioral trends werereported for low-plasticity silty sand by Macari et al. (2003) usingan older version of a true triaxial cell and soil samples preparedthrough tamping compaction.

Models Predictions of Soil Response

Tables 1 and 2 summarize all the calibrated BBM and OMparameters obtained for statically compacted SP-SC soil. Para-meters in Tables 1 and 2 were used for validation of bothmodels through explicit integration of their respective constitutiverelations (Pérez-Ruiz 2009). Figs. 18–20 show the experi-mental and predicted response of compacted SP-SC soil from threesuction-controlled CTC tests conducted at different matricsuction states and initial net mean stresses. Figs. 21 and 22show the experimental and predicted response of compactedSP-SC soil from two suction-controlled TC tests. Predictionsare presented in terms of deviatoric-stress versus total shear strainresponse.

Although the original formulations of the models offer plentyof room for further refinement and elaboration (Sheng et al.

1

1.1

1.2

1.3

1.4

1.5

1.6

0 100 200 300 400 500


Spe

cific

vol

ume,

v =

1 +

e

Γ(s)

1ψ(s)

patm s = 200 kPas = 100 kPas = 50 kPa

0

200

400

600

0 100 200 300 400 500


Dev

iato

ric s

tres

s, q

(kP

a)

M(s)

1

µ(s)

s = 200 kPa

s = 100 kPa

s = 50 kPa

Fig. 16. Critical state lines in q∶p and v∶p planes for matric suction states s ¼ 50, 100, and 200 kPa


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2008; Zhang and Lytton 2009a, b, 2012), predictions of unsaturatedsoil response from either one are, in general, reasonably accurate,particularly in predicting soil response from conventional triaxialcompression tests. The differences observed in their numerical pre-dictions may be attributed to different stress-increase intervals usedby the authors in the respective computational drivers developed forthe explicit integration of the constitutive relations, and differencesin the flow rules postulated by each model. It might have beenpossible to improve OM predictions by using a nonassociatedflow rule; however, the subject is far beyond the scope of thepresent work.

Finally, in most cases the experimental values of peak stress areobserved to be slightly higher than those predicted numerically.This can be partly attributed to the stress-controlled nature of

the testing scheme, which, despite all of the refinementsincorporated into the newly developed cell, makes it challengingto identify definitive peak values of deviatoric-stress for the appro-priate calibration of all model parameters.

Critical State Loci in Octahedral Plane

Peak stress values at critical state condition from the series of 6 TC,3 TE, and 3 SS tests, as shown in Fig. 6(b), can be used to identifythe location and shape of the failure envelopes in the net octahedralstress plane, ðσ1 � uaÞ∶ðσ2 � uaÞ∶ðσ3 � uaÞ. As previously noted,the tests were all conducted under an initial net mean stress,p ¼ 100 kPa, and for matric suction states s ¼ 50, 100, or200 kPa. Fig. 23 shows the experimental values of peak stressassessed from all TCðθ ¼ 0°Þ, SSðθ ¼ 30°Þ, and TEðθ ¼ 60°Þ tests,along with predicted failure envelopes using the yield criteriapostulated by Matsuoka and Nakai (1974) and by Lade and Duncan(1973). The latter shows very good agreement with observed peakstrength of compacted SP-SC soil.

Although a detailed description of both criteria is beyond thescope of the present work (e.g., Davis and Selvadurai 2002), themain intent was to get an insight into how feasible it is to reproducethe suction-dependent failure loci by building on these well-established criteria for dry and fully saturated coarse-grained soils.It is also worth noting the marked effect that matric suction has onthe size of the failure loci, with a significant expansion fors ¼ 200 kPa. Similar behavioral trends have been reported byMatsuoka et al. (2002) and by Hoyos and Arduino (2008) on sandysoils.

Concluding Remarks

Results from a comprehensive series of suction-controlled HC,CTC, TC, TE, and SS tests on statically compacted specimensof poorly graded sand with clay (SP-SC soil) were used to calibrateand further validate two of the most popular constitutive frame-works postulated to date for unsaturated soils: the Barcelona BasicModel and the Oxford Model. The experiments were accomplishedin a newly developed true triaxial apparatus described in a firstcompanion paper.

A 120-hour equalization time (five days), before isotropicloading or true triaxial shearing, was found appropriate forsustained-suction states ranging from 50 to 350 kPa. Duringsuction-controlled ramped consolidation (HC) tests, the soil wasbrought to a full virgin state, with plastic deformations largeenough to identify the loading-collapse yield curve postulatedby the BBM. A minimal degree of anisotropy in the horizontal di-rections was observed for cubical samples prepared through staticcompaction. The test cell is capable of identifying and quantifyingthe compressive (+) and expansive (-) nature of the major, minor,and intermediate principal strains as dictated by the correspondingTC, TE, or SS loading scheme.

Results from suction-controlled CTC and TC tests wereused to evaluate the ability of both models to quantitativelyreproduce the observed stress-strain response of compactedSP-SC soil. Although evidently not perfect, predictions from eithermodel are reasonably accurate, highlighting the potential of bothmodels for use in the analysis of geotechnical boundary-valueproblems that involve geosystemsmade of compacted soil or restingon unsaturated ground. The original formulations of both models,however, offer plenty of room for further refinement and elaboration.

Peak stress values at critical state condition from suction-controlled TC, TE, and SS tests were used to identify the location

0

200

400

600

6004002000

q - Experimental (kPa)

q -

Pre

dict

ed (

kPa)

BBM

OM

Fig. 17. Experimental and predicted values of deviatoric-stress at cri-tical state condition

Table 1. Best-Fit Barcelona Basic Model Parameters for StaticallyCompacted SP-SC Soil

Parameter Best-fit value Units

λð0Þ 0.146 —k 0.031 —β 8.952 ðMPaÞ�1

r 0.649 —pc 0.032 MPa

G 5.500 MPa

M 1.103 —k 0.616 —poð0Þ 0.065 MPa

Table 2. Best-Fit Oxford Model Parameters for Statically CompactedSP-SC Soil

s∶kPa λðsÞ NðsÞ MðsÞ μðsÞ∶kPa ψðsÞ ΓðsÞ0 0.146 1.589 — — — —50 0.128 1.550 0.963 79.29 0.230 1.416

100 0.116 1.529 0.971 105.16 0.242 1.459

200 0.103 1.483 0.975 139.41 0.280 1.530

350 0.097 1.439 — — — —


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and shape of failure envelopes in the net octahedral stress plane,ðσ1 � uaÞ∶ðσ2 � uaÞ∶ðσ3 � uaÞ. Predicted failure envelopes usingthe yield criterion postulated by Lade and Duncan (1973) showgood agreement with the observed peak strength of compactedSP-SC soil.

Even though the research scope and the time frame ofthe present work did not contemplate the comparison of

suction-controlled test data from true (cubical) and conventional(cylindrical) triaxial systems, some previous works have re-ported an acceptable degree of consistency between the two testingmethods for the suction-controlled axisymmetric (σ2 ¼ σ3) case,including Matsuoka et al. (2002) and Reis et al. (2011). The authorsare currently embarked on a similar research endeavor using thesame SP-SC soil.

0

50

100

150

200

250

300

0 5 10 15 20 25

Total shear strain (%)

Dev

iato

ric s

tres

s, q

(kP

a)

Experimental

BBM

(a)

0

50

100

150

200

250

300

0 5 10 15 20 25


Experimental

OM

(b)

Fig. 18. Experimental and predicted stress-strain response of compacted SP-SC soil from s-controlled CTC test conducted at p ¼ 100 kPa ands ¼ 50 kPa: (a) BBM predictions; (b) OM predictions

0

100

200

300

400

500

0 5 10 15 20 25


Dev

iato

ric s

tres

s, q

(kP

a)

Experimental

BBM

(a)

0

100

200

300

400

500

0 5 10 15 20 25


Experimental

OM

(b)



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Acknowledgments

Development of the cubical test cell utilized in this experi-mental and modeling effort was accomplished under U.S. Na-tional Science Foundation Award #CMS-0216545. Thissupport is gratefully acknowledged. Any findings, conclusions

or recommendations expressed in this material are those of theauthors and do not necessarily reflect the views of the NSF.The authors also would like to thank Dr. Arthit Laikramand Mr. Jae Hyun Park, former graduate students at UT-Arlington, for all their assistance during the initial calibrationtesting.

0

100

200

300

400

500

600

0 10 20 30 40


Dev

iato

ric s

tres

s, q

(kP

a)

Experimental

BBM

(a)

0

100

200

300

400

500

600

0 10 20 30 40


Experimental

OM

(b)


0

50

100

150

200

250

300

0 5 10 15 20 25


Dev

iato

ric s

tres

s, q

(kP

a)

Experimental

BBM

(a)

0

50

100

150

200

250

300

0 5 10 15 20 25


Experimental

OM

(b)

Fig. 21. Experimental and predicted stress-strain response of compacted SP-SC soil from s-controlled TC test conducted at p ¼ 100 kPa ands ¼ 50 kPa: (a) BBM predictions; (b) OM predictions


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References

Alonso, E. E., Gens, A., and Josa, A. (1990). “A constitutive model forpartially saturated soils.” Géotechnique, 40(3), 405–430.

Davis, R. O., and Selvadurai, A. P. S. (2002). Plasticity and geomechanics,Cambridge University Press, Cambridge, UK.

Escario, V., and Saez, J. (1986). “The shear strength of partly saturatedsoils.” Géotechnique, 36(3), 453–456.

Fredlund, D. G., and Morgenstern, N. R. (1977). “Stress state variables forunsaturated soils.” J. Geotech. Eng. Div., 103(GT5), 447–466.

Fredlund, D. G., Morgenstern, N. R., and Widger, R. A. (1978). “The shearstrength of unsaturated soils.” Can. Geotech. J., 15(3), 313–321.

0

50

100

150

200

250

300

0 5 10 15 20 25


Dev

iato

ric s

tres

s, q

(kP

a)

Experimental

BBM

(a)

0

50

100

150

200

250

300

0 5 10 15 20 25


Experimental

OM

(b)

Fig. 22. Experimental and predicted stress-strain response of compacted SP-SC soil from s-controlled TC test conducted at p ¼ 100 kPa ands ¼ 100 kPa: (a) BBM predictions; (b) OM predictions

Fig. 23. Experimental and predicted failure loci of compacted SP-SC soil in octahedral plane


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NIV

LIB

RA

RIE

S on

07/

18/1

4. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

http://dx.doi.org/10.1680/geot.1990.40.3.405


http://dx.doi.org/10.1139/t78-029

Hoyos, L. R. (1998). “Experimental and computational modeling ofunsaturated soil behavior under true triaxial stress states.” Ph.D. disser-tation, Georgia Institute of Technology, Atlanta.

Hoyos, L. R., and Arduino, P. (2008). “Implicit algorithm for modelingunsaturated soil response in three-invariant stress space.” Int. J.Geomech., Technical Note, 8(4), 266–273.

Hoyos, L. R., Laikram, A., and Puppala, A. J. (2008). “A novel suction-controlled true triaxial apparatus for unsaturated soils.” UnsaturatedSoils: Advances in Geo-Engineering, Proc. of the First European Conf.on Unsaturated Soils, D. G. Toll, C. E. Augarde, D. Gallipoli, andS. J. Wheeler, eds., CRC Press, Durham, UK, 83–88.

Josa, A. (1988). “Unmodelo elastoplastico para suelos no saturados.” Ph.D.dissertation, Universitat Politécnica de Catalunya, Barcelona, Spain (inSpanish).

Lade, P. V., and Duncan, J. M. (1973). “Cubical triaxial tests on cohesion-less soil.” J. Soil Mech. Found. Div., 99(10), 793–812.

Laikram, A. (2007). “Modeling unsaturated soil response under suction-controlled multi-axial stress states.” Ph.D. dissertation, Univ. of Texasat Arlington, Arlington, TX.

Macari, E. J., and Hoyos, L. R. (2001). “Mechanical behavior of an un-saturated soil under true triaxial stress states.” Geotech. Test. J.,24(1), 14–22.

Macari, E. J., Hoyos, L. R., and Arduino, P. (2003). “Constitutive modelingof unsaturated soil behavior under axisymmetric stress states using astress/suction-controlled cubical test cell.” Int. J. Plast., 19(10),1481–1515.

Matsuoka, H., and Nakai, T. (1974). “Stress-deformation and strength char-acteristics of soil under three different principal stresses.” Proc., Japan

Society of Civil Engineers (JSCE), 232, 59–70.Matsuoka, H., Sun, D. A., Kogane, A., Fukuzawa, N., and Ichihara, W.

(2002). “Stress-strain behaviour of unsaturated soil in true triaxial tests.”Can. Geotech. J., 39, 608–619.

Matyas, E. L., and Radhakrishna, H. S. (1968). “Volume change character-istics of partially saturated soils.” Géotechnique, 18(4), 432–448.

Pérez-Ruiz, D. D. (2009). “A refined true triaxial apparatus for testingunsaturated soils under suction-controlled stress paths.” Ph.D. disserta-tion, Univ. of Texas at Arlington, Arlington, TX.

Reis, R. M., de Azevedo, R. F., Botelho, B. S., and Vilar, O. M. (2011).“Performance of a cubical triaxial apparatus for testing saturated andunsaturated soils.” Geotech. Test. J., 34(3), 177–185.

Sheng, D., Fredlund, D. G., and Gens, A. (2008). “A new modeling ap-proach for unsaturated soils using independent stress variables.”Can. Geotech. J., 45(4), 511–534.

Sivakumar, V. (1993). “A critical state framework for unsaturated soils.”Ph.D. dissertation, Univ. of Sheffield, UK.

Wheeler, S. J., and Sivakumar, V. (1995). “An elasto-plastic critical stateframework for unsaturated soils.” Géotechnique, 45(1), 35–53.

Zhang, X., and Lytton, R. L. (2009a). “Modified state-surface approach tothe study of unsaturated soil behavior. Part I: Basic concept.” Can. Geo-tech. J., 46(5), 536–552.

Zhang, X., and Lytton, R. L. (2009b). “Modified state-surface approach tothe study of unsaturated soil behavior. Part II: General formulation.”Can. Geotech. J., 46(5), 553–570.

Zhang, X., and Lytton, R. L. (2012). “Amodified state-surface approach onunsaturated soil behavior. Part III: Modeling of coupled hydro-mechanical effect.” Can. Geotech. J., 49(1), 98–120.


Int. J. Geomech. 2012.12:292-308.

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http://dx.doi.org/10.1061/(ASCE)1532-3641(2008)8:4(266)

http://dx.doi.org/10.1061/(ASCE)1532-3641(2008)8:4(266)

http://dx.doi.org/10.1520/GTJ11278J

http://dx.doi.org/10.1520/GTJ11278J

http://dx.doi.org/10.1016/S0749-6419(02)00018-9

http://dx.doi.org/10.1016/S0749-6419(02)00018-9

http://dx.doi.org/10.1139/t02-031


http://dx.doi.org/10.1520/GTJ103256

http://dx.doi.org/10.1139/T07-112


http://dx.doi.org/10.1139/T08-136

http://dx.doi.org/10.1139/T08-136

http://dx.doi.org/10.1139/T08-137

http://dx.doi.org/10.1139/t11-089

Modeling Unsaturated Soil Response under Suction-Controlled True Triaxial Stress Paths

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