pore-water pressure and water volume change of an unsaturated soil under infiltration conditions

Pore-water pressure and water volume change ofan unsaturated soil under infiltration conditions

Inge Meilani, Harianto Rahardjo, and Eng-Choon Leong

Abstract: Triaxial shearing–infiltration tests were conducted to study the pore-water pressure and volume change ofunsaturated soils subjected to infiltration conditions. A modified triaxial apparatus with three Nanyang TechnologicalUniversity (NTU) mini suction probes along the specimen height was used for the experimental program. Elastic moduliwere obtained for the soil structure with respect to changes in net confining pressure (E) and matric suction (H). Watervolumetric moduli associated with changes in net confining pressure (Ew) and matric suction (Hw) were also obtainedfrom the shearing–infiltration tests. Water volumetric strain and pore-water pressure during the shearing–infiltrationtests were computed based on volume change theory. This paper presents the significance of obtaining the parameterHw from an appropriate scanning curve of a soil-water characteristic curve (SWCC) for the computation of water volu-metric strain and pore-water pressure changes during a shearing–infiltration test. The appropriate scanning curve shouldbe obtained from the wetting curve of the SWCC at the matric suction where the infiltration test commences.

Key words: infiltration, matric suction, triaxial, unsaturated soils, pore-water pressure, water volume change.

Résumé : Des essais triaxiaux de cisaillement par infiltration ont été réalisés pour étudier le changement de pressioninterstitielle et de volume des sols non saturés assujettis à des conditions d’infiltration. Pour le travail expérimental, ona utilisé un appareil triaxial muni de trois minisondes à succion NTU le long de la hauteur des spécimens. On a ob-tenu les modules élastiques de la structure du sol par rapport à un changement de la pression nette de confinement (E)et à un changement dans la succion matricielle (H). À partir des essais de cisaillement par infiltration, on a égalementobtenu les modules volumétriques associés à un changement de la pression nette de confinement, Ew, et à un change-ment dans la succion matricielle, Hw. Le calcul basé sur la théorie du changement de volume a été réalisé pour la dé-formation volumétrique de l’eau et les pressions interstitielles durant les essais de cisaillement par infiltration. Cetarticle présente la signification de l’obtention du paramètre Hw pour une courbe appropriée de balayage de la courbecaractéristique sol-eau (SWCC) pour le calcul de la déformation volumétrique de l’eau et des changements de pressioninterstitielle durant l’essai de cisaillement par infiltration. La courbe appropriée de balayage devrait être obtenue par lacourbe de mouillage de la SWCC à la succion matricielle où l’essai d’infiltration commence.

Mots clés : infiltration, succion matricielle, triaxial, sols non saturés, pression interstitielle, changement du volume d’eau.

[Traduit par la Rédaction] Meilani et al. 1531

Introduction

Reduction in shear strength due to infiltration of rainfallwas the primary trigger of slope failures in a number ofcases presented in the literature (Lumb 1975; Widger andFredlund 1979; Lim et al. 1996; Yoshida et al. 1991). Thefailure mechanism in soils due to infiltration should simulatethe stress path followed in field conditions. The stress paththat leads to failure (i.e., the field stress path), however, can-not be modelled using a routine triaxial test where a speci-men is sheared by applying deviatoric stress. Brand (1981)suggested that the field stress path should be modelled usinga triaxial test conducted under a constant total stress and in-creasing pore-water pressures. In this study, this triaxial test

is called a shearing–infiltration test. This procedure wasadopted by Brenner et al. (1985), Anderson and Sitar (1995),Anderson and Riemer (1995), Han (1997), Melinda (1998),and Wong et al. (2001). The pore-water pressure and volumechange responses within unsaturated soils during theshearing–infiltration test have not been fully understood,however. The main objective of this research is to study theshear strength, pore-water pressure, and volume changecharacteristics of an unsaturated soil under infiltration condi-tions. In this paper, the water constitutive relation as ex-pressed in terms of water volumetric moduli associated witha change in net confining pressure, Ew, and a change inmatric suction, Hw (Fredlund and Rahardjo 1993), was veri-fied using the shearing–infiltration test results.

Can. Geotech. J. 42: 1509–1531 (2005) doi: 10.1139/T05-066 © 2005 NRC Canada

1509

Received 19 July 2004. Accepted 4 July 2005. Published on the NRC Research Press Web site at http://cgj.nrc.ca on 20 October2005.

I. Meilani, H. Rahardjo,1 and E.-C. Leong. School of Civil and Environmental Engineering, Nanyang Technological University,50 Nanyang Avenue, Block N1, 1A-02, Singapore 639798.

1Corresponding author (e-mail: [email protected]).

Theoretical background

Fredlund and Morgenstern (1976) and Fredlund (1979)formulated the constitutive relations for an unsaturated soil.The soil is assumed to be an isotropic and linearly elasticmaterial. Stress state variables of net normal stress, (σ – ua),and matric suction, (ua – uw) (Fredlund and Morgenstern1977), were used to express the constitutive relations of anunsaturated soil, where σ is the total normal stress, ua is thepore-air pressure, and uw is the pore-water pressure. In an in-cremental form, the soil structure constitutive relation withrespect to volumetric strain can be written as follows:

[1] δε δ µ δ σ δvv

om a a w= = −⎛

⎝⎜⎞⎠⎟

− + −VV E

uH

u u31 2 3

( ) ( )

where δεv is the volumetric strain, µ is Poisson’s ratio, H isthe modulus of elasticity of the soil structure with respect toa change in matric suction (ua – uw), E is the modulus ofelasticity of the soil structure with respect to a change inmean net normal stress (σm – ua), σm is the total mean stress(i.e., (σx + σy + σz)/3), δVv is the total volume change, and Vois the initial total volume.

Fredlund and Rahardjo (1993) formulated the water phaseconstitutive relation for an unsaturated soil in a semiempir-ical manner. The water phase constitutive relation can be ex-pressed in an incremental form as follows:

[2] δε δ δ σ δw

w

o wm a

a w

w

= = − + −VV E

uu u

H3

( )( )

where δεw is the water volumetric strain, δVw is the watervolume change, Ew is the water volumetric modulus associ-ated with a change in (σm – ua), and Hw is the water volu-metric modulus associated with a change in (ua – uw).

Fredlund and Rahardjo (1993) described (3(1 – 2µ)/E)and (3/H) in eq. [1] as the slopes of the soil structure consti-tutive surface with respect to the (σm – ua) and (ua – uw)axes, respectively. In addition, the slopes on the water phaseconstitutive surface are (3/Ew) and (1/Hw) as given in eq. [2]with respect to the (σm – ua) and (ua – uw) axes, respectively.

During a triaxial loading, an all-round pressure change,δσ3, is applied to the soil specimen as an isotropic loading,whereas a deviator stress change, δ(σ1 – σ3), is applied to thesoil specimen as a uniaxial loading in the y direction. The x,y, and z axes are assumed to be the principal stress direc-tions. Therefore, the soil structure constitutive equation fortriaxial loading can be written as follows:

[3] δε µ δ σ δ 13

σ σv 3 a 1 3= −⎛⎝⎜

⎞⎠⎟

− + −⎡⎣⎢

⎤⎦⎥

⎧⎨⎩

⎫⎬⎭

31 2

Eu( ) ( )

+ −3H

u uδ ( )a w

The constitutive equation for the water phase in triaxialloading is

[4] δε δ σ δ 13

σ σ δ(w

w3 a 1 3

a w

w

= − + −⎡⎣⎢

⎤⎦⎥

⎧⎨⎩

⎫⎬⎭

+ −3E

uu u

H( ) ( )

)

Experimental setup

Modified triaxial apparatus for shearing–infiltrationtests

In this study, a triaxial test conducted under a constanttotal stress and decreasing matric suction is called a shearing–infiltration test. The shearing–infiltration tests were con-ducted using a modified triaxial apparatus whose details aredescribed by Wong et al. (2001). The modified triaxial appa-ratus consists of a triaxial cell, three Nanyang TechnologicalUniversity (NTU) mini suction probes, two digital pressureand volume controllers (DPVC), and a diffused-air volumeindicator (DAVI). A data acquisition unit and a personalcomputer were used to automate the measurements.

Matric suction in the soil specimen is controlled using theaxis-translation technique (Hilf 1956). A coarse porous stoneis placed between the specimen and the top cap for control-ling the pore-air pressure. Back pressure is applied from thetop cap during saturation and consolidation stages. A pedes-tal with a water compartment and a 5 bar high-air-entry ce-ramic disk (air-entry value 500 kPa) is attached to the baseof the sample. The pore-water pressure is controlled fromthe base through the 5 bar high-air-entry ceramic disk. Dur-ing the infiltration stage, water is injected into the specimenfrom the base. A force actuator was used to apply the axialload during the shearing stage and maintain a constant axialload on the specimen during the infiltration stage.

NTU mini suction probe for matric suctionmeasurements

The NTU mini suction probe is a 15 bar miniature pore-water pressure transducer, PDCR 81, which has been modi-fied by Meilani et al. (2002). The NTU mini suction probegives a fast response and can measure matric suctions of upto 500 kPa for a long period of testing time. Three NTUmini suction probes were used to measure the pore-waterpressures along the height of a specimen during theshearing–infiltration tests. The probes were placed at thethree-quarter (i.e., top), one-half (i.e., middle), and one-quarter (i.e., bottom) heights of the specimen from its baseand 120° apart in the circumferential direction. The proce-dure used to install the NTU mini suction probe in the speci-men was adopted from Hight (1982).

Specimen preparationCoarse kaolin made by Kaolin Malaysia SDN BHD (Ma-

laysia) was selected for the experimental program. Speci-mens were prepared from reconstituted coarse kaolin tominimize difficulties associated with soil heterogeneity. Inaddition, the saturated coefficient of permeability of thecoarse kaolin with respect to water (ks = 6.42 × 10–8 m/s) issufficiently high for conducting the shearing–infiltration testin a reasonable period of time.

The coarse kaolin has a grain-size distribution of 85% siltand 15% clay-size particles (finer than 2 µm). The liquid andplastic limits of the coarse kaolin are 51% and 35%, respec-tively. From the standard Proctor compaction test, it wasfound that the coarse kaolin has an optimum water contentof 22% with a maximum dry density of 1.35 Mg/m3. Thecoarse kaolin is classified as silt with high plasticity (MH)

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1510 Can. Geotech. J. Vol. 42, 2005

according to the Unified Soil Classification System (ASTM1997).

Static compaction is performed to obtain identical speci-mens with the same initial condition (i.e., at a water contentof 22% and a dry density of 1.35 Mg/m3) and a uniformdensity throughout the length of the specimen. The speci-mens were compacted in 10 layers, each 10 mm thick. Acompression machine with a fixed displacement rate of1 mm/min was used to compact a triaxial specimen of50 mm diameter and 100 mm height. The low energy fromthe static compaction can produce a uniform density to pre-vent the development of a weaker region in the specimen(Rahardjo et al. 2004).

Figure 1 shows the soil-water characteristic curves (i.e.,SWCC) of compacted coarse kaolin as obtained from thepressure plate test and the fitted soil-water characteristiccurve using the equation from Fredlund and Xing (1994).The correction function, C(ψ), for the fitting equation wastaken as 1, as suggested by Leong and Rahardjo (1997). Thefitting parameters a, m, and n are 73.2 kPa, 0.82, and 3.42,respectively, for the drying curve and 42.2 kPa, 1.18, and1.77, respectively, for the wetting curve.

Testing procedureA shearing–infiltration test is a single-stage test that con-

sists of saturation, consolidation, matric suction equalisation,shearing, and infiltration. The specimens were saturated byapplying a cell pressure and a back pressure until a pore-water pressure parameter, B, of at least 0.95 was reached(Head 1986). Specimens were then consolidated under aspecified net confining pressure. Once the excess pore-waterpressure had dissipated and there was no further volumechange (i.e., end of the consolidation stage), the matric suc-tion equalisation stage was carried out. The axis translationtechnique was used during the matric suction equalisation.Matric suction was imposed by applying air pressure

through the top cap while controlling the water pressure atthe bottom of the specimen. As the matric suction equalized,water drained from the bottom of the specimen. The matricsuction equalisation process was considered to be completewhen no more changes in water volume were observed andthe pore-water pressure had equalized throughout the speci-men. The specimen was then sheared using a strain rate of0.0008 mm/min. The pore water and pore air were underdrained conditions during shearing. The infiltration stagewas commenced once the shear stress of the specimenreached 85%–90% of the peak shear stress. In the infiltrationstage, a constant shear stress (i.e., 85%–90% of the peakshear stress) was maintained by a force actuator while waterwas injected from the base using the DPVC at a constant in-filtration rate. In the field, steep slopes often have a mar-ginal factor of safety of close to 1. As a result, the shearstress in the slope can be as high as around 85%–90% ofpeak shear stress. Therefore, the range of 85%–90% of peakshear stress was chosen as the shear stress during the infil-tration stage.

The pore-air pressure was under a drained condition andthe pore-water pressure was under an undrained conditionduring the infiltration stage. Failure was considered to haveoccurred during the shearing–infiltration test when the devi-ator stress started to decline or the strain rate started to in-crease excessively (Anderson and Sitar 1995; Han 1997;Melinda 1998; Wong et al. 2001). Therefore, specimens inthis testing program were considered to have failed when thestrain started to increase rapidly.

Results and discussion

Eleven shearing–infiltration tests were conducted in thisstudy. All the shearing–infiltration testing of unsaturatedspecimens was carried out in a single test. The testing pro-gram is explained in detail in Table 1. Each notation consistsof a pair of numbers, with the first representing the applied

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Meilani et al. 1511

Fig. 1. Soil-water characteristic curve of a compacted coarse kaolin as obtained from pressure plate tests.

net confining pressure and the second corresponding to theapplied matric suction. TU(LR) corresponds to a shearing–infiltration test on an unsaturated specimen with a low infil-tration rate of 0.04 mm3/s, and TU(HR) corresponds to ashearing–infiltration test on an unsaturated specimen with ahigh infiltration rate of 0.25 mm3/s. For example, test TU25-100 (LR) means a shearing–infiltration test on an unsatu-rated specimen under a net confining pressure of 25 kPa andunder an initial matric suction of 100 kPa using a low infil-tration rate of 0.04 mm3/s.

The results of four shearing–infiltration tests on unsatu-rated specimens TU 25-100 (LR), TU 200-200 (LR), TU 25-

100 (HR), and TU 200-200 (HR) are presented herein. Thestress state variables and the volume–mass properties foreach specimen are shown in Tables 2–5 and 6–10, respec-tively. The shearing–infiltration tests under different infiltra-tion rates were conducted to investigate the effect ofinfiltration rate on the shear strength of the specimen. Theresults from nine shearing–infiltration tests on unsaturatedspecimens with a low infiltration rate of 0.04 mm3/s wereused to produce the parameters for the volume changetheory, and two shearing–infiltration tests on unsaturatedspecimens with a high infiltration rate of 0.25 mm3/s (i.e.,TU 25-100 (HR) and TU 200-200 (HR)) were used to verify

© 2005 NRC Canada


Net confining pressure, (σ3 – ua) (kPa)

Matric suction,(ua – uw) (kPa) 25 100 200

50 TU 25-50 (LR) TU 100-50 (LR) TU 200-50 (LR)100 TU 25-100 (LR);

TU 25-100 (HR)TU 100-100 (LR) TU 200-100 (LR)

200 TU 25-200 (LR) TU 100-200 (LR) TU 200-200 (LR);TU 200-200 (HR)

Table 1. Details of the shearing–infiltration test program for unsaturated specimens.

Stageσ3

(kPa)ua

(kPa)uw

(kPa)(σ3 – ua)(kPa)

(ua – uw)(kPa)

Consolidation 315 — 290 25 0Matric suction equalisation 315 290 190 25 100Shearing 315 290 190 25 100Infiltration at beginning 315 290 190 25 100Infiltration at failure 315 290 215 25 75Infiltration at end of test 315 290 218 25 72

Table 2. Stress values for shearing–infiltration test of specimen TU 25-100 (LR).

Stageσ3

(kPa)ua

(kPa)uw


(ua – uw)(kPa)


Table 3. Stress values for shearing–infiltration test of specimen TU 200-200 (LR).

Stageσ3

(kPa)ua

(kPa)uw


(ua – uw)(kPa)


Table 4. Stress values for shearing–infiltration test of specimen TU 25-100 (HR).

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Meilani et al. 1513

the parameters that have been deduced from the shearing–infiltration tests on unsaturated specimens with the low infil-tration rate.

Results of the shearing–infiltration tests on unsaturatedspecimens demonstrate that the failure envelope obtainedfrom the shearing–infiltration tests is the same regardless of

the infiltration rate. The shearing–infiltration test using thelow infiltration rate on unsaturated specimen TU 25-100(LR) and the shearing–infiltration test using the high infiltra-tion rate on unsaturated specimen TU 25-100 (HR) failed atmatric suctions of 75.4 and 74.4 kPa, respectively (Figs. 2,4). Meanwhile, the shearing–infiltration test using the low

Stageσ3

(kPa)ua

(kPa)uw


(ua – uw)(kPa)


Table 5. Stress values for shearing–infiltration test of specimen TU 200-200 (HR).

Shearing and infiltration stages

Initial Saturation ConsolidationMatric suctionequalisation

Beforeinfiltration At failure

End ofinfiltration

Vt (cm3) 203.54 199.07 197.62 193.52 191.49 194.12 196.02

ρ (Mg/m3) 1.65 1.94 1.95 1.75 1.75 1.75 1.73ρd (Mg/m3) 1.35 1.38 1.39 1.42 1.44 1.42 1.41

e 0.96 0.92 0.90 0.86 0.84 0.87 0.89S (%) 60.70 ~100.00 ~100.00 70.02 68.88 70.84 69.88w (%) 21.95 40.31 39.78 22.78 21.90 23.20 23.36θw 0.2970 0.5576 0.5544 0.3241 0.3149 0.3291 0.3283

Note: e, void ratio; S, degree of saturation; Vt, total volume; w, gravimetric water content; ρ, total density; ρd, dry density; θw, volumetric water content.

Table 6. Volume–mass properties of specimen TU 25-100 (LR) at each testing stage.




End ofinfiltration

Vt (cm3) 203.54 200.58 191.06 186.87 184.33 184.63 185.81

ρ (Mg/m3) 1.65 1.90 1.94 1.67 1.68 1.91 1.91ρd (Mg/m3) 1.35 1.37 1.44 1.47 1.50 1.49 1.48

e 0.96 0.93 0.84 0.80 0.77 0.78 0.79S (%) 61.38 ~100.00 ~100.00 43.83 42.06 95.40 96.75w (%) 22.16 38.15 34.70 13.18 12.26 27.91 28.71θw 0.3001 0.5243 0.5006 0.1944 0.1833 0.4166 0.4259

Table 7. Volume–mass properties of specimen TU 200-200 (LR) at each testing stage.




End ofinfiltration

Vt (cm3) 203.54 208.05 206.51 202.41 201.36 203.52 206.28

ρ (Mg/m3) 1.65 1.82 1.83 1.64 1.64 1.64 1.64ρd (Mg/m3) 1.35 1.32 1.33 1.36 1.37 1.35 1.33

e 0.96 1.00 0.99 0.95 0.94 0.96 0.99S (%) 60.71 99.97 99.97 58.45 55.91 59.00 61.19w (%) 21.97 37.81 37.25 20.91 19.79 21.34 22.75θw 0.2972 0.5004 0.4967 0.2844 0.2706 0.2888 0.3037

Table 8. Volume–mass properties of specimen TU 25-100 (HR) at each testing stage.

infiltration rate on unsaturated specimen TU 200-200 (LR)and the shearing–infiltration test using the high infiltrationrate on unsaturated specimen TU 200-200 (HR) failed at ap-proximately the same matric suctions, namely 29.4 and34.8 kPa, respectively (Figs. 3, 5). Table 10 shows compari-sons between specimens TU 25-100 (LR) and TU 25-100(HR) and between specimens TU 200-200 (LR) and TU200-200 (HR). Nevertheless, the shearing–infiltration test re-sults for TU 25-100 (LR) are comparable to the results forTU 25-100 (HR), and similarly for the results of TU 200-200 (LR) and TU 200-200 (HR) (Table 10). The shearing–infiltration test results for specimens TU 25-100 (LR), TU200-200 (LR), TU 25-100 (HR), and TU 200-200 (HR) aredescribed in detail later in the paper.

In presenting the test results, the water volumetric strain,εw, is defined as the ratio of the water volume change to theinitial total volume of the specimen. A positive water volu-metric strain indicates that water infiltrates into the speci-men, and a negative water volumetric strain indicates thecondition where the pore water drains from the specimen.The total volumetric strain, εv, is a ratio between the totalvolume change and the initial total volume of the specimen.Dilation of the specimen is expressed by a positive total vol-umetric strain, and compression is expressed by a negativetotal volumetric strain. A positive axial strain indicates thatthe specimen compresses, and a negative axial strain showsthat the specimen swells in the vertical direction.

Figure 2 shows the test results from specimen TU 25-100(LR). Figure 2a shows the deviator stress, σ1 – σ3, versus ax-ial strain, εy, throughout the shearing–infiltration test. The

specimen was sheared to 245 kPa (i.e., 85% of peak shearstress) and subsequently subjected to the infiltration process.Once failure occurred, the deviator stress could no longer bemaintained by the force actuator. The deviator stressdropped drastically to 128 kPa, which was almost half of thedeviator stress before the infiltration process.

Figure 2b shows matric suction, ua – uw, versus axialstrain, εy, of specimen TU 25-100 (LR). There were no ex-cess pore-air and pore-water pressures built up during theshearing process. The matric suction remained constant be-cause the pore air and pore water were under drained condi-tions during the shearing process. During the infiltrationstage, the pore-air pressure was kept constant, the pore-waterpressure increased, and as a result, the matric suction de-creased. The matric suction measurements during the infil-tration stage from the top, middle, and bottom NTU minisuction probes were similar. At failure, the average matricsuction from the top (i.e., 75.9 kPa), middle (i.e., 75.1 kPa)and bottom (i.e., 74.9 kPa) NTU mini suction probes was75.3 kPa. The pore-water pressure at the base was 10 kPahigher than those along the height of the specimen. In otherwords, the matric suction at the base was 10 kPa lower thanthat inside the specimen. This was due to the low coefficientof permeability of the high-air-entry ceramic disk with re-spect to water at the base (i.e., 2.36 × 10–10 m/s).

Figure 2c illustrates the relation between total volumetricstrain, εv, and water volumetric strain, εw, versus axial strain,εy, during the shearing–infiltration test on specimen TU 25-100 (LR), which compressed during the shearing stage anddilated during the infiltration stage.

© 2005 NRC Canada





End ofinfiltration

Vt (cm3) 203.54 203.04 193.25 188.90 185.74 187.20 189.36

ρ (Mg/m3) 1.65 1.88 1.92 1.66 1.67 1.88 1.90

ρd (Mg/m3) 1.35 1.36 1.42 1.46 1.48 1.47 1.45

e 0.96 0.95 0.86 0.82 0.79 0.80 0.82S (%) 61.28 ~100.00 ~100.00 44.11 42.47 91.97 99.20w (%) 22.18 38.67 35.12 13.62 12.62 27.83 30.79θw 0.3000 0.5244 0.5003 0.1985 0.1871 0.4093 0.4477

Table 9. Volume–mass properties of specimen TU 200-200 (HR) at each testing stage.

TU 25-100(LR)

TU 25-100(HR)

TU 200-200(LR)

TU 200-200(HR)

Net confining pressure (kPa) 25 25 200 200Matric suction before infiltration, (ua – uw)i (kPa) 100 100 200 200

Infiltration rate (mm3/s) 0.04 0.25 0.04 0.25Deviator stress before infiltration, (σ1 – σ3)i (kPa) 245 245 577 578

Failure mode Brittle Brittle Ductile DuctileMatric suction at failure, (ua – uw)f (kPa) 75.3 74.4 29.4 34.8

Water volumetric strain at failure, εwf (%) 0.58 0.59 21.67 20.88

Total volumetric strain at failure, εvf (%) 0.15 0.55 –1.52 –0.91

Axial strain at failure, εf (%) 4.7 4.6 10.6 6.6

Time to reach failure, tf (h) 23.6 4.8 287.6 46.5

Table 10. Comparison of specimens TU 25-100 (LR), TU 25-100 (HR), TU 200-200 (LR), and TU 200-200 (HR).

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Meilani et al. 1515

Fig. 2. Results of shearing–infiltration test on specimen TU 25-100 (LR) (i.e., initially consolidated under 25 kPa net confining pres-sure and 100 kPa matric suction): (a) deviator stress versus axial strain; (b) matric suction versus axial strain; (c) total volumetricstrain and water volumetric strain versus axial strain; (d) determination of failure point.

© 2005 NRC Canada


Fig. 3. Results of shearing–infiltration test on specimen TU 200-200 (LR) (i.e., initially consolidated under 200 kPa net confining pres-sure and 200 kPa matric suction): (a) deviator stress versus axial strain; (b) matric suction versus axial strain; (c) total volumetricstrain and water volumetric strain versus axial strain; (d) determination of failure point.

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Meilani et al. 1517

Fig. 4. Results of shearing–infiltration test on specimen TU 25-100 (HR) (i.e., initially consolidated under 25 kPa net confining pres-sure and 100 kPa matric suction): (a) deviator stress versus axial strain; (b) matric suction versus axial strain; (c) total volumetricstrain and water volumetric strain versus axial strain; (d) determination of failure point.

© 2005 NRC Canada


Fig. 5. Results of shearing–infiltration test on specimen TU 200-200 (HR) (i.e., initially consolidated under 200 kPa net confiningpressure and 200 kPa matric suction): (a) deviator stress versus axial strain; (b) matric suction versus axial strain; (c) total volumetricstrain and water volumetric strain versus axial strain; (d) determination of failure point.

Figure 2d shows the relationship between axial strain, εy,and elapsed time during the infiltration stage. The axialstrain increased sharply after failure occurred. To find theaxial strain at failure, εf, two tangents were drawn on the ax-ial strain versus elapsed time curve. The intersection pointindicates that the axial strain at failure was 4.7%. The aver-age matric suction in the specimen corresponding to thestrain at failure was 75.3 kPa (Fig. 2b), indicating the exis-tence of a significant matric suction at failure.

Figure 3 shows the test results from specimen TU 200-200 (LR). The deviator stress, σ1 – σ3, versus axial strain, εy,curve throughout the shearing–infiltration test is shown inFig. 3a. The specimen was sheared to 85% of peak shearstress at a deviator stress of 577 kPa, and the deviator stresswas kept constant at 577 kPa during the infiltration stage.The deviator stress started to decline slightly to 570 kPa af-ter failure occurred. This decline resembled a ductile failure.The stress–strain relationship for specimen TU 25-100 (LR)(Fig. 2a) shows that the deviator stress dropped drastically,indicating a brittle failure mechanism. Tables 6 and 7 showthe volume–mass properties of the specimen at each testingstage. The degree of saturation of specimen TU 200-200(LR) at the prefailure condition was found to be more than95%, indicating that the soil almost reached the saturatedcondition (Table 7). As a result, the characteristics of the de-viator stress at prefailure and failure conditions of specimenTU 200-200 (LR) are similar to those of a saturated speci-men. Wong et al. (2001) reported a similar observation thatthe deviator stress of a saturated specimen decreased slightlywhile the deviator stress of an unsaturated specimen de-creased sharply after failure in the shearing–infiltration tests.

Figure 3b shows the matric suction, ua – uw, versus axialstrain, εy, during the shearing and infiltration processes. Thematric suction was constant during shearing and decreasedduring infiltration. The average matric suction along thespecimen height at failure from the top (i.e., 29.7 kPa), mid-dle (i.e., 29.0 kPa) and bottom (i.e., 29.6 kPa) NTU minisuction probes was 29.4 kPa.

Figure 3c illustrates the total volumetric strain, εv, andwater volumetric strain, εw, versus axial strain, εy, during theshearing–infiltration test on specimen TU 200-200 (LR).During shearing, the specimen compressed as water drainedout of the specimen. During infiltration, the specimen di-lated as water infiltrated into the specimen.

Figure 3d shows axial strain, εy, versus elapsed time, t,during the infiltration stage for specimen TU 200-200 (LR).The axial strain started to increase sharply 215 h after infil-tration (i.e., at an axial strain of 5%). The intersection pointof the two tangent lines, which were drawn on the curve ofaxial strain versus elapsed time, indicated that εf was 10.6%.The specimen failed 287.6 h after infiltration. The averagematric suction of specimen TU 200-200 (LR) at failure wasapproximately 29.4 kPa.

Figures 4 and 5 illustrate the results of the shearing–infil-tration tests on unsaturated specimens TU 25-100 (HR) andTU 200-200 (HR), respectively, under the high infiltrationrate. The characteristics of shear strength, matric suction,water volumetric strain, and total volumetric strain duringthe shearing–infiltration test of specimen TU 25-100 (HR)(Fig. 4) are similar to those of specimen TU 25-100 (LR)(Fig. 2). The similarity was also observed between speci-

mens TU 200-200 (HR) (Fig. 5) and TU 200-200 (LR)(Fig. 3). The volume–mass properties of specimens TU 25-100 (HR) and TU 200-200 (HR) at each testing stage areshown in Tables 8 and 9, respectively.

Figure 6a shows the relationship between deviator stress,σ1 – σ3, and axial strain, εy, during the shearing stage ofspecimens TU 25-100 (LR) and TU 200-200 (LR). A modu-lus of elasticity or Young’s modulus, E, can be derived fromthe slope of the stress–strain curve. The essentially constantvalues of E during shearing of specimens TU 25-100 (LR)and TU 200-200 (LR) are shown in Fig. 6c.

Figure 6b illustrates deviator stress, σ1 – σ3, versus watervolumetric strain, εw, during the shearing stage of specimensTU 25-100 (LR) and TU 200-200 (LR). The slope of thecurve between σ1 – σ3 and εw is defined as the water volu-metric modulus, Ew. The water volumetric moduli duringshearing of specimens TU 25-100 (LR) and TU 200-200(LR) are shown in Fig. 6d, indicating that the water volu-metric modulus, Ew, is also essentially constant.

The stress–strain curve (Fig. 6a) shows that the relation-ship between σ1 – σ3 and εy is linear for specimens TU 25-100 (LR) and TU 200-200 (LR) up to σ1 – σ3 of 220 and440 kPa, respectively. The E values for specimens TU 25-100 (LR) and TU 200-200 (LR) are constant at 23 000 and8000 kPa, respectively. Figure 6b shows that the relationshipbetween σ1 – σ3 and εw is also linear for specimens TU 25-100 (LR) and TU 200-200 (LR). The Ew values for speci-mens TU 25-100 (LR) and TU 200-200 (LR) are constant at42 000 and 18 500 kPa, respectively.

Figure 7a illustrates the relationship between volumetricstrain, εv, and matric suction, (ua – uw), during the infiltra-tion stage of specimens TU 25-100 (LR) and TU 200-200(LR). The modulus of elasticity for the soil structure with re-spect to a change in matric suction, H, is given by the slopeof the relationship between εv and (ua – uw). Figure 7cshows the parameter H versus matric suction for specimensTU 25-100 (LR) and TU 200-200 (LR).

Figure 7b illustrates the relationship between water volu-metric strain, εw, and matric suction, (ua – uw), during the in-filtration stage of specimens TU 25-100 (LR) and TU 200-200 (LR). The water volumetric modulus associated withmatric suction changes, Hw, is the slope of the relationshipbetween εw and (ua – uw). Figure 7d shows the variation ofHw with changes in matric suction for specimens TU 25-100(LR) and TU 200-200 (LR). The relationship between εv and(ua – uw) is not as smooth as the relationship between εw and(ua – uw) (compare Figs. 7a and 7b). In other words, the val-ues of parameters H and Hw vary significantly with matricsuction.

Figures 8a and 8b show the parameters E and Ew fromnine shearing–infiltration tests on unsaturated specimens un-der the low infiltration rate. It was observed that E and Ew atdifferent initial matric suctions (i.e., 50, 100, and 200 kPa)increase as the net confining pressure increases.

Values of the parameter H from nine shearing–infiltrationtests on unsaturated specimens under the low infiltration rateare not presented here because of the inaccuracy in total vol-umetric measurements. The volumetric strains from thecomputation based on the volume change theory and the ex-perimental results are not examined. The total volumechange measurement was conducted by monitoring the flow

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Meilani et al. 1519

of water in or out of the triaxial cell. As such a method oftotal volume change measurement is affected by temperaturechanges, stiffness of the triaxial system, water absorption bythe acrylic cell, and piston displacement, the measurementsmay not be the exact volume changes of the soil specimen(Sivakumar 1993).

Figure 9 shows the values of parameter Hw from theshearing–infiltration tests on unsaturated specimens under

the low infiltration rate at different net confining pressures(i.e., 25, 100, and 200 kPa) and the same initial matricsuctions of 100 and 200 kPa, respectively. Equations [5] and[6] give the best-fit curves drawn from the relationships ofHw and matric suction obtained from the shearing–infiltrationtests on unsaturated specimens under the low infiltration rateas shown in Figs. 9a and 9b, respectively. The best-fit curvesin eqs. [5] and [6] have some limitations, however, because

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Fig. 6. Determination of parameters E and Ew for specimens TU 25-100 (LR) and TU 200-200 (LR): (a) deviator stress versus axialstrain; (b) deviator stress versus water volumetric strain; (c) E versus axial strain; (d) Ew versus water volumetric strain.

of the fact that the measurement of matric suction changewas not reliable after failure had occurred. Nevertheless, thecoefficients of correlation, R2, of the best-fit curves in eqs. [5]and [6] are greater than 0.85. Equations [5] and [6] onlyillustrate the best-fit curve for a certain range of matric suc-tion, namely 40–100 kPa for eq. [5] (Fig. 9a) and 80–200 kPafor eq. [6] (Fig. 9b), in which Hw is given in kilopascals:

[5] Hw =

− −⎡

⎣⎢

⎤

⎦⎥ + −⎡

⎣⎢

⎤

⎦⎥ +20840 16 644 6a w

ao

0.5

a w

ao

( ) ( )u uu

u uu

759

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Fig. 7. Determination of parameters H and Hw for specimens TU 25-100 (LR) and TU 200-200 (LR): (a) total volumetric strain (εv)versus matric suction (ua – uw); (b) water volumetric strain (εw) versus matric suction (ua – uw); (c) H versus matric suction; (d) Hw

versus matric suction.

[6] Hw =

− −⎡

⎣⎢

⎤

⎦⎥ + −⎡

⎣⎢

⎤

⎦⎥ +1 10 3 5a w

ao

0.5

a w

ao

4877 12( ) ( )u u

uu u

u616

where uao is the atmospheric pressure (i.e., 101.3 kPa)The parameter Ew (Fig. 8b) and the relationship between

Hw and matric suction (eqs. [5] and [6]) were verified usingdata from the shearing–infiltration tests on unsaturated spec-imens under a high infiltration rate, i.e., specimens TU 25-100 (HR) and TU 200-200 (HR). The comparison of the

computed and experimental results on the water volumetricstrains and pore-water pressure change is described in thefollowing section.

Comparison of volume change theory andexperimental data

Equation [4] is the constitutive equation for the waterphase for a triaxial loading. The terms (σ3 – ua) and (ua – uw)

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Fig. 8. Parameters E (a) and Ew (b) from shearing–infiltration triaxial tests on unsaturated specimens under a low infiltration rate.

were constant during shearing. Therefore, eq. [4] can besimplified for the shearing stage as

[7] δε δ 13

σ σww

1 3= −⎡⎣⎢

⎤⎦⎥

⎧⎨⎩

⎫⎬⎭

3E

( )

Equation [4] can also be simplified for the infiltration stage as

[8] δε δ( − )w

a w

w

= u uH

Using the volume change theory, the water volumetric strainand the changes in pore-water pressures during the shearing–infiltration tests on unsaturated specimens can be computed.The (σ1 – σ3) data obtained during the shearing process andEw (Fig. 8b) were used in the computation of water volumechange during shearing. The water volume change duringthe infiltration process is computed using the parameter Hw(eqs. [5] and [6]) and changes in (ua – uw) from the shearinginfiltration test results. The changes in pore-water pressure

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Fig. 9. Parameter Hw from shearing–infiltration triaxial tests on unsaturated specimens under initial matric suctions of (a) 100 kPa and(b) 200 kPa.

during the infiltration stage can be calculated using the wa-ter volume change and Hw (eqs. [5] and [6]) from the shear-ing infiltration test results. Poisson’s ratio, µ, was assumedto be 0.33.

Figure 10 shows a comparison of the computed and mea-sured values of water volumetric strains obtained from thetests on specimens TU 25-100 (HR) and TU 200-200 (HR).

The computed water volumetric strain shows a closeagreement with the measured data during the shearing andinfiltration stages of specimens TU 25-100 (HR) (Fig. 10a)and TU 200-200 (HR) (Fig. 10b).

Figure 11 shows a comparison between the computed pore-water pressure and the experimental pore-water pressurechanges during the shearing–infiltration test on specimens

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Fig. 10. Water volumetric strain versus axial strain on specimens (a) TU 25-100 (HR) and (b) TU 200-200 (HR).

TU 25-100 (HR) and TU 200-200 (HR). During shearing, thepore-water pressure change was not computed because therewere no pore-water pressure changes in the specimen duringshearing under a drained condition. During the infiltrationstage, the computed pore-water pressures give a good agree-ment with the measured pore-water pressures for specimensTU 25-100 (HR) (Fig. 11a) and TU 200-200 (HR) (Fig. 11b).

The good agreement between the computed and measuredwater volumetric strains (Fig. 10) and between the computedand experimental pore-water pressures (Fig. 11) during theshearing–infiltration test on specimens TU 25-100 (HR) andTU 200-200 (HR) can be attributed to the use of the parame-ter Hw from the scanning curve of the SWCC. The signifi-cance of Hw on the computation of water volumetric strain

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Fig. 11. Pore-water pressure versus axial strain on specimens (a) TU 25-100 (HR) and (b) TU 200-200 (HR).

and pore-water pressure during a shearing–infiltration test isdiscussed in the following section.

Parameter Hw

Figure 12 illustrates the comparison between the volumet-ric water content versus matric suction data from pressureplate tests and the volumetric water content versus matric

suction during the matric suction equalisation and infiltra-tion stages for specimens TU 25-100 (HR) and TU 200-200(HR). Figure 12 shows that during the matric suction equali-sation, the volumetric water content decreased as the matricsuction increased, similar to that of the drying SWCC fromthe pressure plate test. During the shearing stage, the matricsuction was constant because the pore air and the pore waterwere under drained conditions. During the infiltration stage,

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Fig. 12. Scanning curve of volumetric water content from matric suction equalisation and shearing–infiltration stages on specimens(a) TU 25-100 (HR) and (b) TU 200-200 (HR).

the volumetric water content increased as the matric suctiondecreased, following the scanning curve between the dryingand wetting SWCC. For specimen TU 25-100 (HR), failureoccurred when the scanning curve met the wetting SWCC(Fig. 12a). In the case of specimen TU 200-200 (HR), thescanning curve eventually met the wetting SWCC at amatric suction of 80 kPa (Fig. 12b, point A to point B), andthe experimental data continued to move along the wettingSWCC as matric suction continued to decrease from 80 to0 kPa during the infiltration stage (Fig. 12b, point B to point C).

Figure 13 shows a comparison of the values of Hw ob-tained from the wetting SWCC (Fig. 1) and those obtainedfrom the scanning and wetting curves associated with theshearing–infiltration tests on specimens TU 25-100 (HR)and TU 200-200 (HR) (Fig. 12). The scanning curve(Fig. 12b, from point A to point B) gives Hw from point A topoint B in Fig. 13. For a given matric suction, the scanningcurve and the wetting SWCC give different values of Hw(Fig. 13). The value of Hw from the shearing–infiltrationtests will eventually be similar to Hw from the wettingSWCC (point B to point C in Fig. 13), however, after thescanning curve meets the wetting SWCC, as in the case ofspecimen TU 200-200 (HR) (point B to point C in Fig. 12b).

The best-fit curves that were drawn through the Hw datafrom the scanning and wetting curves during the infiltrationstage of the shearing–infiltration tests with the low infiltra-tion rate under the initial matric suctions of 100 and 200 kPaare expressed in eqs. [5] and [6], respectively. The relation-ships between Hw and matric suction in eqs. [5] and [6] werethen used to compute the water volumetric strain and pore-water pressure during the infiltration stage of the shearing–infiltration test with the high infiltration rate. The computedwater volumetric strain shows good agreement with the ex-perimental water volumetric strain, as demonstrated inFigs. 10a and 10b. The computed pore-water pressure also

gives a good match with the experimental pore-water pres-sure, as shown in Figs. 11a and 11b. The good agreementcan be attributed to the use of Hw values from the scanningcurves (i.e., Figs. 12a and 12b).

To demonstrate the significance of Hw in the computationof water volumetric strain and pore-water pressure changes,the following analysis was conducted. As shown in Fig. 13,there are three different values of Hw, which were obtainedfrom the scanning curve, the drying SWCC, and the wettingSWCC. The water volumetric strain and the pore-water pres-sure were then computed using these three different valuesof Hw. Subsequently, the experimental water volumetricstrain and the experimental pore-water pressure were com-pared with the computed water volumetric strain and thecomputed pore-water pressure.

Figure 14 shows the comparison between the experimen-tal and computed water volumetric strain. In this case, thevalues of Hw obtained from the scanning curve, the dryingSWCC, and the wetting SWCC of specimens TU 25-100(HR) and TU 200-200 (HR) were used in the computation.The computed water volumetric strain using Hw from thescanning curve gives a better match to the experimental wa-ter volumetric strain than those computed using Hw from thedrying and wetting SWCCs. This observation is also foundin the comparison between the experimental and computedpore-water pressure of specimens TU 25-100 (HR) and TU200-200 (HR) (Figs. 15a, 15b). Figure 13 shows that the Hwvalues obtained from the drying and wetting SWCCs arelower than those obtained from the scanning curve at matricsuctions from 65 to 200 kPa. This is because the slopes ofthe drying curve (point A to point B in Fig. 16) and the wet-ting curve (point D to point C in Fig. 16) are greater than theslope of the scanning curve (point A to point C in Fig. 16).The Hw values are the inverse of the slope of the relationshipbetween volumetric water content, θw, and (ua – uw). As a re-

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Meilani et al. 1527

Fig. 13. Comparison of parameter Hw from SWCC and shearing–infiltration tests.

sult, the greater the slope of the θw versus (ua – uw) relation-ship, the lower the value of Hw. Therefore, the Hw valuesobtained from the drying and wetting SWCCs are lower thanthose obtained from the scanning curve. A lower Hw valuewill cause a higher water volumetric strain change for

the same matric suction change, as illustrated in eq. [8]. As aresult, the computed water volumetric strains using theHw values obtained from the drying and wetting SWCCs areoverestimated compared with the experimental water volu-metric strains (Figs. 14a, 14b). In addition, the computed

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Fig. 14. Comparison between the experimental and computed water volumetric strain using the Hw value obtained from the scanningcurve, the drying SWCC, and the wetting SWCC on specimens (a) TU 25-100 (HR) and (b) TU 200-200 (HR).

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Meilani et al. 1529

pore-water pressures using the Hw values obtained from thedrying and wetting SWCCs are underestimated comparedwith the experimental pore-water pressures (Figs. 15a, 15b).This is due to the fact that a lower Hw value gives a lower

pore-water pressure change for the same water volumetricchange.

It is concluded that the water volumetric strain and pore-water pressure during the shearing–infiltration test can be

Fig. 15. Comparison between the experimental and computed pore-water pressure using the Hw value obtained from the scanningcurve, the drying SWCC, and the wetting SWCC on specimens (a) TU 25-100 (HR) and (b) TU 200-200 (HR).

computed using the Hw value from the appropriate scanningcurve of the SWCC. The appropriate scanning curve shouldstart from the matric suction value at the beginning of theinfiltration stage.

Conclusions and recommendation

In the shearing–infiltration test, the stress–strain relation-ship of an unsaturated soil is similar to that of a saturatedsoil, when the degree of saturation of the unsaturated soil atfailure is close to 100%. It appears that the degree of satura-tion and the matric suction at a prefailure or failure condi-tion have an effect on the failure mode. The failure mode isductile for specimens that failed at a degree of saturation, Sf,higher than 90% or at a matric suction in the range 0–50 kPa. On the other hand, the failure mode is brittle forspecimens that failed at a degree of saturation, Sf, lower than90% or at a matric suction higher than 50 kPa. The degree ofsaturation at failure, Sf, of 90% can be used as a limit to de-termine the failure mode.

This study demonstrates that the semiempirical waterphase constitutive relation for an unsaturated soil as formu-lated by Fredlund and Rahardjo (1993) and expressed interms of the parameters Ew and Hw is correct. The volumechange theory for unsaturated soil was verified using the wa-ter volumetric strain and pore-water pressure changes duringthe shearing–infiltration tests.

The parameter Hw from the appropriate scanning curvecan be used to compute the water volumetric strain andpore-water pressures during the shearing–infiltration stage.The appropriate scanning curve should start from the matricsuction value when infiltration begins.

It is suggested that more values of Hw from scanning andwetting need to be collected to find the correlation betweenHw and matric suction on different soil types and conditionsfor practical purposes. The Hw values can be obtained fromthe pressure plate tests, which are conducted under drying

conditions to maximum matric suction in the field and underwetting conditions subsequently.

Acknowledgements

The first author would like to express her gratitude toNanyang Technological University for the research scholar-ship. This work forms part of a project funded by researchgrants from the National Science and Technology Board ofSingapore (NSTB 17/6/16: Rainfall-induced slope failures)and the Nanyang Technological University (RG 7/99: Capil-lary barrier for slope stabilization). The helpful suggestionprovided by Prof. D.G. Fredlund is also acknowledged.

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Fig. 16. Comparison of wetting, drying, and scanning curves from the SWCC.

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pore-water pressure and water volume change of an unsaturated soil under infiltration conditions

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