This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg)Nanyang Technological University, Singapore.

Stress‑strain behavior and shear strength ofunsaturated residual soil from triaxial tests

Leong, Eng Choon; Rahardjo, Harianto; Nyunt, T. T.

2012

https://hdl.handle.net/10356/96866

© 2011 Kasetsart University. This paper was published in Asia‑Pacific Conference onUnsaturated Soils: Theory and Practice and is made available as an electronic reprint(preprint) with permission of Kasetsart University. The paper can be found at the followingofficial DOI: [http://www.unsat.eng.ku.ac.th/Proceeding/index.html]. One print orelectronic copy may be made for personal use only. Systematic or multiple reproduction,distribution to multiple locations via electronic or other means, duplication of any materialin this paper for a fee or for commercial purposes, or modification of the content of thepaper is prohibited and is subject to penalties under law.

Downloaded on 23 Oct 2021 15:43:14 SGT

221

Unsaturated Soils: Theory and Practice 2011Jotisankasa, Sawangsuriya, Soralump and Mairaing (Editors)

Kasetsart University, Thailand, ISBN 978-616-7522-77-7

1 INTRODUCTION

Residual soils cover about the two-thirds of the land area of Singapore. The groundwater tables in these residual soils are well below the ground sur-face and thus the bulk of the residual soils are unsa-turated (Leong et al. 2003). The residual soils are derived from the two formations, namely: Bukit Ti-mah Granite residual soils and Jurong Formation se-dimentary residual soils. Figure 1 depicts the geo-logical map of Singapore. The Bukit Timah Granite is one of the oldest formations in Singapore and was formed approximately 200 to 250 million years ago. The heavily weathered residual soils were formed in the top portions of the Bukit Timah Granite up to depth of 60 m. Generally, residual soils from Bukit Timah Granite consist of reddish to yellow brown clayey soils. The Jurong formation was formed about 100 to 200 million years ago. The upper por-tions of the Jurong Formation were heavily wea-thered and the residual soils are found approximate-ly up to depth of 30 m. The residuals soils of Jurong Formation consist mainly of silty clays. In this pa-per, the stress-strain relationship and shear strength of unsaturated undisturbed residual soils from Bukit Timah Granite formation are presented. The location of the sampling site is indicated in Figure 1.

Shear strength parameters for unsaturated soils can be obtained by performing triaxial tests, namely:

Figure 1. Geological map of Singapore with location of sam-pling site. consolidated drained test (CD),constant water con-tent test (CW), consolidated undrained test with pore pressures measurement (CU) and unconfined com-pression test (UC) (Fredlund and Rahardjo 1993). In this study, CU (i.e. undrained pore-air and pore-water pressure condition) and CW (i.e. drained pore-air pressure and undrained pore-water pressure con-dition) triaxial tests were performed to investigate the stress-strain relationship and shear strength of undisturbed residual soils under different drainage conditions in terms of pore-air phase.

Stress-strain Behavior and Shear Strength of Unsaturated Residual Soil from Triaxial Tests T.T. Nyunt, E.C. Leong & H. Rahardjo School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, th0002nt@e.ntu.edu.sg, cecleong@ntu.edu.sg, chrahardjo@ntu.edu.sg

ABSTRACT: Multi-stage triaxial compression tests were performed on undisturbed samples of residual soils from Bukit Timah Granite formation in Singapore. Tests were carried out under two conditions, namely, con-solidated undrained test (CU) (i.e. both pore-air and pore-water pressure were not allowed to drain during shearing) and constant water content test (CW) (i.e. drained pore-air but undrained pore-water condition dur-ing shearing). Stress-strain relationships and shear strength of unsaturated soils were studied at different ini-tial matric suctions of 50 kPa, 100 kPa, 200 kPa, and 400 kPa, by performing CU and CW tests. The varia-tions of matric suction during shearing at two different test conditions (CU and CW tests) are also presented. From the experiments, it was observed that the stress-strain relationship from CU test is less stiff than that from CW test. A single relationship of total cohesion intercept with matric suction was obtained from CU and CW tests. KEYWORDS: stress-strain behavior; shear strength; unsaturated residual soil; matric suction

LegendOld AlluviumKallang FormationJurong Formation residual soilsTekong FormationBukit Timah Granite residual soilsGombak NoriteSajahat Formation

Location of sampling site 

Stress-strain behavior and shear strength of unsaturated residual soil from triaxial tests

T.T. Nyunt, E.C. Leong & H. RahardjoSchool of Civil and Environmental Engineering, Nanyang Technological University, Singapore,th0002nt@e.ntu.edu.sg, cecleong@ntu.edu.sg, chrahardjo@ntu.edu.sg

222

2 SHEAR STRENGTH THEORY FOR UNSATURATED SOILS

Fredlund et al. (1978) proposed an extended Mohr-Coulomb failure envelope for unsaturated soil as fol-lows:

bfwafaf tan)u(utan)u(σc'τ φφ −+−+= ' (1)

where τf is shear stress at failure, c’ and φ ’ are effec-tive stress shear strength parameters obtained from saturated test, (σ-ua)f is net normal stress at failure, (ua-uw)f is matric suction at failure and φ b is angle describing increase in shear strength with matric suction. Equation 1 can be written in two-dimensional representation as:

'φtan)u(σcτ faf −+= (2)

where, bfwa tan)u(uc'c φ−+= (3)

3 TEST SET-UP A modified triaxial apparatus was used to study the stress-strain relationship and shear strength of unsa-turated residual soil. The triaxial apparatus is equipped with a 3 kN submersible load cell, an ex-ternal linear variable differential transformer (LVDT), a submersible LVDT, and a pair of local displacement transducers (LDT) for axial strain measurement at different strain levels, a pair of proximity transducers for radial strain measurement and pressure transducers for pore-air and pore-water pressure measurements. A 5-bar high air entry ce-ramic disk was fixed in the bottom pedestal using epoxy for unsaturated soils testing. Figure 2 shows the modified triaxial apparatus used in this study.

4 TEST PROCEDURE Soil specimens of 50 mm diameter and 100 mm height were trimmed from 70 mm diameter undis-turbed residual soil samples. The undisturbed resi-dual soil samples were obtained using Mazier sam-pling. The residual soil specimens used for CU and CW tests were from depths of 2 to 3 m. Table 1 summarizes the basic properties of the residual soils. The average initial water content and the average in-itial degree of saturation of the undisturbed residual soil sample were 43% and 90%, respectively. The soil specimens were saturated in the triaxial cell prior to consolidation to ensure identical initial wa-ter content in the specimens. The pore-water

Figure 2. Schematic drawing of triaxial test set-up (modified from Leong et al. 2006).

parameter B obtained was greater than 0.96 for the soil specimens during saturation. Near or full satura-tion was assumed when pore-water pressure parame-ter B was greater than 0.96 (Head 1980).

After saturation, the soil specimens were isotropi-cally consolidated to the in situ effective confining pressure and subsequently at the required net confin-ing pressure (σ3-ua) and matric suction (ua-uw) via the axis-translation technique (Hilf 1956). For the application of matric suction, a constant air pressure of 450 kPa was supplied at the top of the soil speci-men through a porous disk and water pressure was controlled via a digital pressure volume controller (DPVC) through a 5-bar high air entry ceramic disk. The amount of water flowing out of the soil speci-men during matric suction equalization was moni-tored via DPVC. The matric suction equalization was assumed to have been completed when the amount of water flowing out of the soil specimen had leveled off.

Multi-stage shearing was adopted to study the stress-strain behavior and shear strength of the un-disturbed residual soil at different initial matric suc-tions. Shearing was carried out in four stages at ini-tial matric suctions of 50 kPa, 100 kPa, 200 kPa and 400 kPa under net confining pressure of 50 kPa and constant air pressure of 450 kPa. At the end of each matric suction equalization stage, the specimen was sheared until failure was imminent and unloaded be-fore imposing the next required matric suction.

The soil specimens were tested under two differ-ent test conditions: consolidated undrained test (CU) and constant water content test (CW). A constant strain rate of 0.5 mm/min was used for both CU and CW tests. In CU test, both pore-air and pore-water pressure were not allowed to drain during shearing and in CW test, air was allowed to flow freely, how-ever, pore-water pressure was undrained during shearing. The variations of pore-air and pore-water pressure during shearing were recorded. At the end

  

 Proximity transducer

Submersible LVDT

LVDT 

Computer

Submersible load cell

Pore‐water pressure transducerLocal displacement transducer

Soil specimen

Pore‐air pressure transducerControl & Data Acquisition 

Air Pressure Supply

Pneumatic Servo 

Amplifier & signal conditioners  

Actuator 

System 

223

Table 1. Basic properties of residual soils from Bu-kit Timah Granite Formation

Soil properties ValueBorehole I-AMA2Depth (m) 2.0-3.0Liquid limit (%) 45 Plastic limit (%) 30 Plasticity index (%) 15 Sand (%) 46 Silt (%) 45 Clay (%) 9 Specific gravity 2.74

Unified Soil Classification System (USCS) ML (Low plasticity silt)

of the test, water content was measured to obtain the variation of water content with respect to the im-posed matric suction.

5 RESULTS AND DISCUSSIONS Stress strain relationship and shear strength of the undisturbed residual soil specimens from CU and CW tests are presented. The stress-strain relation-ship at initial matric suctions, (ua-uw)i, of 50 kPa, 100 kPa, 200 kPa and 400 kPa for CU and CW tests are shown in Figure 3. Peak deviator stress increases with initial matric suction for both CU and CW tests. The strain at which the soil specimen reaches the peak deviator stress decreases with initial matric suction for both CU and CW tests.

The stress-strain relationships obtained for CU test exhibit less stiff behavior as compared with that for CW test. Moreover, the values of peak deviator stress obtained from CU tests are lower than the cor-responding values from CW tests. The differences become more significant with higher initial matric suctions. This behavior can be explained by differ-ences in drainage condition of pore-air phase during shearing. In CU test, excess pore-air pressure was undrained during shearing resulting in higher void ratio at failure under lower (σ3-ua)f compared with the corresponding CW test where pore-air pressure was drained and thus, the stress-strain relationship for CU test was less stiff. In addition, the resulting higher void ratio at failure due to excess pore-air pressure that developed in the CU test may have in-fluenced the decrease in peak deviator stress com-pared with the corresponding CW test.

The variations of matric suction with axial strain for CU and CW tests at different initial matric suc-tions are plotted in Figure 4. Table 2 summarizes the values of peak deviator stress, pore-air pressure, pore-water pressure, and matric suction at failure for CU and CW tests. The excess pore-water pressures

0

200

400

600

800

0 5 10 15 20 25

Deviator stress (kPa)

Axial strain (%)

(a) CU test

0

200

400

600

800

0 5 10 15 20 25

Deviator stress (kPa)

Axial strain (%)

(b) CW test

Figure 3. Stress-strain relationship at initial matric suctions of 50 kPa, 100 kPa, 200 kPa and 400 kPa. at failure were very close for both CU and CW tests with the same initial matric suction. In addition, the excess pore-air pressures at failure in CU tests at dif-ferent initial matric suction were observed to be sim-ilar as shown in Table 2. Therefore, matric suction at failure, (ua-uw)f, for CU test was higher than that for the corresponding CW tests. Similarly, net confining pressure at failure, (σ3-ua)f, in CU test was lower than that for the corresponding CW test.

The effective shear strength parameters (c’and φ ’) for the saturated residual soils are c’= 22 kPa and φ ’ = 33o obtained in another study. The extended Mohr-Coulomb failure envelopes for the CU and CW tests were plotted using Equation 2 by drawing the tangent line to the Mohr circles of the

(ua‐uw)i = 400 kPa 

(ua‐uw)i = 200 kPa 

(ua‐uw)i = 100 kPa 

(ua‐uw)i = 50 kPa 

(ua‐uw)i = 400 kPa 

(ua‐uw)i = 200 kPa 

(ua‐uw)i = 100 kPa 

(ua‐uw)i = 50 kPa

224

‐50

50

150

250

350

450

0 5 10 15 20 25

Variation

 of matric suction (kPa)

Axial strain (%)

(a) CU test

‐50

50

150

250

350

450

0 5 10 15 20 25

Variation

 of matric suction (kPa)

Axial strain (%)

‐50

50

150

250

350

450

0 5 10 15 20 25

Variation

 of matric suction (kPa)

Axial strain (%)

(b) CW test

Figure 4. Matric suction versus axial strain at different initial matric suctions of 50 kPa, 100 kPa, 200 kPa and 400 kPa. unsaturated soil specimens at different initial matric suctions with slope of φ ’. Peak deviator stress was used to plot the Mohr circle to obtain the extended failure envelopes for unsaturated soils. Figure 5 shows the Mohr circles with total cohesion inter-cepts for CU and CW tests. The values of total cohe-sion intercept increase non-linearly with matric suc-tions. Similar non-linear behavior of total cohesion intercept with matric suction has been reported by Gan et al. (1988) and Thu et al. (2006).

The φ b angle for CU and CW tests were obtained by plotting the total cohesion intercept with matric suction at failure as shown in Figure 6. The values of φ b angle obtained from CU test are close to the

Table 2. Summary of deviator stress, pore pressures and matric suction at failure

(ua-uw)i (kPa)50 100 200 400

CU test

(σ1-σ3)f (kPa) 156 226 319 469uaf (kPa) 472 465 470 468uwf (kPa) 467 427 360 92(ua-uw)f (kPa) 5 39 110 377

CW test

(σ1-σ3)f (kPa) 159 230 332 518uaf (kPa) 450 450 450 450uwf (kPa) 450 427 362 92(ua-uw)f (kPa) 0 23 88 358

0

200

400

600

800

0 200 400 600 800

τ(kPa)

σ‐ua   (kPa)

(a) CU test

0

200

400

600

800

0 200 400 600 800

τ (kPa)

σ‐ua   (kPa)

(b) CW test

Figure 5. Mohr circles at different initial matric suctions of 50 kPa, 100 kPa, 200 kPa and 400 kPa.

  (ua‐uw)i = 50 kPa 

(ua‐uw)i = 100 kPa 

(ua‐uw)i = 200 kPa 

(ua‐uw)i = 400 kPa 

  (ua‐uw)i = 50 kPa 

(ua‐uw)i = 100 kPa 

(ua‐uw)i = 200 kPa 

(ua‐uw)i = 400 kPa 

  (ua‐uw)i (kPa) 

c (kPa) 

50  22 100  39200  68400  108

  (ua‐uw)i (kPa) 

c (kPa) 

50  14 100  30 200  58 400  110 

225

φ b values obtained from CW tests. For non-linear variation of φ b angle with matric suction, Equation 3 can be written as:

fwabf)wua(u

0)ud(utanc'c −∫+=

−φ (4)

where

[ ]fwab )u(utan −= fφ (5)

Figure 6 shows the calculated and measured total cohesion intercept with matric suction for CU and CW tests. Figure 6 also shows that the total cohesion intercept with matric suction relationship from CU and CW tests can be represented by a single curve. The initial φ b angle obtained is 33 same as φ ’ and approaches 0 at high matric suction. The φ b angle was normalized with φ ’ and compared with the normalized water content, w/wo, (where wo is the water content at low matric suction) obtained from the experiments as shown in Figure 7. It was ob-served that the ratio of φ b /φ ’ with matric suction re-lationship has similar trend as the normalized water content (i.e. w/wo) with matric suction relationship.

0

50

100

150

200

0 200 400 600

Total coh

esion intercep

t (kPa)

ua‐uw (kPa)

CU test

CW test

Figure 6. Total cohesion intercepts versus matric suction for CU and CW tests.

0

0.5

1

1.5

0 1 100 10,000

w/w

oor     φ

b /φ'

ua‐uw (kPa) Figure 7. Comparison of normalized φ b angle and water con-tent with matric suction. 6 CONCLUSION Stress-strain relationship and shear strength of unsa-turated undisturbed residual soil from Bukit Timah Granite formation were studied by performing CU and CW tests. From the experimental results, it was observed that the stress-strain relationship from CU test showed less stiff behavior than the correspond-ing CW test. A single curve can be used to represent the relationship of total cohesion intercept with ma-tric suction for CU and CW tests. Non-linear rela-tionship of φ b angle with matric suction was ob-served and it has similar trend as the water content with matric suction relationship.

ACKNOWLEDGEMENTS The work described in this paper is supported under research grant PTRC–CEE/DSTA/2006.01. The first author gratefully acknowledges the research scholar-ship from Nanyang Technological University, Sin-gapore and financial support from PTRC–CEE/DSTA/2006.01.

φb/φ' 

w/wo‐CU 

w/wo‐CW 

  φ ’=33

226

REFERENCES Fredlund, D. G., Morgenstern, N. R., and Widger, R. A.

(1978). "The shear strength of unsaturated soils." Canadian Geotechnical Journal, Vol. 15(3), pp.313-321.

Fredlund, D. G., and Rahardjo, H. (1993). Soil Mechanics for Unsaturated Soils, Wiley, NewYork.

Gan, J., Fredlund, D. G., and Rahardjo, H. (1988). "Determination of the Shear Strength Parameters of an Unsaturated Soil Using the Direct Shear Test." Canadian Geotechnical Journal, Vol. 25(3), pp. 277-283.

Head, K. H. (1980). Manual of Soil Laboratory Testing, Effective Stress Tests, Vol. 3, Pentech Press.

Hilf, J. W. (1956). "An Investigation of Pore-Water Pressure in Compacted Cohesive Soils," PhD dissertation, Technical Memorandum No. 654, U. S. Department of the Interior, Bureau of Reclamation, Design and Construction Division,Denver.

Leong, E. C., Cahyadi, J., and Rahardjo, H. (2006). "Stiffness of a Compacted Residual Soil." Geotechnical Special Pub-lication, No 147, Vol 1, 1169-1180.

Leong, E. C., Rahardjo, H., and Tang, S. K. (2003). "Charac-terisation and Engineering Properties of Singapore Residual Soils." Proc., International Workshop on Characterisation and Engineering Properties of Natural Soils, Singapore, Vol 2, 1279-1304.

Thu, T. M., Rahardjo, H., and Leong, E. C. (2006). "Shear Strength and Pore-Water Pressure Characteristics during Constant Water Content Triaxial Tests." Journal of Geotechnical and Geoenvironmental Engineering, Vol. 132(3), pp. 411–419.