J. Cent. South Univ. Technol. (2010) 17: 653-657

DOI: 10.1007/s11771-010-0536-y                                                                    

Stress-strain relationship of unsaturated cohesive soil

MEI Guo-xiong(梅国雄)¹, CHEN Qi-ming(陈启明)², JIANG Peng-ming(姜朋明)¹

1. School of Civil Engineering and Architecture, Jiangsu University of Science and Technology,

Zhenjiang 212003, China;

2. Louisiana Transportation Research Center, Louisiana State University, Baton Rouge, LA 70810, USA

? Central South University Press and Springer-Verlag Berlin Heidelberg 2010

Abstract: A moisture-content based constitutive model was proposed based on the hyperbolic model as an attempt to move towards the implementation of unsaturated soil mechanics into routine geotechnical engineering practice. The stress-strain behavior of in-situ soil at a depth of 5 m was investigated by conducting undrained triaxial compression tests using the remolded soil samples. The test results show that the stress-strain relationship of unsaturated cohesive soil is still hyperbolic. The values of parameters a and b given in the model decrease with increasing the confining pressure for soil samples with the same moisture content and increase with increasing the moisture content for soil samples under the same confining pressure. The relationships between parameters a, b and moisture content were studied for confining pressures of 100, 150, 200 and 250 kPa. The comparison between the measured and predicted stress-strain curves for an additional group of soil samples, having a moisture content of 25.4%, shows that the proposed moisture content-dependent hyperbolic model provides a good prediction of stress-strain behavior of unsaturated cohesive soil.

Key words: unsaturated cohesive soil; moisture content; triaxial compression test; stress-strain relationship

1 Introduction

An unsaturated soil is recognized to have four phases, i.e. soil, water, air, and air-water interface or contractile skin phases [1-2]. This four-phase system concept has been accepted by most researchers in the unsaturated soil community today. Matric suction, acting on the contractile skin, is considered as an important stress state variable in an unsaturated soil. Significant research has been carried out to understand and measure the matric suction, in terms of soil water characteristic curve (SWCC) [3-5]. However, the process for obtaining SWCC is tedious and time-consuming [6-7]. As a result, most studies of matric suction-based unsaturated soil mechanics still stay in academic research and its application in routine engineering practice is limited [8-9].

The research progress in the field of unsaturated soil mechanics indicated that more and more researchers move towards the implementation of unsaturated soil mechanics into routine geotechnical engineering practice. BAO and ZHANG [10] once pointed out that future development of unsaturated soil mechanics needs to move towards its implementation into engineering practice, otherwise the sustainable development of unsaturated soil mechanics is not possible. Today, most engineers still use conventional triaxial test apparatus to determine the properties of unsaturated soil and use conventional saturated soil mechanics to analyze them.

The moisture content or degree of saturation, as a basic soil property in routine engineering practice, can be easily determined in the laboratory or field. YIN et al [11], therefore, pointed out that a constitutive model with moisture content dependency may be easier for engineers to understand and can thus be more readily to spread to engineers than matric suction-based model. As such, the moisture content-based model, as an approximate simulation model, is worth further study and development [12-15]. Based on the above-mentioned facts and reasons, modified conventional triaxial compression tests were performed in this study as an attempt to directly build a stress-moisture content-strain relationship for unsaturated cohesive soil and bypass the suction concept.

2 Material and laboratory tests

The soil used was Xiashu soil, a yellow silty clay. The soil samples were oven dried and all lumps were broken into small particles. The dry soil was passed through a 1 mm sieve and the fine soil was then stored in an air-tight container until test preparation commenced.

2.1 Basic consideration

In-situ stress conditions are restored to the samples prior to application of the deviator stress. During this stress recovery process, if the drainage is allowed, the moisture content of soil will be decreased. Based on this consideration, the soil samples were conditioned under undrained condition during the stress recovery period in this study.

2.2 Basic physical properties

Basic physical properties of soil, including dry density, unit weight, specific gravity, liquid limit, plastic limit, coefficient of compressibility, and modulus of compressibility, were determined, and the values are presented in Table 1.

Table 1 Physical properties of soil

2.3 Sample preparation and testing program

During the testing process, the following two steps were usually taken: (1) recovery of in-situ stress conditions of soil samples, i.e., the soil sample was first subjected to a confining pressure of 100 kPa (corresponding to soil at a depth of 5 m) under undrained condition until the pore water pressure reached a steady state, and this step took about 12 h; (2) conduction of conventional undrained triaxial compression tests.

Undrained triaxial compression tests were conducted on samples with the dry density of 1.52 g/cm³ at 16 different moisture contents (10.32%, 11.84%, 12.53%, 14.84%, 15.58%, 16.59%, 17.09%, 17.65%, 19.65%, 19.82%, 20.21%, 23.05%, 23.82%, 24.94%, 27.13% and 28.18%), which were measured after each test. The strain rate was set as 1 mm/min. At each moisture content, four undrained triaxial compression tests were performed at confining pressures of 100, 150, 200 and 250 kPa.

3 Test results and analysis

3.1 Hyperbolic stress-strain model

The test results were plotted as a curve of deviatoric stress, σ₁-σ₃, against axial strain, ε₁. σ₁ and σ₃ are major and minor principal stresses, respectively. Typical stress-strain curves are presented in Fig.1 for moisture contents of 23.05% and 23.82%. As can be seen from this figure, the stress-strain curves could be approximated by hyperbolas.

To further study the stress-strain relationship of

Fig.1 Stress-strain curves for different moisture contents:    (a) 23.05%; (b) 23.82%

unsaturated cohesive soil, the data were analyzed using the hyperbolic mathematical model, which is plotted in Fig.2(a) and expressed as:

               (1)

where a and b are constants, whose value may be determined from conventional triaxial compression tests; 1/a is the initial tangent modulus, E_i; and 1/b is the ultimate principal stress difference.

Rearrange terms in Eq.(1) and obtain

                  (2)

where ε₁/(σ₁-σ₃) is a linear function of the axial strain, ε₁, as graphically shown in Fig.2(b). The test results can now be plotted as a line of ε₁/(σ₁-σ₃) against axial strain, ε₁. Typical lines are presented in Fig.3 for moisture contents of 23.05% and 23.82%. The linear regression indicates that the linear model provides excellent fits to the experimental data. This confirms again that the stress- strain relationship of unsaturated cohesive soil is still hyperbolic.

Fig.2 Hyperbolic forms of stress-strain relationship: (a) (σ₁-σ₃) vs ε₁; (b) ε₁/(σ₁-σ₃) vs ε₁

Fig.3 Typical stress-strain responses in ε₁/(σ₁-σ₃)—ε₁ space under different moisture contents: (a) 23.05%; (b) 23.82%

3.2 Parameters a and b

Parameters a and b can be obtained through the linear regression analysis of experimental data. Figs.4 and 5 present the variation of parameters a and b with the moisture content and confining pressure. As can be seen from these figures, the values of parameters a and b decrease with increasing the confining pressure for soil samples with the same moisture content. This is because the initial tangent modulus, E_i, and the ultimate principal stress difference, (σ₁-σ₃), increase with increasing the confining pressure. On the other hand, the values of parameters a and b increase with increasing the moisture content under the same confining pressure. This is because the initial tangent modulus, E_i, and the ultimate principal stress difference, (σ₁-σ₃), decrease with increasing the moisture content.

Fig.4 Variation of parameter a with moisture content and confining pressure

Fig.5 Variation of parameter b with moisture content and confining pressure

Further data analysis shows that there is no obvious relationship between parameters a, b and the confining pressure. The variation of parameters a and b with the moisture content at different confining pressures are shown in Figs.6 and 7. The following functions are proposed:

a=r₁+s₁w                  (3)

b=r₂+s₂exp(w/t₂)               (4)

where w is the moisture content; r₁, s₁, r₂, s₂, and t₂ are regression parameters. The regression parameters (r₁, s₁, r₂, s₂, and t₂) and the corresponding coefficients of correlation are summarized in Tables 2 and 3.

Fig.6 Relationship between a and moisture content at different confining pressures

Fig.7 Relationship between b and moisture content at different confining pressures

Table 2 Model regression parameters and corresponding coefficients of correlation for a

Table 3 Model regression parameters and corresponding coefficients of correlation for b

3.3 Verification of model

The regression models in Eqs.(3) and (4) were verified by comparing the results of regression models with the results obtained from triaxial compression tests for an additional group of soil samples, which have a measured moisture content of 25.42%. The values of parameters a and b, which were calculated using Eqs.(3) and (4), are presented in Table 4 for different confining pressures. Fig.8 shows the detailed comparison of the measured and predicted stress-strain curves. The comparison indicates that good agreement exists between the measured and predicted stress-strain behavior of cohesive soil, with coefficients of correlation equal to 0.966 77, 0.976 85, 0.971 50 and 0.964 33 for confining pressures of 100, 150, 200, and 250 kPa, respectively.

Table 4 Calculated values of parameters a and b at different confining pressures

Fig.8 Comparison of measured and predicted stress-strain curves

4 Conclusions

(1) As an attempt to move towards the implementation of unsaturated soil mechanics into routine geotechnical engineering practice, a moisture- content based constitutive model was developed based on the Kondner’s hyperbolic model. The stress-strain behavior of in-situ soil at a depth of 5 m was then investigated by conducting undrained triaxial compression tests using remolded soil samples.

(2) The stress-strain relationship of unsaturated cohesive soil is still hyperbolic. The values of parameters a and b in the Kondner’s model decrease with increasing the confining pressure for soil samples with the same moisture content and increase with the increasing the moisture content for soil samples under the same confining pressure.

(3) The comparison of the measured and predicted stress-strain curves for an additional group of soil samples, which have a measured moisture content of 25.42%, shows that the proposed moisture content- dependent hyperbolic model provides a good prediction of the stress-strain behavior of unsaturated cohesive soil.

(4) It should be pointed out that the test results for undisturbed soil samples are not available for comparison. Future research is recommended to evaluate the difference between the remolded and undisturbed soil samples.

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Foundation item: Project(50608038) supported by the National Natural Science Foundation of China

Received date: 2009-03-12; Accepted date: 2009-07-07

Corresponding author: MEI Guo-xiong, PhD; Tel: +86-791-3953422; E-mail: meiguox@163.com

(Edited by YANG Bing)