The nonlinear constitutive relations of clay are investigated considering different initial conditions. Highly compressible clay is selected as the test sample. Two groups of triaxial compression tests are performed, respectively, after
In geotechnical engineering, the nonlinearity nature of soil not only is influenced by a stress path but also has a close relationship with a load and a loading method. Therefore, it is a key to choose a suitable mechanical model of the medium material in geotechnical calculation.
Duncan [
Subsequently, some researchers attempted to improve the DuncanChang model and studied different soil constitutive models and their influence on results [
In these modified models, the initial stress state was assumed to be isotropic. However, the initial stress state of naturally deposited clay is usually anisotropic, known as
In this study, natural saturation clay sampled from Wuhan is studied. Considering the anisotropic initial stress and strain state, two parallel drain triaxial tests were carried out. In these tests, the static lateral pressure coefficient
Physical properties of the studied clay.
Physical property 








Value  28.53  1.961  2.697  28.18  47.82  0.897  98.9 
Considering the inevitable influence of disturbance and the difference characteristics in mechanics and physics of undisturbed soil sampling from different place, definite divergence was inevitable. Therefore, the moisture content is decided by field investigation. The remodeling soil sample of test passed by a series process: the undisturbed soil samples are made into uniform saturation samples, then tamping in 5 layers in tramper, and then extraction air before test. After the sample is installed, counterpressure saturation is carried out until the saturation reaches larger than 99%. Then triaxial shear test can be carried out under specified stress path.
Consolidated trained triaxial compression tests (
Experiment testing machine and sample.
Stress path of compression experiment.
In the
Initial stresses of




50  70.6  39.7 
100  141.3  79.4 
150  211.9  119.1 
200  282.4  158.7 
250  353.1  198.4 
300  423.9  238.2 
Figure
The two figures indicate that there are different stressstrain relationships for different stress paths. In the initial stage of load, the stress in isotropic pressure test (
Assuming that the elastic relationship of
The relationship between
Based on experimental data, Duncan assumed that the unloading modulus
In
Initial tangent elastic modulus





0.794  0.0045  222.2  242.8 
1.587  0.0040  250.0  
2.381  0.0039  256.0 
In loglog coordinates, the relationship between
Figure
Based on the result of test, axial strain
Based on (
Mohr’s circle can be drawn based on parameters of limit states for different ambient pressures. It is shown in Figure
Limit state parameter.






0.794  264.1  286.0  0.9140  0.820 
1.587  446.0  600.0  0.7433  
2.381  630.7  786.0  0.8024 
Mohr circle of shearing limit state.
Similar to the solution to elastic modulus
Integrating the results of the above calculation, the
The tangent Poisson ratio is shown in the following:
The coefficient
In (
To verify the validity of the model proposed in this paper, the authors have implemented the constitutive relationship into a finite element program and made a numerical simulation of triaxial tests. The height and diameter of the clay sample are 8 cm and 3.91 cm, respectively. Taking the symmetry of the sample into consideration, a half of the sample is adopted in the numerical simulation. In view of symmetry, horizontal displacement of nodes on the axes of symmetry is zero. Similarly, because of rigid fastening of test base, vertical constraints are applied to all the nodes of the sample. Moreover, the other two boundaries are force boundaries. The upper boundary is applied with
Computation diagram of FEA.
The relationship of
Comparison between numerical simulation and test curves.
Figure
The initial condition of natural clay is usually under
According to the tests, a factor of lateral pressure coefficient is introduced into the
With the average slope of the unloadingreloading curve selected as the unloading modulus, the constitutive relations can be promoted to an elastoplastic model. The proposed model can reflect the stressstrain relationship under
The authors declare that there is no conflict of interests regarding the publication of this paper.
The study was supported by the Natural Science Fund of Hubei Province under Grant 2012FKC14201, Scientific Research Fund of Hubei Provincial Education Department D20134401, and the Innovation Foundation in Youth Team of Hubei Polytechnic University under Grant Y0008. Their financial support is gratefully acknowledged.