Towards a Unified Soil Mechanics Theory: The Use of Effective Stresses in Unsaturated Soil, Revised Edition

The use of the effective stress principle led to a general theory for the strength and volumetric behavior of saturated soils. Presently, all constitutive models for saturated soils are based on this principle. In 1959, Bishop proposed an equation for the effective stress of unsaturated soils. However, it was severely criticized because it could not explain by itself the phenomenon of collapse upon wetting. Moreover, an analytical expression for the determination of its main parameter χ was not provided and in addition, its value could not be easily determined in the laboratory. Since then several equations to determine the value of parameter χ have been proposed. Fifty years later, it has been acknowledged that Bishop’s effective stress equation can be employed to simulate the behavior of unsaturated soils when it is complemented with a proper elastoplastic framework.

Based on the analysis of the equilibrium of solid particles of an unsaturated sample subject to certain suction it is possible to establish an analytical expression for Bishop´s parameter χ. The resulting stress can be used to predict the shear strength and volumetric behavior of unsaturated soils. The effective stress is written as a function of the net stress and suction and requires three parameters: the saturated fraction, the unsaturated fraction and the degree of saturation of the unsaturated fraction of the sample. This equation clarifies some features of the strength of unsaturated soils that up to now had no apparent explanation. A drawback to this expression is that the determination of these three parameters cannot be made from current experimental procedures.

Based on the study of the equilibrium of the particles of a soil sample subject to certain suction, in the previous chapter it was possible to establish an analytical expression for the value of Bishop´s parameter χ. This parameter can be written as function of the saturated fraction, the unsaturated fraction and the degree of saturation of the unsaturated fraction of the soil. However, the determination of these three parameters cannot be made from current experimental procedures. Therefore, a porous-solid model simulating the structure of the soil is proposed herein and used to determine these parameters. The data required to build the porous-solid model are the void ratio and the grain and pore size distributions.

In the previous chapter, a computational network porous-solid model was developed to simulate the hydraulic behavior of unsaturated soils. However, important computational constraints make this model unpractical. In this chapter, a probabilistic porous-solid model is developed to overcome these constraints. The probabilistic model is an alternative to the use of computational network models and shows important advantages. This model is built by analyzing the probability of a certain pore to be filled or remain filled with water during a wetting or drying process, respectively. The numerical results of the probabilistic model are compared with those of the computational network model showing only slight differences. Then the model is validated by doing some numerical and experimental comparisons. Finally, a parametric analysis is presented.

In the previous chapter, a probabilistic porous-solid model with the ability to simulate both branches of the soil-water retention curve was developed. In this chapter, the model is used to interpret more realistically the results of mercury intrusion porosimetry tests. Moreover, it is used to obtain the pore size distribution of soils employing both branches of the soil-water retention curve as data. The numerical and experimental comparisons for different soils show that the model approximately reproduces the pore size distribution obtained from mercury intrusion porosimetry tests. Finally, a procedure to fit the numerical with the experimental soil-water retention curves in order to obtain the pore size distribution of soils is presented.

In this chapter, the probabilistic porous-solid model is used to determine the mean effective stress of soils at failure. The plots of the deviator stress against the mean effective stress show a unique failure line for a series of triaxial tests performed at different confining net stress and suctions for both wetting and drying paths. This result confirms that the proposed effective stress equation is adequate to predict the shear strength of unsaturated soils. It also results in different strengths for wetting and drying paths as the experimental evidence indicates.

In this chapter, the probabilistic porous-solid model is used to simulate the tensile strength of unsaturated soils tested at different water contents. The strength of unsaturated soils can be split in two parts: one related to the net stress and the other to suction. The strength generated by suction has its origin on the additional contact stresses induced to solid particles by water meniscus. This additional contact stress is called matric suction stress. In that sense, the tensile strength of soils represents the matric suction stress of the material at that particular water content. The numerical and experimental comparisons of the tensile strength of unsaturated soils tested at different water contents show that the probabilistic porous-solid model can simulate this phenomenon with sufficient accuracy.

An equation to account for the volumetric behavior of unsaturated soils is proposed in this chapter. This equation is based on the effective stress principle and results in a unifying framework for the volumetric behavior for both saturated and unsaturated soils. The results of the proposed equation are compared with experimental results published by different researchers. These comparisons show that the equation is adequate to account for wetting-drying and net stress loading-unloading paths. This analysis confirms that the effective stress principle can be applied to the volumetric behavior of unsaturated soils.

This chapter presents the modeling of the phenomenon of collapse upon wetting using the effective stress equation established in Chapter 2 and the elastoplastic framework proposed in the previous chapter. Using the probabilistic porous-solid model, Bishop’s parameter χ can be obtained to determine the current effective stress. The proposed framework includes the hysteresis of the SWRC and to some extent the hydro-mechanical coupling of unsaturated soils. This model is able to reproduce some particularities of the phenomenon of collapse upon wetting that other models cannot simulate.

In this chapter, an elastoplastic framework for the volumetric behavior of expansive soils based on effective stresses is proposed. This framework is grounded on the volumetric and collapsing behavior of soils developed in Chapters 8 and 9. The hydraulic behavior of the soil is simulated using the porous-solid model developed in Chapter 4. The result is an elastoplastic framework based on the equation of the volumetric behavior of saturated soils presented in Chapter 8 where the value and sign of the compression index depends on the position of the state of stresses and the direction of the increment of the effective stress with respect to the yield surfaces in the plane of effective mean stress against suction. Experimental and numerical comparisons show the ability of the model to simulate the behavior of expansive soils under different stress paths.

The phenomenon of hysteresis during wetting-drying cycles can be simulated by the porous-solid model developed in chapter 3. This model employs the current pore-size distribution of the material. The term “current pore-size distribution” means that the size of pores can be updated as the soil deforms. In that sense, the porous-solid can be used advantageously for the development of fully coupled hydromechanical constitutive models as the influence of the volumetric deformation on the retention curves and effective stresses can be easily assessed. This is done by including some experimental observations related to the behavior of the pore size distribution of soils subjected to loading or suction increase. This methodology avoids using any additional parameter or calibration procedure for the hydro-mechanical coupling of unsaturated soils.

In previous chapters, it has been shown that the principle of effective stresses can be applied to the shear strength, the tensile strength and the volumetric behavior of unsaturated soils. This chapter shows that the critical state line for unsaturated soils shifts with respect to the saturated critical sate line in a quantity that depends on the suction stress. Taking into account this phenomenon and the influence of hydro-mechanical coupling on the behavior of unsaturated soils, a fully coupled general constitutive models for soils is developed. This model is based on the modified Cam-Clay model and includes a yield surface with anisotropic hardening that takes into account the shift of the critical state line with suction. The result is a very simple model with a symmetric stiffness matrix that can be used for saturated, unsaturated and compacted materials.