International Journal of Geomechanics

This paper presents the formulation and application of a composite element method, which is intended for numerical modeling of discontinuous rock masses. This method allows analysis of fractured rock masses using regular meshes that do not need to rigorously respect the orientations and positions of discontinuities. It can be incorporated in conventional finite-element programs. The performance of this method are illustrated through its use for the analysis of the mechanical behavior of the Baozhusi gravity dam which is constructed on a complex rock foundation.

In 1959 Bishop stated his effective stress equation for unsaturated soils. However, the difficulties in estimating the value of its main parameter $\chi$ , made this equation useless and it was abandoned for some time. Only recently, it has been recognized that the use of Bishop’s stress equation can lead to simpler and more realistic constitutive models for unsaturated soils. However, up to now the most successful equations to quantify the value of parameter $\chi$ are empirical and not satisfactory for most soils. Based on the analysis of the equilibrium of the solid particles of a soil showing a bimodal structure and subject to certain suction, it was possible to establish an analytical expression for Bishop’s parameter $\chi$ . The resulting stress has been called equivalent stress (in contrast with effective stress) and can be used to predict the shear strength of unsaturated soils. The equivalent stress is written as a function of the net stress and suction and requires two parameters: the saturated fraction and the degree of saturation of the unsaturated fraction of the soil. This equivalent stress clarifies some features of the strength of unsaturated soils that up to now had no apparent explanation. However, the determination of its two parameters cannot be made from current experimental procedures. A method for the determination of these parameters and a comparison between experimental and theoretical results for the shear strength of unsaturated soils are presented in a companion paper.

Based on the study of the equilibrium of the particles of a soil showing a bimodal structure and subject to certain suction, it was possible to establish an analytical expression for the value of Bishop’s parameter $\chi$ (see the companion paper). This parameter can be written as a function of the saturated fraction and the degree of saturation of the unsaturated fraction of the soil. However, the determination of these last two parameters cannot be made from current experimental procedures. Therefore, a solid-porous model simulating the structure of the soil is proposed herein and used to determine these parameters. The data required for the solid-porous model are obtained from the grain and pore size distributions, void ratios, and secondary soil–water retention curves of the soil. The plots of the deviator stress versus equivalent stress shows a unique failure line for a series of tests performed at different confining net stresses and suctions, confirming that the proposed equivalent stress equation is adequate to predict the shear strength of unsaturated soils. It also results in different strengths for wetting and drying, as the experimental evidence suggests.

Immediate and long-term settlement checks are an integral part of foundation design. Therefore, reasonably accurate estimates of the immediate settlement of shallow foundations bearing on clay are necessary, particularly for highly plastic clays or organic soils, for which the immediate settlement may be significant. This immediate settlement is due entirely to the distortion of the clay underneath the shallow foundations because, in the short term, there is no opportunity for change in the clay volume. Since soil stress-strain response is nonlinear even at small strains, design procedures based on linear elasticity cannot accurately predict soil deformations. Hence, an immediate settlement analysis that takes soil nonlinearity into account is needed. In this paper, finite-element analysis is used to develop design charts that can be used to estimate the immediate settlement of axially loaded square, rectangular, and strip footings bearing on clay. The clay is modeled with a simple nonlinear constitutive relationship. A design example is included to illustrate how the proposed procedure can be readily applied in practice with the knowledge of the undrained shear strength and the initial shear modulus of the clay.

Simulation of a biaxial test by finite-element calculations may lead to unexpected localized deformations even for an elastic-perfect plastic Mohr–Coulomb model. The effects of localization lead to difficulties in computations. This paper describes a simple model for the strength development after occurrence of localization. The localization model describes the postfailure behavior assuming elastoplastic behavior inside the shear band and elastic behavior of the material outside the shear band. The resulting two nonlinear equilibrium equations are analyzed with a rigorous nonlinear scheme. The nonlinear equations show snap-through and snap-back behavior. Snap-back occurs due to energy release of unloading of the material outside the shear band. The simulations show that localization in shear bands is possible for orientations between the Roscoe and Mohr–Coulomb direction. Shear bands with orientations close to the Roscoe direction show a more gradual decrease of strength in comparison to bands with orientations close to the Coulomb direction. The flexibility of the shear band is shown to be important for postbifurcation behavior.