| The mechanical behavior of porous media such as geomaterials is largely governed by the interactions of the solid skeleton (or grains) with the fluids existing in the pores. These interactions occur through the interfaces between bulk components. Traditional analysis procedures of porous media, based on the principle of effective stress and Darcy's law, commonly fail to account for these interactions. In this dissertation, a continuum theory of multiphase porous media is developed, capable of rigorously characterizing the interactions among bulk components. Central to the theory is the implementation of the dynamic compatibility conditions that microscopically represent the constraints on the pressure jumps through interfaces. It is shown that Terzaghi's effective stress and capillary pressure can be characterized within a common framework. Within this context, a theoretical framework for poroelastoplasticity is developed, allowing the hysteresis in capillary pressure and plastic deformation of skeleton to be simulated in a hierarchical way. It is found that the mixture theory-based models of porous media can be linked with Biot's poroelasticity theory. A linear model based on the proposed theory is developed and used to analyze the propagation of acoustic waves in unsaturated soils and favorable comparisons to experimental results are obtained. A finite element procedure is developed and implemented into a computer code (called U_DYSAC2) for elastoplastic static and dynamic analyses of saturated and unsaturated porous media. Numerical examples including wave propagation, two-phase flow, consolidation, and seismic behavior of an embankment are presented. These examples show the capability of the theory for modeling a wide variety of behaviors of porous media. |
