Strain localization in unsaturated porous media [electronic resource]
Keywords: Civil and Environmental Engineering.

Motivated by new imaging techniques for quantifying density and the degree of saturation in geomaterials at a scale smaller than the specimen, the research presented in this dissertation formulated and implemented two mathematical frameworks for coupled solid deformation/fluid diffusion in unsaturated porous media. One framework is based on infinitesimal strain and another on finite strain theory. Based on these two mathematical formulations, I conducted meso-scale finite element modeling of strain localization in unsaturated porous media. The strain localization was triggered by heterogeneous density and degree of fluid saturation, which were quantified either deterministically or stochastically. These numerical investigations demonstrate that the material heterogeneity could initiate strain localization in saturated and unsaturated porous materials. Strain localization is a ubiquitous feature of granular materials undergoing nonhomogeneous deformation. In soils and rock, the zone of localized deformation is generally referred to as a shear band, a fault, a rupture zone, or simply a failure plane. The numerical study of strain localization in geomaterials plays a crucial role in our understanding of the fundamental mechanism of progressive and catastrophic failures of geomaterials in nature and industrial practice, for example, landslides, avalanches, and borehole instability. In the past, arbitrary imperfection in the form of weak elements was used in finite element simulations to trigger strain localization, because imaging techniques were not sophisticated enough to quantify actual specimen imperfections. However, current testing techniques allow nondestructive and non-invasive measurement of density and the degree of saturation at meso-scale, a scale larger than the grain scale but smaller than the specimen scale, through high-resolution imaging. Therefore, this dissertation focused on meso-scale finite element simulation of the strain localization in unsaturated porous material triggered by inherent material heterogeneities, such as density and degree of saturation. I conducted meso-scale finite element simulations of a dry sand specimen with experimentally determined heterogeneous density under the plane strain condition. The combined experimental imaging and finite element modeling demonstrates that the spatial density variation is a determining factor in the development of a persistent shear band in a symmetrically loaded sand body. Density is characteristic of the state of the solid phase, whereas degree of saturation is a fluid state variable; interaction between these two sources of material imperfection requires a fully coupled hydro-mechanical formulation. Accordingly, I have developed a mathematical framework based on infinitesimal strain theory for partially saturated soils. In this framework, two advanced elasto-plastic models were cast to capture the solid constitutive response, one for clay and another for sand. For both models, the pre-consolidation pressure is a function of the so-called bonding variable as a product of two factors: the degree of saturation of the air and a function of suction. The meso-scale finite element simulation based on this framework is the first such procedure developed to trigger a shear band in soils with two types of heterogeneity, namely, density and degree of saturation. These numerical simulations demonstrate that both heterogeneities have first-order effects on the triggering of a shear band in unsaturated soils. To consider geometric nonlinearity of the solid matrix, I developed another mathematical framework for coupled solid-deformation/fluid-diffusion in unsaturated porous material. This framework relies on the continuum principle of thermodynamics to identify an effective stress for the solid matrix as well as an experimentally consistent water retention law that characterizes the interdependence of the degree of saturation, suction, and porosity of the porous material. To model the deformation of the solid matrix, I then extended the three-invariant elasto-plastic constitutive model for unsaturated sand to the finite deformation regime. This new study considers stochastically determined heterogeneities in density and the degree of saturation as triggers of localized deformation in porous media. The specific problem simulated by this framework shows that bifurcation manifests itself not only through a localized deformation pattern, but also through the hydromechanical movement of the field variables on the water retention surface.