Strain localization in a solid-water-air system with random heterogeneity via stabilized mixed finite elements

Unsaturated soils are solid-water-air systems that include a solid skeleton, pore water, and pore air. Heterogeneities in porosity or degree of saturation are salient features of unsaturated soils. These heterogeneities may trigger localized deformation (eg, shear banding) in such materials as demonstrated by numerical simulations via a pseudo three-phase model. In this article, we formulate a true three-phase mathematical framework implemented via stabilized low-order mixed finite elements. With this mathematical framework, we study the evolution of pore air pressure and its role in the inception of strain localization triggered by initial heterogeneity either in porosity or suction. The numerical simulations show that pore air pressure is nonzero and nonuniform in the process of progressive failure in unsaturated soils. The heterogeneity of pore air pressure may also play a significant role in the onset of localized deformation of unsaturated soils. Therefore, a three-phase model considering the pore air phase is physically more appropriate for modeling strain localization in unsaturated soils.