Finite Deformation and Fluid Flow in Unsaturated Soils with Random Heterogeneity

The first law of thermodynamics suggests an energy‐conjugate relationship among degree of saturation, suction stress, and density of an unsaturated porous material. Experimental evidence affirms that this constitutive relationship exists and that the water retention curves are dependent on the specific volume or density of the material. This constitutive feature must be incorporated into the mathematical formulation of boundary‐value problems involving finite deformation. We present a fully coupled hydromechanical formulation in the finite deformation range that incorporates the variation of degree of saturation with the Kirchhoff suction stress and the Jacobian determinant of the solid‐phase motion. A numerical simulation of solid deformation–fluid flow in unsaturated soil with randomly distributed density and degree of saturation demonstrates an intricate but well‐established coupling of the hydromechanical processes. As deformation localizes into a persistent shear band, we show that bifurcation of the hydromechanical response manifests itself not only in the form of a softening behavior but also through bifurcation of the state paths on the water‐retention surface.