Critical state plasticity. Part VII: Triggering a shear band in variably saturated porous media

In a previous paper (Part VI), the impact of spatially varying density on the localization of deformation of granular materials has been quantified using mesoscopic representations of stresses and deformation. In the present paper, we extend the formulation to unsaturated porous media and investigate the effect of spatially varying degree of saturation on triggering a shear band in granular materials. Variational formulations are presented for porous solids whose voids are filled with liquid and gas. Two critical state formulations are used to characterize the solid constitutive response: one developed for clay and another for sand. Stabilized low-order mixed finite elements are used to solve the fully coupled solid-deformation/fluid-flow problem. For the first time, we present the consistent derivative of the effective stress tensor with respect to capillary pressure considering full coupling of solid deformation with fluid flow, which is essential for achieving an optimal convergence rate of Newton iteration.