Finite Element Formulation and Algorithms for an Unsaturated Soil Model in Stress-saturation Space: Theory and implementation

This paper presents a complete finite element solution for an unsaturated soil model in stress-saturation space [1, 2]. Generalised constitutive equations for stress update are derived. Suction or pore water pressure in the soil model is treated as a strain variable, and the degree of saturation is treated as a stress variable. In the stress update, the change of degree of saturation is dependent on the suction and volume change instead of only suction and the scanning process of water retention curve between main drying and wetting curves is considered. An explicit integration scheme is adopted to integrate the constitutive equations. At the system level, the global solution of the finite element method is developed based on the governing equation considering the influence of deformation on the degree of saturation as well. The finite element implementation is then validated against Terzaghi’s analytical consolidation solution for the saturated condition, and experimental results of a loading-collapse test on Pearl clay. Several one-dimensional consolidation and infiltration scenarios for different soils (hypothesis sand and silty clay) due to various mechanical and hydraulic loads are analysed by using the developed finite element codes, including a fast loading with a pore pressure dissipation process after slow drying, and a slow drying-loading-wetting circle. The results show that the numerical implementation gives better prediction on the chance of the degree of saturation of soils with constant suction, and well predicts consolidation behaviours with unsaturated soils, such as displacement induced by soil expands or collapses upon wetting.