Finite element method and constitutive modelling and computation for unsaturated soils

Abstract

This paper presents a numerical model for the finite element analysis of transient deformation and seepage problems in unsaturated soils. A definition of the generalized effective stress for unsaturated soils is introduced and its rational formula is derived on the basis of the classical definition of the effective stress for saturated soils by Terzaghi and the two stress variables formula accepted for unsaturated soils. The governing equations for unsaturated soils modelled as deforming porous media with immiscible porous water and air are re-formulated.. The passive air assumption is then introduced to result in a simplified form of the governing equations for unsaturated soils. The finite element method is applied to discretize the governing equations in space. The Alonso constitutive model to simulate the non-linear mechanical behaviour of unsaturated soils is integrated into the present numerical model. With introduction of the natural coordinate system in the stress space a backward-Euler integration algorithm and a consistent elastoplastic tangent modulus matrix for the non-smooth multisurface pressure dependent plasticity are derived for the model. Numerical results are illustrated to demonstrate the capability and performance of the present model.