Numerical and constitutive modelling of monotonic and cyclic loading in variably saturated soils

摘要

A fully coupled, effective stress based elasto-plastic model is presented for a rigorous analysis of flow and deformation in variably saturated porous media subjected to monotonic and cyclic loading. The governing equations are derived based on the effective stress concept, equations of equilibrium, and conservation equations of mass and momentum using a systematic macroscopic approach. Both elastic and elasto-plastic constitutive equations are developed. All model coefficients are identified in terms of measurable parameters. The governing equations presented are general in nature, embodying all previously presented formulations in the field. A unified bounding surface plasticity model is developed to describe the stress-strain behaviour of variably saturated soils subjected to monotonic and cyclic loading. The model is formulated incrementally within the critical state framework using the effective stress approach. The model takes into account the effects of both plastic volumetric strain and matric suction on the hardening of the bounding surface. Cyclic behaviour is captured through a new mapping rule in which the point of stress reversal is taken as the centre of projection. The effect of particle crushing at high stresses is considered through a three-segmented critical state and isotropic compression lines. A non-associative flow rule is employed to generalise application of the model to all soils. Solution to the governing equations is obtained numerically using the finite element approach, with the finite difference method employed for the time integration of the rate equations. The elasto-plastic constitutive equations are integrated explicitly using Euler’s forward and the modified Euler integration schemes. Yield surface correction schemes are adopted to improve accuracy of the solution. Essential elements of the proposed model are validated by comparing numerical predictions with experimental data from the literature for fully and partially saturated soils subjected to monotonic and cyclic loadings in drained, undrained, isotropic and deviatoric conditions. The results demonstrate capability of the coupled model to predict essential characteristics of variably saturated soils subjected to monotonic and cyclic loadings in a unified manner.