A Bounding Surface Viscoplasticity Model for Time dependent Behaviour of Saturated and Unsaturated Soils including Tertiary Creep

Abstract

A bounding surface viscoplasticity constitutive model is developed for describing the time-dependent stress-strain behaviour of fully saturated and unsaturated soils. The proposed model is formulated within the context of bounding surface plasticity using the consistency viscoplastic framework and the critical state theory. The model provides a continuous transition from rate-independent plasticity to rate-dependent viscoplasticity. The hardening parameter representing the size of the bounding surface is defined as a function of the viscoplastic volumetric strain and the viscoplastic strain rate. For unsaturated soils, the effect of suction is included as another parameter controlling the size of the bounding surface. The suction hardening effect is described using the coupled influence approach where suction has a multiplicative effect to the viscoplastic volumetric hardening. A non-associated flow rule is defined to generalize application of the model to a wide range of soils. The capability of the model to capture drained and undrained tertiary creep is particularly emphasized. The model requires minimal material parameters determined using standard laboratory testing equipment. A fully coupled flow-deformation model is then presented for describing time-dependent behaviour of variably saturated soils. The proposed model is formulated based on the theory of multiphase mixtures using the effective stress approach. The governing equations for the flow model are derived using the equilibrium equations and the conservation equations of mass and momentum. The constitutive relations of the solid skeleton are described using the bounding surface viscoplasticity model in order to capture the time-dependent behaviour of geomaterials. The essential elements of the model are validated by comparing the numerical results with the experimental data from the literature. The application of the model to predict the time-dependent behaviour of fully saturated and unsaturated soils is demonstrated for creep tests, constant strain rate tests and unloading-reloading relaxation tests subject to different geometric, loading, and drainage boundary conditions. Special attention is paid to the capability of the proposed model in capturing the tertiary creep and creep rupture. It is demonstrated that the model is able to capture drained creep rupture in over-consolidated clays which is the primary mode of failure in marginally stable over-consolidated soil slopes.