Mixed Hardening Models for Frictional Soils

Abstract

A new material model mainly for frictional soil is developed and implemented in a finite element program. The model is applied to simulate a deep excavation with a supporting tie back wall.

The model is based on elastoplasticity and is expressed in terms of effective stresses. A combined kinematic and isotropic hardening rule is applied in order to model a stiff small strain response and describe the permanent strains developing during repeated unloading and reloading. This involves the introduction of a small elastic region bounded by an inner, conical yield surface which is the elastic small strain limit. The inner yield surface may move inside an outer, bounding failure surface defined by a Lade criterion (Lade 1977). If some isotropic hardening is selected, the inner surface expands while it translates deviatorically under kinematic hardening. Nonassociated plastic flow is assumed with a description of plastic volumetric strains developed by extending Rowe’s dilatancy concept (Rowe 1971). A special feature is the new formulation for dilatancy upon reversed loading. No rate effects are included in the model. The model is called Mobilized Friction Mixed Hardening (MFMH) model, since friction hardening is an important feature of the model.

Soil behaviour under small strains and during cyclic loading as observed in laboratory experiments is given special attention in this thesis. A summary of selected results from tests focusing on small strain and cyclic loading is given as a basis for the development of the model.

The soil model describes the behaviour of the soil skeleton and can therefore be used both for drained and undrained conditions. For undrained conditions the effect of trapped and almost incompressible water can be introduced by restricting the volume change. It is observed that the dilatancy will have a considerable effect on both stiffness and strength for undrained conditions. In repeated and cyclic loading the accumulation of pore pressure is simulated reasonably well by the proposed model, which appears to also have the potential for simulating liquefaction.

Significant effort has been put into developing a robust and efficient numerical algorithm for integrating the constitutive equations. A fully implicit Euler formulation of the constitutive rate equations, solved by a Newton-Raphson iteration scheme is used for this purpose. The derivatives of the Lade surface at elastic trial stress states revealed special difficulties that finally were solved.

The model is tested on the stress strain level by simulating various triaxial tests assuming homogeneous stress and strain distribution within the sample. The model is further implemented in the finite element program PLAXIS and applied as a user defined soil model.

A deep excavation in Berlin sand has been simulated by the user defined MFMH-1 and MFMH-3 soil models, and the results have been compared to those obtained by using the internal Hardening Soil model in PLAXIS. The results show less heave in the bottom of the excavation by the MFMH models and a stiffer remote region.