Finite element modelling of two-component, solid-liquid mixtures

Abstract

<p>The scope of this thesis is to present a framework for the modelling of two-component, liquid/solid mixtures using the finite element method. The presentation is applicable to a wide range of two-component phenomena, however, special attention is paid to the liquefaction of sandy soils which is of particular concern to the civil engineer. In the past, much of the focus of research has been placed on the creation of models capable of capturing the mechanism of excess pore pressure development leading to liquefaction. Comparatively little attention has been placed on modelling the post-liquefaction event. This thesis provides a framework that allows the civil engineer to model soil deposits, predicting the onset of liquefaction and simulating the events that follow, namely post-liquefaction flow and the reconsolidation of the soil. The mixtures considered in this thesis are treated as two viscous fluids having momentum exchange between them via hydrodynamic drag. Two sets of Navier-Stokes equations are used to model the two-component mixture. The thesis presents the derivation of these equations along with the closure equations required to model the hydrodynamic drag and shear stress constitutive behaviour. A simple, novel approach to modelling the compaction/dilation behaviour of granular materials under the action of shear strain is also presented. It is shown that a recasting of the equations with anew set of variables is helpful in solving the equations via standard Galerkin finite element methods. An outgrowth of this recasting is also presented, that allows, for one-dimensional problems, to reduce the variable set from four unknowns to one, greatly simplifying the solution process and computation effort. Finally, several applications of the model are presented in order to validate the model and to demonstrate the wide range for which the model may be used.</p>