Continuum Consolidation Theory And Its Engineering Applications

Based on the continuum model of saturated soils and the axiomatization methods in classic continuum mechanics, a mathematical framework of continuum consolidation theory (CCT) taking into account of variable-mass effect during consolidation process is presented in this paper. The reasons of variable-mass effect in soils can be ascribed to seepage and source-sink. The former occurs more generally than the latter which met occasionally in pumping foundation pit. Within the framework of CCT, Truesdell rate-type constitutive relation is introduced into the geometrically-nonlinear consolidation analysis as well as simplified Jaumann stress rate-type and the other cases. The soil-water potential equation (SWPE) is discussed in CCT. A simplified saturated-unsaturated method and an equivalent source-sink method are proposed to deal with the free surface problem and pumping well-point problem respectively in the project of pumping foundation pit. Through the case studies of ID consolidation, 2D plane strain consolidation and coupling analysis of seepage and deformation in foundation pit, the engineering applications of CCT are discussed. The major work and achievement of this paper are as follows.Differential governing equations of CCT using Eulerian description such as continuity equation, conservation equation of momentum and conservation equation of angular momentum are derived based on representative element of volume (REV), continuum hypothesis and the presented notion of soils' configuration. CCT is briefly compared with Biot's consolidation theory (BCT) and theory of mixture, and can be deduced to BCT under given conditions.The governing equations with Total Lagrangian (T.L.) description are presented in both tensor form and matrix form. The more objective Truesdell stress rate has advantages over the generally used Jaumann stress rate, which can consider the deformation in neighboring domain and overcome the unreasonable shear oscillation phenomenon for Jaumann stress rate. The SWPE is found to reveal a coupling between seepage energy, equilibrium state and vertical displacement of soils.Using virtual work principle and Galerkin's weighted residual method, the incremental T.L. FEM equations for CCT are formulated based on various basic field variables. A vertical displacement selector matrix is put forward to make CCT conveniently reduce to the traditional case. A residual iteration method (RIM) with the new concept of unbalance vector for non-linear consolidation FEM equations are presented to get a more precise and efficient numerical solution.