Finite element formulation of one-dimensional uncoupled and coupled consolidation

Abstract

This thesis presents the formulation of finite element method for one-dimensional consolidation problem based on uncoupled and coupled consolidation theories. The consolidation of cohesive soils as a result of dissipation of the excess pore pressures generated by external loading is a problem of considerable concern amongst geotechnical engineers. Theories of consolidation fall into two main categories which are uncoupled and coupled theories. The uncoupled theory only considers the interaction of the pore fluid with the porous media ensuring the continuity equation of the pore fluid whereas the coupled theory is formulated on the basis of solid-fluid interaction which is more realistic but is more difficult to solve. In this study, both theories are solved using finite element method using the formulation of Galerkin weighted residual method and variational approach. The derived formulation is used to develop a computer program for uncoupled and coupled analysis. This was written using the MATLAB® programming code. The proposed finite element code was firstly verified and results were comparable with Terzaghi consolidation theory in both cases. For the case one-dimensional problem of homogenous soil, the numerical results showed very good agreement between the uncoupled and coupled consolidation analyses with difference less than 5%. The criteria for selecting preferable method were based on several factors such as accuracy and stability. From the result, the relative discrepancy for the uncoupled theory is not much significant compared to the coupled theory by giving less than 10% value of difference. Consequently, the uncoupled 1-D consolidation theory was adopted for the subsequent analysis for a layer and multi-layered soil. A case study of multi-layered consolidation problem was compared and the results demonstrated that the layered characteristics of soils have significant influences on the overall consolidation settlement performance.