Investigation of mixed finite elements for analysis of geotechnical engineering problems

Mixed finite element methods have been studied for decades primarily in computational fluid dynamics and aerospace engineering. Relatively few researches have been conducted in applying mixed elements in geotechnical engineering problems. The purposes of this research are twofold: (1) mixed elements with discontinuous pressure approximation were used to analyze the incompressible or nearly incompressible materials, in general and several structural and geotechnical engineering problems in particular. (2) Mixed elements with continuous pressure approximation were used to analyze the soil-fluid coupled geotechnical engineering problems.;In addition, the commonly used two-dimensional heuristic approaches have been extended to three-dimensional case. In the first part, typical two- and three-dimensional mixed elements with discontinuous pressure approximation have been developed. Those elements combined with other elements were used to heuristically assess the performance based on the generalized heuristic approaches. Several structural and geotechnical engineering problems were numerically tested by those elements. Numerical results show that the newly developed and proposed mixed elements have superior performance than their irreducible counterparts.;In the second part, mixed element equations were formulated based on the well-known Biot's general consolidation theory. Both two- and three-dimensional mixed elements with continuous pressure approximation have been proposed and assessed using the general heuristic approaches. Numerical tests on plane strain, axisymmetric and three-dimensional geotechnical consolidation were then conducted. Most proposed elements perform well compared to the known solutions.;Finally, some byproducts such as general formulation of consistent nodal forces have been created during the studies and were attached in the appendices.