Meshfree vs. Mesh-based Numerical Methods in Hydro-Mechanically Coupled Analysis of Soils
Open AccessSoil is a multiphase material composed of solid particles, liquid and gas. In case of fully saturated soils, the deformation and stress analysis of soils subjected to external loading requires simultaneous satisfaction of balance of linear momentum, constitutive behavior of soil skeleton, and flow of water with respect to soil skeleton. Hence stress-deformation analysis of soils requires a hydro-mechanically coupled framework where interaction of pore fluid with soil skeleton is accounted for. A key ingredient of this framework for saturated soil is Terzaghi's effective stress principle which decomposes the total stress in soil to the effective stress carried by soil skeleton and pore water pressure. Explicit presence of pore pressure in the governing equations will lead to emergence of displacements and pore water pressure as two independent variables. In order to solve for these two independent variables the equilibrium and the continuity equations have to be solved simultaneously. The resulting partial differential equations are usually too complex to be solved in closed form. Hence, numerical methods such as finite difference method, finite element method, and meshfree technique are often used. In this thesis a detailed comparison of the mesh-based and meshfree analysis methods for analysis of stress and deformation in saturated soils is presented. The finite element method is selected as a mesh-based method which uses an element-based interpolation to represent distributions of displacements and pore water pressure within an element of the mesh. The meshfree method on the other hand is based on node-based interpolations which do not rely on a mesh. This has been shown to be advantageous for analysis of problems involving large deformations and fracture. Various analysis methods based on meshfree analysis have been proposed in literature. In this thesis the Local Radial Point Interpolation Method (LRPIM) is used. The method is fully developed and implemented for analysis of 1D and 2D consolidation problems. The results of the meshfree analyses are compared with those obtained from the finite element analysis and the available closed-form solution for 1D consolidation. The results show that the LRPIM method provides accurate solutions and it has a convergence rate close to the finite element method. However, the finite element method is shown to be superior in computational speed.
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ElGhoraiby_gwu_0075M_11224.pdf | 2018-01-16 | Open Access |
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