Revisit of Poroelastic Half Space Subjected to Cylindrical Vertical Load
Date Issued
2012
Date
2012
Author(s)
Shen, Shih-Hung
Abstract
The major goal of this thesis is to discuss the inverse transform parts by a classic case : the response of poroelastic half space subject to circular vertical load under the cylindrical coordinate system. By using the different simplification of procedures and inverse transform method to discuss the advantage and fault. The basic theory of this thesis is based on a series theory about three-dimensional consolidation which had developed by Biot, M.A. since 1941. The objective is to solve more accurate then use the original linear elasticity theory to analysis the common civil engineering problem – the columns acting on a solid ground surface.
First of all, we introduce the theory of Biot, M.A. developed at 1941, “General theory of three-dimensional consolidation.”, and the series research about displacement potential for porous elastic media which developed by other scholar earlier of after few years, for example, the Papkovitch-Neuber potential(1925), the McNamee-Gibson displacement potential(1960), the Verruijt displacement potential(1971) and Schiffman-Fungaroil potential(1971).
Second, we analysis a classic consolidation case: The poroelastic half space subject to circular vertical load. The elasticity solid and pore liquid is assumed to be incompressible, and the ground surface considers two cases, permeable or impermeable. In this part the main method we used are Laplace transform and Hankel transform, the transforms parameters are time and space respectively. We can solve the displacement and pore pressure field by integral equations.
Third part we discuss the inverse transforms by Complex variable theory and numerical method. For inverse Hankel transform, we discussion and choose an integral path which avoid the pole, branch point and branch cut by using the Change of variables. The double-Hankel function shows very good convergence through new integral path. So that, we can direct use the Gauss quadrature trough new integral path to solve the inverse Hankel transform. For inverse Laplace transform, we discussion three different numerical method and analysis the their integral path: Durbin method, Talbot method and use complex variable theory to separate the integrand into the contribution of pole and branch point and branch cut and transform the integrand into the steepest descent type. Finally, we use Durbin method as the main numerical method of this thesis to analysis the problem.
Subjects
Poroelastic
Potential function
Complex variable theory
Type
thesis
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