Finite Difference-Boundary Element Methods in Infinite and Semi-infinite Media in Geomechanics
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The engineering problems in Geomechanics and Geotechnical fields are commonly treated through the infinite or semi-infinite media. The best approach to solve these problems numerically is by coupling a finite element or a finite difference with boundary element numerical methods. Coupling the bounded domain modelled by Flac3D, a well-known program that implements an explicit finite difference method, with the boundary element method, which satisfies exactly the governing Partial Differential Equations (PDE) in the surrounding infinite or semi-infinite medium, combines the capabilities and the advantages of both methods. The Domain Decomposition Method (DDM) partitions the task of solving the PDE into separate computations over the coupled sub-domains. This method allows the FDM (Flac3D program) and the Boundary Element Method (BEM) program to work independently and interactively. In contrast, at the level of discretized equations, the coupling method requires building a complicated unified system of equations. Therefore, a Domain Decomposition Sequential Dirichlet-Neumann Iterative Coupling Method is developed in this thesis to couple both programs. The method is applied in four cases, 2D and 3D infinite and semi-infinite domains, using the appropriate fundamental solutions in the Boundary Integral Equation required for each case. After applying this method, the mechanical responses computed by Flac3D is corrected and the same responses far from the bounded domain are computed with less computer runtime (CPU) compared with the uncoupled Flac3D solution. The method is also verified by comparing the obtained numerical results with the corresponding analytical solutions. Two BEM pre and post processing intrinsic plug-ins are created, which provide access to the data of Flac3D, as well as the internal structure of the programming language embedded within Flac3D program. These intrinsics are 10 to 100 times faster to execute than the functions created using the Flac3D embedded language. Furthermore, the complementary part of the Kernels is derived based on Mindlin's fundamental solutions. These Kernels are required to compute the stress inside the 3D semi-infinite domain.
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Ziad Halabi (2013). Finite Difference-Boundary Element Methods in Infinite and Semi-infinite Media in Geomechanics. UWSpace. http://hdl.handle.net/10012/7353