Two-dimensional numerical modelling of wave propagation in soil media
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Wave propagation in soil media is encountered in many engineering applications. Given that the soil is unbounded, any numerical model of finite size must include absorbing boundary conditions implemented at the artificial boundaries of the domain to allow waves to radiate away to infinity. In this work, a finite element model is developed under plane strain conditions to simulate the effects of harmonic loading induced waves. The soil can be homogeneous or multi-layered where the soil properties are linear elastic. It may overlay rigid bedrock or half-space. It may also incorporate various discontinuities such as foundations, wave barriers, embankments, tunnels or any other structure. For the case of soil media over rigid bedrock, lateral wave radiation is ensured through the implementation of the consistent transmitting boundaries, using the Thin Layer Method (TLM), which allow replacing the two semi-infinite media, on the left and right of a central domain of interest, by equivalent nodal forces simulating their effect. Those are deduced from an eigenvalue problem formulated in the two semi-infinite lateral media. In the case of soil media over half-space, the Thin Layer Method is combined to the Paraxial Boundary Conditions to allow the incoming waves to radiate away to infinity laterally and in-depth. The performance of this coupled model is enhanced by incorporating a buffer layer between the soil medium and the underlain half-space. For extensive analyses, the eigenvalue problem related to the TLM may become computationally demanding, especially for soil media with multi-wavelength depths. As the TLM involves thin sub-layers, in comparison to the wavelength, the size of the eigenvalue problem increases with increasing depth. A modified version of the TLM is proposed in this work to reduce the computational effort of the related eigenvalue problem. This dissertation work led to the development of a Fortran computer code capable of simulating wave propagation in two-dimensional soil media models with either structured or unstructured triangular mesh grids. This latter option allows considering soil-structure problems with geometrical complexities, different soil layering configurations and various loading conditions. The pre- and post-processing as well as the analysis stages are all user friendly and easy.