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In this paper, an advanced formulation of time-domain, two-dimensional Boundary Element Method (BEM) with material damping is presented. Full space two-dimensional visco-elastodynamic time-convoluted kernels are proposed in order to incorporate proportional damping. This approach is applied to carry out site response analysis of viscoelastic topographic structures subjected to SV and P incident waves. Seismic responses of horizontally layered site, semi-circular canyons, slope topography and ridge sections subjected to these incident waves are analyzed in order to demonstrate the accuracy of the kernels and the applicability of the presented viscoelastic boundary element algorithm. The results show an excellent agreement with recent published results obtained in frequency domain. Also, the effects of different material damping ratios on site response are investigated.

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In this paper, an advanced formulation of the spectral finite element method (SFEM) is presented and applied in order to carry out site response analysis of 2D topographic structures subjected to vertically propagating incident in-plane waves in time-domain. The accuracy, efficiency and applicability of the formulation are demonstrated by solving some wave scattering examples. A numerical parametric study has been carried out to study the seismic response of rectangular alluvial valleys subjected to vertically propagating incident SV waves. It is shown that the amplification pattern of the valley and its frequency characteristics depend strongly on its shape ratio. The natural frequency of the rectangular alluvial valley decreases as the shape ratio of the valley decreases. The maximum amplification ratio along the ground surface occurs at the center of the valley. A simple formula has been proposed for making initial estimation of the natural period of the valley in site effect microzonation studies.