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A finite-difference based continuum numerical model is developed for the pile-soil dynamic response during pile driving. The model is capable of simulating the wave propagation analysis along the pile shaft and through the soil media. The pile-soil media, loading and boundary conditions are such that axisymmetric assumption seems to be an optimized choice to substantially reduce the analysis time and effort. The hydrostatic effect of water is also considered on the effective stresses throughout the soil media and at the pilesoil interface. The developed model is used for signal matching analysis of a well-documented driven pile. The results showed very good agreement with field measurements. It is found that the effect of radiation damping significantly changes the pile-soil stiffness due to the hammer blow. The pile tip response shows substantial increase in soil stiffness below and around the pile tip due to driving efforts.

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This paper presents time domain fundamental solutions for the extended Biot's dynamic formulations of two-dimensional (2D) unsaturated poroelasticity. Unsaturated porous media is considered as a porous media in which the voids are saturated with two immiscible fluids, i.e. liquid and gas. At first, the corresponding explicit Laplace transform domain fundamental solution is obtained in terms of skeleton displacements, as well as liquid and gas pressures. Subsequently, the closed-form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Finally, a set of numerical results are presented which verifies the accuracy of the analytically inversed transient fundamental solution and demonstrates some salient features of the elastic waves in unsaturated media..

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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.

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It is well-known that dam-reservoir interaction has significant effects on the response of dams to the earthquakes. This phenomenon should be considered more exactly in the seismic design of dams with a rational and reliable dynamic analysis method. In this research, seismic analysis of the dam-reservoir is studied as a wave propagation problem by using Legendre Spectral element method (SEM). The special FEM and SEM codes are developed to carry out the seismic analysis of the dam-reservoir interaction system. The results of both SEM and FEM models are compared considering the accuracy and the time consumption of the analysis. Attractive spectral convergence of SEM is obtained either by increasing the degree of the polynomials in the reservoir or by the number of elements of dam. It is shown that all boundary conditions of the reservoir domain in the SEM are evaluated by the exact diagonal matrices. The SEM leads to the diagonal mass matrix for both dam and reservoir domains. The stiffness matrices obtained from the SEM are more sparse than the corresponding stiffness matrices in the FEM consequently the SEM needs a significant less time consumption of the analysis.