Assistant Professor, Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran.
To evaluate the earth seismic response due to earthquake effects, ground response analyses are used to predict ground surface motions for development of design response spectra, to compute dynamic stresses and strains for evaluation of liquefaction hazards, and to determine the earthquake induced forces that can lead to instability of earth and earth-retaining structures. Most of the analytical solutions presented are affected by the defect that the stress-strain relationship must be of rather simple form (linear elastic, with perhaps linear hysteretic damping), and that the soil properties must be homogeneous. Real soils are often composed of several layers of variable properties, and often they exhibit non linear properties. Therefore, a numerical solution may be considered, because this can more easily be generalized to non-linear and non-homogeneous properties. In this paper, a simple numerical solution method is presented, again with damping property. The considerations will be restricted to one-dimensional wave propagation in a linear elastic layer which the equation of motion will be resolved with weighted residual method and the advantages of using this method will be ultimately discussed. Of course, the most important benefit of this element free approach is having a suitable approximated function for wave displacement in height of a soil layer.