الفهرس 
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Abstract
The mechanical behaviors of fully saturated porous media under dynamic loads are governed by a set of nonlinear partial differential equations (NPDEs) with proper boundary conditions. Mostly, it is very difficult to obtain the exact solution of these equations. On the other hand, the solution of these NPDEs is always needed due to practical interests.
In this study, we have used an efficient technique to obtain semi-analytical solutions for the NPDEs which include the nonlinear terms for geometry and material; this technique is called ”Perturbation Method”. The convergence of the perturbation series is insured for weakly nonlinear cases. The soil layer is assumed to be homogenous and resting on a rigid and impervious layer.
Results have been presented in both analytical and graphical forms. For the one dimensional problem, three cases of solutions are introduced and listed as;
-the complete nonlinear case,
-the Z-approximation case which neglects the acceleration of the fluid,
and
-the quasi-static case which neglects both fluid and solid accelerations.
The effect of the frequency, the soil permeability, and the nonlinear terms on the pore pressure, stresses, and displacements of fluid and solid are discussed and shown in graphs. The analysis of quasi-static two dimensional problem is introduced. The effect of the Poisson’s ratio of the distribution of stresses and displacements are discussed and shown in graphs. All results show that, the