Response of the non-homogeneous saturated foundation to incident plane P-SV waves

Based on Biot's model for saturated porous media,the dynamic responses of non-homogeneous saturated soil was studied by using Helmholtz vector decomposition principle and exact dynamic stiffness method (EDSM) when P-SV wave was incident from bedrock.Reflection and transmission of incident plane P-SV wave in non-homogeneous saturated soil were analyzed considering the continuous variation of physical and mechanical properties about saturated foundation along the thickness direction.As a consequence,the general calculation formulas about the reflection coefficient and transmission coefficient of bedrock and free-field on the both surfaces were given.As numerical examples,assuming that the material properties of the saturated foundation had an exponential law distribution and gradient variation along the thickness-coordinate,the dynamic response of non-homogeneous saturated soil and free-field to incident plane SV was discussed.The numerical results indicate that the ratio of ground displacement to bedrock displacement decreases with the increase of the thickness and heterogeneity index of saturated soil,incident angle and frequency of seismic wave.The vertical displacement ratio decreases more significantly than the horizontal one.The dissipation of seismic wave caused by the thickness of soil layer is obvious,which all should be taken into account in engineering practice especially on complex layered situations.