Reduction of peak ground velocity by nonlinear soil response–Ⅱ:excitation by a P-wave pulse

We study the reduction of peak velocity on the ground surface of a soil valley caused by loss of wave energy by large nonlinear strains and strain localization inside the valley,for excitation by a half-sine P-wave pulse.This study is a follow up to our previous study of out of plane response for excitation by an SH-pulse.In this paper,we consider the in-plane response,and assume that the soil material does not support tension,but the normal stress at a point in the soil can be compression(negative)or zero.A point in the soil with zero stress behaves as a stress-free point,it does not transmit normal stress and appears as a crack point.Because of this,along with the nonlinear response associated with compression and shear,the in-plane response in this study is more complex than that of the out-of-plane SH response.We study the interplay of two opposing effects:(i)jump in impedance from a higher value(half-space)to a lower value(valley),which amplifies the linear motions at the free surface of the valley,and(ii)the occurrence of nonlinear zones in the valley,which reduce the motion at the valley surface.