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.