Reduction of peak ground velocity by nonlinear soil response – III: Excitation by an SV-wave pulse

Abstract

We study how the peak velocity of an SV-wave pulse on the ground surface of a two-dimensional soil valley is reduced by loss of wave energy during large nonlinear response inside the valley. This is a follow-up on our previous studies in which we considered excitation by an SH-pulse and a P-wave pulse. We consider in-plane response for incident angle below critical and assume that the soil material does not support tension, but the normal stress at a point in the soil can be compression. A point in the soil with zero stress behaves as stress-free, does not transmit normal stress and appears as a crack. We study the interplay of two opposing effects. The first effect is a jump in impedance from a higher value (in the half-space) to a lower value (in the valley), which amplifies the linear motions at the free surface of the valley. The second effect is the occurrence of nonlinear zones in the valley, which reduce the motion at the valley surface. We show how, for small excitations, when the response is linear or almost linear, the valley amplifies the motion. As the excitation amplitudes increase, at low frequencies, at which the nonlinearities are weak, the effect of decrease in impedance is stronger than the effect of nonlinear zones and the valley amplifies the motion. At higher frequencies, the effect of nonlinearity becomes stronger and the amplitudes of motion are reduced. As the excitation further increases, the effect of nonlinear soil response prevails at all frequencies and the motion is reduced significantly.