Motions of gently sloping ground during earthquakes

Abstract

During past earthquakes, gently sloping ground surfaces have been observed to shift laterally over areas as large as a few square kilometers. These permanent downward motions have been attributed to temporary and partial reductions in shear strength of soil deposits (e.g., liquefaction), static gravity forces, and transient earthquake shakings. These motions, the amplitudes of which remain challenging to predict, have been frequently modeled using Newmark sliding blocks for ground that is statically stable and occasionally partially or completely loses its shear strength during earthquakes. This paper investigates in more details the deformations of gently sloping ground that becomes temporarily unstable under the combined effects of gravitational forces and earthquake shakings. Using a physical model, we propose two definitions of earthquake contributions to the displacement of gently sloping ground, which may include or not the effects of initial velocity. In both cases, Monte Carlo simulations reveal that motions of gently sloping ground are influenced by pulses of earthquake ground velocity for a wide range of reduction in soil shear strength, even for very severe loss of shear strength. For practical purposes, when large soil deposits become unstable during earthquakes, the analysis concludes that the motions of gently sloping ground are likely influenced by earthquake ground velocity.