Plane shear waves under a periodic boundary disturbance in a saturated granular medium

摘要

We study an initial-boundary value problem for a fully nonlinear system which describes the propagation of plane shear waves in a three-dimensional soil, assuming a hypoplastic flow rule. This model was derived to study liquefaction of soils. For a periodic square-wave velocity disturbance on the boundary, the solution is found to saturate away from the boundary. We calculate the asymptotic state, in terms of the initial and boundary data. This formula exhibits fractal behavior as the shape of the square wave is varied. Our analysis is confirmed by numerical computations. (C) 1998 Elsevier Science B.V. [References: 13]