Weakly Nonlinear Deformation of a Thin Poroelastic Layer With a Free Surface

Abstract

Using the biphasic theory of Biot (1941), we examine the evolution of deformations of a poroelastic layer, secured at its base to a rigid plane and having a stress-free, impermeable upper surface. By identifying a limit in which the layer is very thin but the wavelength of disturbances is very long, we show how nonlinear effects due to the finite slope of the free surface cause local elevations of the free surface to decay more slowly than depressions.