Surface instability due to initial compressive stress

Abstract

Abstract Utilizing a linearized theory of isotropic, homogeneous elasticity that includes the effects of initial stress, it is demonstrated that Rayleigh and Love surface instabilities occur when the compressive stress reaches appropriate critical values. The Rayleigh surface instability exists for a half-space, as well as for a finite slab, and the critical stress value depends only on Poisson's ratio. The Love surface instability exists for a layer and a substratum, and the critical stress value depends on two parameters: the ratio of the shear moduli and a nondimensional number related to the geometry of the layer. It is suggested that these two instabilities may offer possible, although highly idealized, mechanisms for earthquake initiation and prehistoric land-mass formations such as mountain chains.