A Refined Theory of the Layered Medium with the Slip at the Interface

Abstract

The equations for layered medium with slippage are obtained using the asymptotic method of homogenisation. The terms of second order respectively the small parameter of layer thickness are taken into account. The linear slip condition defines the dependence between the tangential jumps of displacements at the contact boundary and the shear stresses. The derived equations introduce asymptotically complete generalization of some models of layered media, which are based on the engineering approach or approximate hypotheses about the nature of the inter-layer deformation. Such generalized models are needed in the study of static and dynamic deformations of layered rock media. The wave properties of the resulting system of equations and dispersion relations for harmonic waves are described. The propagation of Rayleigh surface waves along the elastic layered half-plane boundary is investigated.