Stability of a frictional material layer resting on a viscous half-space

Abstract

a geological two-layer system composed of a frictional material layer of finite thickness, called the overburden, resting on a viscous half-space of lower density is investigated. The salient features of this study are a realistic description of the stiffness of the overburden and its state of (in situ) prestress. and the use of the viscosity of the substratum to define a characteristic time for the stability analysis. A general variational formulation for the linearized, non-selfadjoint stability problem is presented, followed by asymptotic analyses for the cases of large and small perturbation wavelengths and by an analytical solution in the absence of gravity. Results obtained by a finite-element method are compared with the analytical and asymptotic predictions; they permit the detection of various modes of instability: interface and beam-type modes in the compressive range of deformation, and neck-type modes in the tensile range. It is found that the system's stability is not only governed by geometry and density contrast, as expected from the conclusions of earlier studies on viscous and viscoelastic models, but is also sensitive to the state of in situ stress. A complete parametric study reveals that the overburden material cohesion and workhardening properties have more influence on stability than the friction angle. Furthermore, it is found that critical stresses at neutral stability predicted by deformation theory, which is an appropriate model for studying the initiation of faulting in rocks, are smaller in magnitude than those obtained by the corresponding How theory with a smooth yield surface. Implications of this work for the interpretation of various laboratory analogue model experiments pertaining to geological two-layer systems are also discussed.