STABILITY OF A FRICTIONAL MATERIAL LAYER RESTING ON A VISCOUS HALF-SPACE

THE STABILITY OF a geological two-layer system composed of a frictiona l material layer of finite thickness. called the overburden, resting o n a viscous half-space of lower density is investigated. The salient f eatures of this study are a realistic description of the stiffness of the overburden and its state of (in situ) prestress, and the use of th e viscosity of the substratum to define a characteristic time for the stability analysis. A general variational formulation for the lineariz ed, non-selfadjoint stability problem is presented, followed by asympt otic analyses for the cases of large and small perturbation wavelength s and by an analytical solution in the absence of gravity. Results obt ained 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 models in the compressive range o f deformation, and neck-type modes in the tensile range. It is found t hat the system's stability is not only governed be geometry and densit y contrast, as expected from the conclusions of earlier studies on vis cous 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 work-hardening properties have more influence on stability than the friction angle. Furthermore, it is found that crit ical stresses at neutral stability predicted by deformation theory, wh ich is an appropriate model for studying the initiation of faulting in rocks, are smaller in magnitude than those obtained by the correspond ing flow theory with a smooth yield surface. Implications of this work for the interpretation of various laboratory analogue model experimen ts pertaining to geological two-layer systems are also discussed.