STABILITY OF A FRICTIONAL, COHESIVE LAYER ON A VISCOUS SUBSTRATUM - VARIATIONAL FORMULATION AND ASYMPTOTIC SOLUTION

This contribution is concerned with the stability of a frictional, coh esive material layer, called the overburden, resting on a viscous, inc ompressible layer of lower density referred to as the substratum. The viscous layer is either perfectly bonded or free to slip with no frict ion on a rigid basement. The in situ stress is assigned a realistic gr adient in the overburden and is assumed to be purely hydrostatic in th e substratum. A general variational formulation of the linearized stab ility problem for the stratified system is obtained in which the visco us response of the substratum provides the characteristic;time, To a g iven state of stress and perturbation corresponds a rate of growth or decay which is calculated by an asymptotic method for small overburden thickness compared to the perturbation wavelength. It is found that t he substratum's thickness influences the rate of growth of the instabi lity if its product by the perturbation wavenumber is smaller than 3 o r 4, depending on the type of boundary condition at the basement. Howe ver, these conditions and the substratum thickness have no influence o n neutral stability. Furthermore, the conditions for stability depend on the tectonic stress distribution in the overburden and not solely o n the density contrast, as is the case for viscoelastic systems. It is also shown that the classical flow theory of plasticity adopted for t he overburden, which successfully captures the onset of folding, fails to predict initiation of faulting for similar stress conditions.