Constitutive relations for an isotropic poro-power-law fluid are proposed in which the effective viscosities in both shear and dilation have the same power-law dependence on the second invariant of the deviatoric stress alone, but the viscosity in dilation is 1/ν times the viscosity in shear. The shear rate is otherwise proportional to the deviatoric stress and the dilation rate to an effective mean stress. The behavior may either involve Darcy flow of a pore fluid whose viscosity is much less than that of the solid matrix, or involve dissolution, diffusive transport, and precipitation of a soluble phase, as in pressure-solution. Linearized relations for small additional rate-of-deformation and stress superposed on a basic-state flow are obtained. These are used to treat the deformation due to a shallow, narrow indentation at the interface between a layer and an adjacent medium when both undergo bulk uniform layer-parallel shortening or extension. If the layer, the medium, or both, are nonlinear fluids with large stress exponent, shear-band like structures, extending from the indentation, and 'reflecting' from any weak, slipping interface, occur in both the instantaneous velocity field and in the strain field. Since the materials considered have constant and uniform properties - e.g., they do not exhibit strain-softening - these features leave no imprint in the medium. They persist over mean strains of 10-20%, but are, like the indentation, ephemeral. It is hypothesized that localization due to an interfacial irregularity of this sort would produce bona fide shear bands if the material were strain-softening. The development of shear bands is enhanced if the adjacent medium has a large stress exponent, or if it is a poroviscous fluid with low resistance to dilation. In a poroviscous medium, dilation is concentrated in paired positive and negative lobes at the terminations of shear bands in the adjacent layer. The development of shear bands in a poroplastic layer is mildly suppressed, relative to that in an incompressible layer. Dilation is concentrated in paired loci at shear band terminations, with weaker, paired bands of positive and negative dilation on either side of the shear zone.
All Science Journal Classification (ASJC) codes
- Earth-Surface Processes