Shear-induced porosity bands in a compacting porous medium with damage rheology

Abstract

Shear-induced porosity bands have been observed experimentally and have been the subject of a number of theoretical and numerical analyses in which a number of rheological laws governing the partial melt system have been proposed. These bands have been suggested to be important in Earth’s interior in focussing melt to Earth’s mid-ocean ridges, in reducing the effective viscosity of the asthenosphere, and in affecting seismic and electrical properties. Recently, a linear analysis of the formation of melt bands has been presented in which the viscosity of the solid matrix depends on the grain size and a parameter characterizing the roughness of the grain-liquid interface For some parameter values, this “damage” rheology mimics the effect of very strongly strain-rate dependent viscosity which can produce low angle bands, similar to those seen in experiments. In the present paper, I show full nonlinear simulations of melt bands with damage rheology. In agreement with the linear analysis, low angle bands are possible when the grain size and grain roughness evolve rapidly compared with the deformation of the sample. The grain size field evolves to form bands where grain-size anticorrelates with porosity. The effective viscosity and electrical conductivity of bands are also investigated. For low angle bands, the effective viscosity relative to the mean viscosity decreases and the electrical conductivity anisotropy increases with strain, indicating significant strain and electrical conduction localization.