Visco‐poroelastic damage model for brittle‐ductile failure of porous rocks

Abstract

AbstractThe coupling between damage accumulation, dilation, and compaction during loading of sandstones is responsible for different structural features such as localized deformation bands and homogeneous inelastic deformation. We distinguish and quantify the role of each deformation mechanism using new mathematical model and its numerical implementation. Formulation includes three different deformation regimes: (I) quasi‐elastic deformation characterized by material strengthening and compaction; (II) cataclastic flow characterized by damage increase and compaction; and (III) brittle failure characterized by damage increase, dilation, and shear localization. Using a three‐dimensional numerical model, we simulate the deformation behavior of cylindrical porous Berea sandstone samples under different confining pressures. The obtained stress, strain, porosity changes and macroscopic deformation features well reproduce the laboratory results. The model predicts different rock behavior as a function of confining pressures. The quasi‐elastic and brittle regimes associated with formation of shear and/or dilatant bands occur at low effective pressures. The model also successfully reproduces cataclastic flow and homogeneous compaction under high pressures. Complex behavior with overlap of common features of all regimes is simulated under intermediate pressures, resulting with localized compaction or shear enhanced compaction bands. Numerical results elucidate three steps in the formation of compaction bands: (1) dilation and subsequent shear localization, (2) formation of shear enhanced compaction band, and (3) formation of pure compaction band.