Numerical Simulation of Compaction Bands in High-Porosity Sedimentary Rock

Geologists have recently discerned naturally occurring discrete localized planar zones of deformation, associated with compaction of initially high-porosity rock. Compaction bands are characterized by significant porosity reduction and grain crushing, which may influence fluid transport, and stress and strain distribution in sedimentary formations. Thus, it is important to understand the conditions whereby compaction bands form and develop. A theoretical continuum approach of Issen and Rudnicki, associates an instability in the elastic constitutive relation with the emergence of planar compaction bands, perpendicular to the compressive principal stress. In order to gain insight into the formation mechanisms of the compaction bands under a variety of boundary conditions, we developed a discrete model, where the material is represented as a hexagonal lattice of springs that can transfer only normal forces (Central Force Spring model). In contrast to a continuum formulation the discrete lattice model allows for a statistical distribution of material properties (e.g., Young modulus, stress threshold etc). The occurrence of grain crushing and porosity reduction is represented by a change in the elastic properties of each element that exceeds a certain stress threshold. The emergence of compaction bands is simulated by the response to the redistribution of forces of the subsequent modified spring-network (with now altered elements) under the same tri-axial loading regime. Parametric analysis is conducted to explore the conditions under which compaction bands form and develop.