Influence of the intermediate principal stress on the strain localization mode in porous sandstone

Compaction bands and dilation bands are zones of either pure compaction or pure dilation, characterized by decreased or increased porosity, respectively. In contrast with commonly observed shear bands, there are relatively few reports of compaction bands or dilation bands, particularly in field settings. This work explores one possible explanation for these isolated observations: unique stress conditions, which occur infrequently, are required to form these bands. In particular, the influence of the intermediate principal stress on localization conditions is examined. Theoretical results, using a bifurcation approach to localization, reveal that conditions for compaction band formation are least restrictive when the intermediate principal stress is equal to the minimum compressive stress, while dilation band conditions are least restrictive when the intermediate principal stress is equal to the maximum compressive stress. However, the occurrence of one of these favorable stress states does not guarantee formation of one of these deformation modes, since certain conditions on the inelastic material parameters (i.e., friction factor and dilation coefficient) must also be satisfied. These material parameters vary with mean stress; thus satisfaction of compaction band or dilation band conditions requires not only a specific relationship between the principal stresses but also a loading path resulting in a favorable mean stress, such that inelastic material parameters fall in the required range. In a laboratory environment, where principal stresses are controllable, these conditions should be readily achievable. However, if these specialized stress conditions are uncommon in field settings, theory suggests that compaction bands and dilation bands may form infrequently.