Dynamical effects during compaction band formation affecting their spatial periodicity

Compaction bands (CBs) are responsible for significant anisotropy alterations of permeability in geological materials; hence, understanding their formation conditions appears of key importance to all applications involving fluid extraction/injection from/into the ground. While most of the available models to understand CB formation are focused on interpreting the onset of a single CB, little effort has been so far dedicated to understand the documented periodicity of CBs. In this paper, the role of dynamical effects in inducing the post onset evolution of CBs is analyzed by means of a dedicated model for porous media with compressible constituents, with reference to a horizontal layer of sandy, water-saturated material. Elastic waves are generated as a first CB occurs due to sudden, localized volumetric collapse. If the waves are reflected at the interface with a softer material or with a previously formed CB, they produce significant local effective stress concentrations, which can promote the formation of further CBs in a cascade fashion, according to a regular geometric pattern. The spatial distribution of dynamically generated CBs, as well as the extent of the phenomenon, depends on the geometry of the domain and on the material's permeability. Sensitivity analysis is also performed to assess the key properties that promote dynamical CB in situ formation, identifying as the most influential conditions large stratum stiffness (increasing with depth) and the presence of softer layers. In contrast, the presence of less permeable and/or stiffer layers is not believed to play a major role in the proposed mechanism.