Multi-scale study of permeability evolution of a bentonite clay owing to pollutant transport: Part I. Model derivation

This work deals with the modelling of permeability evolution of compacted natural bentonite clay owing to pollutant migration. The Homogenization of Periodic Media approach employed to derive the permeability tensor fully acknowledges the heterogeneous and multiscale microstructure of clay, as well as structural and textural changes induced by fixation of a metallic cation. In complementarity with existing experimental investigations of clay/metallic interaction, structural modifications that range from the nanometer scale to the micrometer scale have been accounted for and special attention is given to inter-aggregate porosity development. Consequently, three levels of description are considered: the microscopic level of clay particles, the mesoscopic level of clay aggregates, mineral grains and inter-aggregate porosity, and the macroscopic level of the sample subjected to permeability tests in the laboratory. Several cases are distinguished as inter-aggregate pores are not present within the compacted material before contaminant migration, while during macropores opening, inter-aggregate pores may form a connected flow path or remain occluded. For all three cases considered, starting from the local description of fluid flow, the expression of the effective permeability tensor is derived. The local problems to solve within the unit cells to obtain the macroscopic permeability are solved using the Finite Element Method. Numerical computations have allowed us to investigate the influence of several microstructural parameters, such as clay saturation, grain shape, macro-porosity in the connected and non connected configurations, eccentricity ratio for the non connected microstructures, threshold porosity for the connected microstructures.