A two-scale time dependent damage model for preferential gas flow in clayey rock materials

Abstract

Understanding of the gas migration within the host rock is critical for the safety assessment of a deep geological repository for radioactive wastes. However, localized gas flow in clayey host rock materials is a complex behavior associated with dynamic and unstable network of dilatant pathways, which are accompanied by micro-cracking that indicates macroscopic tensile fractures. The subcritical crack propagation at the microscale may represent the mechanism of time dependent damage observed at the macroscale. A two-scale damage model is developed in this study to explicitly simulate the preferential gas flow in clayey rock materials. A homogenization method based on asymptotic developments is employed to deduce the macroscopic damage behavior coupled with the poroelastic system, which initiates from the periodically distributed microstructures with micro-cracks. A time dependent damage evolution law is constructed based on the microscopic phenomena and the corresponding intrinsic permeability model is proposed which implicitly accounts for the fracture opening induced permeability change. The local macroscopic response of the model is analyzed and validated against the experimentally measured direct tensile strength, which illustrates the homogenized elastic and permeability coefficients, and highlights the influence of several parameters, i.e., the initial damage, the microstructural size and the strain rate. Numerical examples are presented in order to illustrate the global macroscopic response, in which a pure mechanical test, i.e., uniaxial tension test is simulated and verified against the laboratory results, then the simulation of preferential gas flow is illustrated together with the comparison of experimental explanation. The numerical results showed that the proposed two-scale model can explicitly simulate the gas induced fracturing, in which the damage propagation and the dilatant gas pathways are well captured.