Cracking Induced by Desiccation: A Mixed-Dimensional Unsaturated-Thermo-Hydro-Mechanical Model

Modeling and simulation of crack propagation in dried soils have been the focus of the research and industrial communities for decades. There is an ongoing interest in understanding the underlying mechanisms of such a complex process. The difficulty lies, not only on its inherent randomness but also in the mathematical and computational challenges associated with the highly coupled physical processes taking place in the initiation and ultimate propagation of cracks in a soil sample, e.g.: transfer of mass/heat/momentum, accurate geometric representation of the cracks, several fluid phases, high computational cost, etc.

Motivated by contributing to the advances of this field, we present a novel Unsaturated Thermo-Hydro-Mechanical (UNSAT-THM) model. Our mathematical model is based on a mixed-dimensional representation of the matrix and the fractures, where the latter are included as lower-dimensional geometric objects, following the standard Discrete Fracture Matrix (DFM) approach. This results in a non-linear coupled problem, where the simultaneous flow of water and air is described by the Richards' equation, whereas the thermo-poroelastic behavior is described by the Biot equations coupled with the energy equation. The system of equations is discretized using multipoint finite volume schemes in space (specifically MPFA/MPSA-FV), and backward Euler in time. Under the assumption that nucleation points are known, we let the cracks propagate following a heuristic energy minimization criterion, which is directly related to the rate of evaporation and the thermal conditions of the surroundings.