Unsaturated flow in a quasi‐three‐dimensional fractured medium with spatially variable aperture

Abstract

Transient moisture flow in a variably saturated quasi‐three‐dimensional fracture‐rock matrix system is investigated. The fracture is assumed to possess a spatially variable aperture in its two‐dimensional plane, whereas the rock matrix is treated as a two‐dimensional homogeneous and tight porous medium. The aperture fluctuations in the fracture plane are described stochastically. Moisture exchange between the fracture and the rock matrix is accounted for via an advective coupling term that governs the transfer of moisture at the fracture‐matrix interface and takes into account the effect of a fracture‐surface coating material. Although the variable aperture fracture is two‐dimensional, the coupling term between the fracture and the rock matrix accounts for the three‐dimensional nature of the physical system. The stochastic nonlinear set of partial differential equations is solved numerically by the Galerkin finite element method in conjunction with the Picard iterative scheme and an automatic time step marching. Simulations are performed to investigate phenomena which have been ignored in previous studies. It is demonstrated that, for the case of no moisture exchange with the rock matrix, the moisture follows preferential flow paths within the fracture plane and exhibits pronounced fingering effects. Furthermore, it is shown that the larger the fracture aperture fluctuations the more extended the moisture flow in the fracture. In addition, for the case where there exists moisture exchange with the rock matrix, the movement of the moisture front is considerably reduced, whereas fracture‐surface coatings tend to slow down moisture absorption by the rock matrix.