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A semianalytical solution for steady infiltration in unsaturated fractured rock

A semianalytical solution is developed for an equivalent continuum model of one‐dimensional steady infiltration in unsaturated fractured rock. The differential form of the mass conservation equation is integrated to yield an analytical expression relating elevation to a function of capillary pressure and relative permeability of the fracture and rock matrix. Constitutive relationships for unsaturated flow in this analysis are taken from van Genuchten [1980] and Mualem [1976], but alternative relations can also be implemented in the integral solution. Expressions are presented for the liquid saturations and pore velocities in the fracture, matrix, and effective continuum materials as a function of capillary pressure and elevation. Results of the analytical solution are applied to examples of infiltration in fractured rock consisting of both homogeneous and composite (layered) domains. The analytical results are also compared to numerical simulations to demonstrate the use of the analytical solution as a benchmarking tool to address computational issues such as grid refinement.