A semianalytical solution for steady infiltration in unsaturated fracturedrock

A semianalytical solution is developed for an equivalent continuum model of one-dimensional steady infiltration in unsaturated fractured rock. The dif ferential form of the mass conservation equation is integrated to yield an analytical expression relating elevation to a function of capillary pressur e and relative permeability of the fracture and rock matrix. Constitutive r elationships for unsaturated flow in this analysis are taken from van Genuc hten [1980] and Mualem [1976], but alternative relations can also be implem ented in the integral solution. Expressions are presented for the liquid sa turations and pore velocities in the fracture, matrix, and effective contin uum materials as a function of capillary pressure and elevation. Results of the analytical solution are applied to examples of infiltration in fractur ed rock consisting of both homogeneous and composite (layered) domains. The analytical results are also compared to numerical simulations to demonstra te the use of the analytical solution as a benchmarking tool to address com putational issues such as grid refinement.