Infiltration of a Liquid Front in an Unsaturated, Fractured Porous Medium

We consider liquid infiltrating by gravity flow into a system of parallel, regularly spaced fractures in an unsaturated porous medium. The position of the fracture liquid front as a function of time, under some simplifying assumptions, is shown to obey a nonlinear integrodifferential equation. Approximate analytic solutions are developed, showing that the movement of the liquid front exhibits three major flow periods: (1) at early time, the frontal position is determined by the fracture inlet boundary condition and the gravity‐driven flow behavior of the fracture with negligible influence by the matrix; (2) at intermediate time, matrix imbibition retards the frontal advance against the pull of gravity; (3) at late time, the matrix approaches saturation and the frontal velocity approaches a limiting value. A two‐dimensional numerical model is used to confirm the approximate solutions. Implications of the model for nuclear waste storage are discussed. The analysis is applicable not only to fractured rock but also to lateral infiltration into coarse‐grained sediments lying between layers of fine‐grained soil.