The apparent conductivity for steady unsaturated flow in periodically fractured porous media

Abstract

The influence of horizontal fractures on the steady seepage of moisture in variably saturated porous media is analyzed by analytical and numerical means. The fractures are assumed to contain many open (dry) regions, and to be distributed periodically in two dimensions. The dry regions of the fracture form a barrier to moisture flow through the geologic medium. An idealized two‐dimensional model that maximizes the barrier effect of the fractures is analyzed. The results of the analysis quantify the effect of the dry regions of the fractures on global water flow through the fractured medium. An apparent conductivity is determined such that the fractured system can be replaced by a homogeneous medium for describing steady unsaturated flow. An asymptotic analysis yields an analytic expression for the apparent hydraulic conductivity through such a system in the limit of small sorptive number (fracture spacing divided by a characteristic capillary suction) for the intact matrix material. The apparent hydraulic conductivity for arbitrary spacing and sorptive number is determined by numerical means. The numerical model accounts for variable hydraulic conductivity as a function of the local pressure head, whereas the asymptotic solution represents the limit of constant conductivity. The numerical results confirm the analytical solution as a lower bound on the apparent hydraulic conductivity.