A Darcian integral approximation to interblock hydraulic conductivity means in vertical infiltration

Abstract

Previous work has demonstrated that using non-Darcian interblock conductivity means in mass-conservative models of unsaturated infiltration can produce mass infiltration errors up to 20 times larger than those that mass conservation corrected. But the method to generate true Darcian means from solutions to elliptic boundary value problems is too computationally intensive to be used effectively in models, especially with variable porous media. A previously introduced piecewise approximation did not estimate Darcian means well near saturation for relations, such as a van-Genuchten form, which curves strongly near saturation. This paper introduces a generally more accurate approximation to Darcian means, the Darcian Integral Mean, using the examples of matrix and fracture flow conductivity relations for Topopah Spring welded volcanic tuff (Yucca Mountain, Nevada, USA). It compares the new approximation to the geometric and arithmetic means for matrix and fracture flow, respectively. Although the new approximation may have significant computational overhead of its own, compared to standard means, as well as imperfections, it offers to other investigators a reasonable tool to examine the properties of Darcian means in running models.