Theoretical interpretation of a pronounced permeability scale effect in unsaturated fractured tuff

Abstract

Numerous single‐hole and cross‐hole pneumatic injection tests have been conducted in unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona. Single‐hole tests have yielded values of air permeability at various locations throughout the tested rock volume on a nominal scale of ∼1 m. Cross‐hole tests have yielded equivalent air permeabilities (and air‐filled porosities) for a rock volume characterized by a length scale of several tens of meters. Cross‐hole tests have also provided high‐resolution tomographic estimates of how air permeability (and air‐filled porosity), defined over grid blocks having a length scale of 1 m, vary throughout a similar rock volume. The results have revealed a highly pronounced scale effect in permeability (and porosity) at the ALRS. We examine the extent to which the permeability scale effect is amenable to interpretation by a recent stochastic scaling theory, which treats the rock as a truncated random fractal.