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

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.