Sample bias and the scaling of hydraulic conductivity in fractured rock

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Abstract
Compilations of the hydraulic conductivity of fractured rock suggest an increase in conductivity between laboratory and field scales. This scaling is inconsistent with recent suggestions that natural fracture networks are near the percolation threshold as the effective conductivity of networks near the percolation threshold decreases with increasing scale. The predicted decrease in conductivity with increasing scale may not be apparent in laboratory data due to a systematic bias in laboratory scale samples; many laboratory scale samples may not contain fractures that are larger than the size of the sample. When this bias is accounted for, the conductivity of simulated networks near the percolation threshold is consistent with the compiled data and increases with the sample dimension. Therefore, observed scaling in conductivity can be interpreted as consistent with the idea that many fracture networks are near the percolation threshold.