Percolation and conductivity of self-affine fractures

The percolation and conductivity of self-affine fractures are investigated over the whole range of their mean aperture and roughness exponent H, by direct three-dimensional numerical simulations. A scaling behavior is exhibited for the conductivity of tight fractures in the self-affine scale range, with exponent H. All the data can be summarized by two simple models, valid for small to moderate and for large apertures, respectively.