We study experimentally and numerically the permeability of a rough fractur
e at laboratory scale when viscous forces are dominating (low Reynolds numb
er). The experimental setup includes a granite fracture surface (10 x 10 cm
(2)) opened in mode I. It allows a continuous opening of the fracture paral
lel to its mean plane. The fracture roughness is measured and characterized
in terms of self-affine heterogeneities. Its isotropy is checked. The depa
rture from the cubic law is measured as a function of the aperture opening
(for mean separations between 4.0 and 10.3 mm) and the pressure drop orient
ation by rotating the fracture by 90 degrees. A strongly anisotropic hydrau
lic behavior is observed and results from the geometrical heterogeneities t
hat exist up to the fracture macro-scale.