We analyze the problem of the geometrical aperture between the two faces of a crack described as a self-affine surface. We consider the contact of the two surfaces after a relative rigid-body displacement (translation and/or rotation) of one side of the crack with respect to the opposite one. A number of properties are obtained analytically and illustrated by numerical simulations on generated self-affine surfaces. The results concern the scaling of the average aperture, which is shown to include a very slowly varying correction term (logarithmic with respect to the displacement); this affects severely the dependence of the measured aperture on the displacement. These results are used to analyze experimental data obtained on a granite sample and to estimate the roughness exponent from a global measurement. This estimate is shown to agree with an analysis of the roughness based on profilometry measurements.
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