Experimental analysis of self-affine fractured rock surfaces through shadow length measurements

Geometrical properties of fractured basalt and sandstone surfaces are studied by measuring the length distribution of shadows appearing under grazing illumination. For self-affine surfaces, the distribution is predicted to follow a power law of the shadow length with an exponent depending only on the self-affine exponent and an upper cut-off length related to the incidence angle and the amplitude of the roughness. A local thresholding procedure is described and allows to detect small shadows inside large illuminated zones and small light patches surrounded by dark regions. The dependence of the distribution on the incidence angle and on the local threshold value is studied and a criterion, based on the total length of the illuminated zones, for optimizing these parameters is introduced. For both basalt and sandstone samples, self-affine exponents obtained from length distributions verifying the criterion are in agreement with theoretical expectations using classical profilometry results. Limitations in the lowest usable incidence angle values due to deviations of the surface from self-affine characteristics are discussed and the possible determination of a roughness amplitude characterization parameter is evaluated