In an effort to investigate the link between failure mechanisms and the geometry of fractures of compacted grains materials, a detailed statistical analysis of the surfaces of fractured Fontainebleau sandstones has been achieved. The roughness of samples of different widths $W$ is shown to be self-affine with an exponent $\zeta =0.46\pm 0.05$ over a range of length scales ranging from the grain size $d$ up to an upper cutoff length $\xi \simeq 0.15W$. This low $\zeta$ value is in agreement with measurements on other sandstones and on sintered materials. The probability distributions ${\pi }_{\delta z}\left(\delta h\right)$ of the variations of height over different distances $\delta z>d$ can be collapsed onto a single Gaussian distribution with a suitable normalization and do not display multiscaling features. The roughness amplitude, as characterized by the height-height correlation over fixed distances $\delta z$, does not depend on the sample width, implying that no anomalous scaling of the type reported for other materials is present. It is suggested, in agreement with recent theoretical work, to explain these results by the occurrence of brittle fracture (instead of damage failure in materials displaying a higher value of $\zeta \simeq 0.8$).

• Received 19 April 2007

DOI:https://doi.org/10.1103/PhysRevE.76.036108