J. Phys. I France
Volume 6, Numéro 8, August 1996
Page(s) 1127 - 1139
J. Phys. I France 6 (1996) 1127-1139
DOI: 10.1051/jp1:1996119

The Imaginary Part of Rock Jointing

G. Ouillon1, D. Sornette1, 2, A. Genter3 and C. Castaing3

1  Laboratoire de Physique de la Matière Condensée CNRS URA 190, Université de Nice-Sophia Antipolis, Parc Valrose, BP 71, 06108 Nice Cedex 2, France
2  Department of Earth and Space Science and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095, USA
3  B.R.G.M., avenue de Concyr, BP 6009, 45060 Orléans Cedex 2, France

Received 20 February 1996, revised 3 April 1996, accepted 2 May 1996

The distribution of joint spacings in a granitic massive in Saudi Arabia is found to be well-described by a power-law with characteristic exponent $\mu\simeq 0.5$. We compare the cumulative and density distributions and show how to correct the cumulative distribution for bias due to the finite sampling size. the exponent $\mu$ is close to those obtained for size distribution in fragmentation processes. We study simple models of fragmentation/jointing processes, which predict that the power law distribution must be decorated by a log-periodic modulation if the fragmentation involves a preferred ratio (even approximately so, i.e. with disorder) corresponding to an approximate discrete scale invariance. We corroborate this prediction by carrying out a more detailed analysis of the density distribution and find at least 6 log-periodic oscillations. This implies that the exponent $\mu$ possesses an imaginary part, embodying the existence of an average discrete scaling structure with preferred fragmentation ratio close to 1/2. The confidence level of this result is found better than 97% from synthetic tests.

© Les Editions de Physique 1996