Scaling in fracture systems has become an active field of research in the last 25 years motivated by practical applications in hazardous waste disposal, hy- drocarbon reservoir management, and earthquake haz- ard assessment. Relevant publications are therefore spread widely through the literature. Although it is rec- ognized that some fracture systems are best described by scale-limited laws (lognormal, exponential), it is now recognized that power laws and fractal geometry provide widely applicable descriptive tools for fracture system characterization. A key argument for power law and fractal scaling is the absence of characteristic length scales in the fracture growth process. All power law and fractal characteristics in nature must have upper and lower bounds. This topic has been largely neglected, but recent studies emphasize the importance of layering on all scales in limiting the scaling characteristics of natural fracture systems. The determination of power law expo- nents and fractal dimensions from observations, al- though outwardly simple, is problematic, and uncritical use of analysis techniques has resulted in inaccurate and even meaningless exponents. We review these tech- niques and suggest guidelines for the accurate and ob- jective estimation of exponents and fractal dimensions. Syntheses of length, displacement, aperture power law exponents, and fractal dimensions are found, after crit- ical appraisal of published studies, to show a wide vari- ation, frequently spanning the theoretically possible range. Extrapolations from one dimension to two and from two dimensions to three are found to be nontrivial, and simple laws must be used with caution. Directions for future research include improved techniques for gathering data sets over great scale ranges and more rigorous application of existing analysis methods. More data are needed on joints and veins to illuminate the differences between different fracture modes. The phys- ical causes of power law scaling and variation in expo- nents and fractal dimensions are still poorly understood.

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Scaling of fracture systems in geological media

Characterizing rock joint geometry with joint system models

Keywords: Mecanique des roches ; Gros bloc ; Methode des elements discrets Reference Record created on 2004-09-07, modified on 2016-08-08

Block theory and its application to rock engineering

Measurement and characterisation of spatial distributions of fractures

http://uu.diva-portal.org/smash/get/diva2:1153724/FULLTEXT01

The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks

Abstract Knowledge of the spacing and size of discontinuities in a rock mass is of considerable importance for the prediction of rock behaviour. The characteristics of discontinuities can be estimated using scanline surveys but the precision of the estimates must be obtained and the bias caused by linear sampling must be eliminated before they can validly be used. Initially, an expression is presented which gives the degree of confidence that can be assigned to the measured mean discontinuity spacing. A reduced form of this expression is obtained for cases where the discontinuity spacings follow the negative exponential distribution. The precision of discontinuity frequency and RQD estimates is also explained. The distribution of trace lengths produced by the intersection of planar discontinuities with a planar rock face is used to determine the distribution of trace lengths, the distribution of semi-trace lengths and the distribution of censored semi-trace lengths intersected by a randomly located scanline. Comparison of the actual and sampled distributions demonstrates the bias introduced by scanline sampling of trace lengths. Relations between the distributions can be used to produce analytical or graphical methods of estimating mean trace length from censored measurements at exposures of limited extent.

S. D. Priest

Papers

Estimation discontinuity spacing and trace length using scanline surveys