Ackermann

Agterberg

Anders

Arcangelis

Aviles

B. Berkowitz

Bahat

Barton

Belfield

Berkowitz

Bodin

Borgos

Bour

Brooks

Burg

Carbotte

Carter

Cartwright

Castaing

Cello

Charlaix

Childs

Chilès

Cladouhos

Clark

Cowie

Crave

Cruden

Dauteuil

Davy

Dershowitz

Dyer

E. Bonnet

Einstein

Falconer

Feder

Fossen

Frisch

Gauthier

Genter

Gertsch

Gervais

Giaquinta

Gillespie

Gonzato

Grassberger

Griffith

Gross

Gudmundsson

Hamburger

Hansen

Harris

Hatton

Heffer

Henderson

Hentschel

Heuze

Hirata

Hobbs

Hudson

I. Main

Irwin

Jackson

Johnston

Kagan

Kakimi

Kanamori

Kendall

King

English

Scaling in fracture systems has become an active field of research in the last 25 years motivated by practical applications in hazardous waste disposal, hydrocarbon reservoir management, and earthquake hazard assessment. Relevant publications are therefore spread widely through the literature. Although it is recognized 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 exponents and fractal dimensions from observations, although outwardly simple, is problematic, and uncritical use of analysis techniques has resulted in inaccurate and even meaningless exponents. We review these techniques and suggest guidelines for the accurate and objective estimation of exponents and fractal dimensions. Syntheses of length, displacement, aperture power law exponents, and fractal dimensions are found, after critical appraisal of published studies, to show a wide variation, 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 physical causes of power law scaling and variation in exponents and fractal dimensions are still poorly understood

Bonnet, E.

Bour, O.

Odling, N. E.

Davy, P.

Main, I. G.

Berkowitz, B.

Edinburgh Research Explorer

380 ß Bonnet et al.:

A comparison of seismic and structural measurements of fractal dimension during tensile subcritical crack growth,

A criterion for percolation threshold in a random array of plates,

A fractal model for crustal deformation,

A fractal relationship between vein thickness and gold grade in drill core from La Codosera, Spain,

A fracture-mechanical cellular automaton model of seismicity,

A modern regression approach to determining fault displacement-length scaling relationships,

A multiple-crack model of brittle fracture, 1, Non-time-dependent simulations,

A stereological interpretation of joint traces data,

A survey of product integration with a view toward application in survival. analysis,

Aggregate properties of fracture populations,

Analysis of the relationship between displacement and dimensions of faults,

Anticlustering of small normal faults around larger faults,

Aperture distribution of rock fractures,

Apparent breaks in scaling in the earthquake cumulative frequency-magnitude distribution: Fact or artifact?,

Apparent fractality emerging from models of random distributions,

Application of Cantor's method for fractal analysis of fractures in the Toyoha

Arctic sea ice leads from advanced very high resolution radiometer images,

Are fault growth and linkage models consistent with power-law distribution of fault length?,

Bedrock geological map of Hubbard Brooks experimental forest and maps of fractures and geology in road cuts along Interstate 93, Grafton County,

Buckling of the oceanic lithosphere from geophysical data and experiments,

Censoring and edge effects in areal and line transect sampling of rock joint traces,

Change in the frequency-size relationship from small to large earthquakes,

Characterization and interpretation of rock mass joint patterns,

Characterizing rock joint geometry with joint system models, Rock Mech.

Clustering and size distribution of fault patterns: Theory and measurements,

Comparative analysis of direct (core) and indirect (borehole imaging tools) collection of fracture data in the Hot Dry Soultz reservoir

Comparison of seafloor tectonic fabric at intermediate, fast, and super fast spreading ridges' Influence of spreading rate, plate motions, and ridge segmentation on fault patterns,

Computationally efficient models for the growth of large fracture systems,

Connectivity of random fault networks following a power law fault length distribution,

Crack aperture statistics and pore space fractal geometry of Westerly granite and Rutland quartzite: Implications for an elastic contact model of rock compressibility,

Damage development during rupture of heterogeneous brittle materials: A numerical study, in Deformation Mechanisms, Rheology and Tectonics,

Deformation partitioning in a slow spreading ridge undergoing oblique extension: Mohns Ridge,

Describing the size of discontinuities,

Determination of total strain from faulting using slip measurements,

Discontinuities and rock mass geometry,

Discontinuity frequency in rock masses,

Discontinuity spacing in rock,

Disorder and fracture,

Distribution logarithmique self similaire des rejets et longueurs de failles: Exemple du bassin Houiller Lorrain,

Dynamics and scaling properties of fractures in clay-like materials,

Earthquake and fault populations and the calculation of brittle strain,

Effect of mechanical interactions on the scaling of fracture length and aperture,

Effects of lithology on geometry and scaling of small faults in Triassic sandstones, east Greenland,

Effets d'fichelle dans la fracturation des granites,

Estimates of strain due to brittle faulting: Sampling of fault populations,

Estimating the mean length of discontinuity traces,

Estimation of discontinuity spacing and trace length using scanline surveys,

Estimation of mean trace length discontinuities, Rock Mech.

Experimental discovery of scaling laws relating fractal dimensions and the length distribution exponent of fault systems,

Extension of continental lithosphere: A model for two scales of basin and ranges deformation,

Extreme deviations and applications,

Fault growth and fault scaling laws: Preliminary results,

Fault growth by segment linkage: An explanation for scatter in maximum displacement and trace length data from the Canyonlands grabens of SE

Fault growth in brittleductile experiments and the mechanics of continental collisions,

Fault growth model and the universal fault length distribution,

Fault population de- 382 ß Bonnet et al.:

Fault size distributionsmare they really power-law?,

Fault spacing in E1 Teniente mine, central Chile: Evidence for nonfractal fault geometry,

Fractal analysis applied to characteristic segments of the San Andreas fault,

Fractal analysis of a Quaternary fault array in the central Apennines,

Fractal analysis of fault systems

Fractal analysis of fracture pattern using the standard box-counting technique: Valid and invalid methodologies,

Fractal analysis of fractures applied to Soulz-sous-forets hot dry rock geothermal program,

Fractal analysis of fractures in rocks: The Cantor's Dust method--Comment,

Fractal analysis of fractures in rocks: The Cantor's dust method,

Fractal analysis of fracturing in two African regions, from satellite imagery to ground scale,

Fractal analysis of the upper Quaternary faults in the central Appenines (in

Fractal and geostatistical methods for modeling of a fracture network,

Fractal and length analysis of fractures during brittle to ductile changes,

Fractal and multifractal measures of natural and synthetic fracture networks,

Fractal dimension of fault systems in Japan: Fractal structure in rock fracture geometry at various scales,

Fractal geometries of filled fracture systems--Scaling of mechanism,

Fractal geometries of vein systems and the variation of scaling relationships with mechanism,

Fractal geometry in the San Andreas fault system,

Fractal Geometry: Mathematical Foundations and Applications,

Fractal Growth Phenomena, 488 pp., World Sci.,

Fractal nature of normal faults in the Espafiola basin, Rio Grande rift, New Mexico: Implications for fault growth and brittle strain,

Fractal patterns of fractures in granites,

Fractal plastic shear bands,

Fractal relations for the diameter and trace length of disc-shaped fractures,

Fractal scaling of fracture and fault maps at Yucca Mountain, southern Nevada (abstract), Eos Trans.

Fractals and Chaos in Geology and Geophysics,

Fracture in heterogeneous medium: A network approach,

Fracture Mechanics of Rocks, Academic,

Fractures statistics from horizontal wellbores,

Frequency of occurrence of moderate to great earthquakes in intracontinental regions: Implications for changes in stress, earthquake prediction, and hazards assessment,

Generalizations of power-law distributions applicable to sampled fault-trace length: Model choice, parameter estimation and caveats,

Generalized dimensions of strange attractors,

Geometric analysis and scaling relations of deformation bands in porous sandstone from the San Rafael Desert,

Geometrical and fractal analysis of a three-dimensional hydrothermal vein network in a fractured granite,

Geometry and scaling of a population of very small rift-related normal faults,

Geometry, formation and development of tectonics fractures on the Reykjanes Peninsula, southwest Iceland,

Hierarchical geometry of faulting,

Incorporating spatial distribution into stochastic modelling of fractures: Multifractals and L•vy-stable statistics,

Introduction to Percolation Theory, Taylor and Francis,

Investigating the fractal properties of geological fault systems: The Main Ethiopian Rift case,

Joint formation in granitic rock of the Sierra Nevada,

Joint spacing: Analogue and numerical simulations,

Jointing and fracture interactions in middle Eocene chalks near Beer-Sheva, Israel,

Scaling of fracture systems in geological media

Abstract

Similar works

Full text

Available Versions

Edinburgh Research Explorer

Crossref