Statistics of fracture surfaces

Santucci, Stéphane; Måløy, Knut Jørgen; Delaplace, Arnaud; Mathiesen, Joachim; Hansen, Alex; Bakke, Jan; Schmittbuhl, Jean; Vanel, Loïc; Ray, Purusattam

doi:10.1103/physreve.75.016104

Cited by 96 publications

(141 citation statements)

References 31 publications

(32 reference statements)

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“…In both cases, a single exponent is enough to describe the scaling invariance of the roughness [19]: this confirms the relevance of the self-affine description of fracture surfaces for both types of materials.…”

Section: Discussionsupporting

confidence: 58%

“…While most studies dedicated to the roughness of cracks dealt with surfaces with ζ ≃ 0.8 [5,6,7,8,9,10,16,17,18,19], the present work investigates these problems through an extensive analysis of the statistical properties of the roughness of fractured Fontainebleau sandstone for which ζ ≃ 0.4 − 0.5.…”

Section: Introductionmentioning

confidence: 99%

“…In addition to the self-affine exponent ζ, another important statistical characteristic is the π distribution of the surface height variations: On granite surfaces (ζ = 0.8), it was found to be Gaussian [19] and a single self-affine exponent was needed to describe the correlation of the surface heights along the crack front direction.…”

Section: Introductionmentioning

confidence: 99%

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Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

et al. 2007

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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 ζ = 0.46 ± 0.05 over a range of length scales ranging from the grain size d up to an upper cut-off length ξ ≃ 0.15W . This low ζ value is in agreement with measurements on other sandstones and on sintered materials. The probability distributions π δz (δh) of the variations of height over different distances δz > d can be collapsed onto a single Gaussian distribution with a suitable normalisation and do not display multifractal features. The roughness amplitude, as characterized by the height−height correlation over fixed distances δz, 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 occurence of brittle fracture (instead of damage failure in materials displaying a higher value of ζ ≃ 0.8).

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Section: Discussionsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 99%

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Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

et al. 2007

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“…2). An extended description of the height statistics, in particular the departure from a Gaussian statistics, is proposed in [31].…”

Section: Height Statisticsmentioning

confidence: 99%

Fracture morphology and viscous transport

Schmittbuhl

Steyer

Jouniaux

et al. 2008

International Journal of Rock Mechanics and Mining Sciences

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The morphology of a fracture in a granite block is sampled using a high resolution profiler providing a 3999 Â 4000 pixel image of the roughness. We checked that a self-affine model is an accurate geometrical model of the fracture morphology on the basis of a spectral analysis. We also estimated the topothesy of the experimental surface to be l r % 2 Â 10 À7 mm and the roughness exponent to be z % 0:78. A finite difference scheme of the Stokes equation with a lubrication approximation was used to model the viscous flow through a fracture aperture defined as the gap between the experimental fracture surface and a flat plane. We finally compare our numerical results to experimental measurements of the flux through the fracture of a glycerol/water mixture (to be at sufficiently low Reynolds number where Stokes equations holds) changing the average aperture of the fracture. The comparison is successful despite a limited resolution of the experimental measurements. Interestingly we show that only long wavelengths of the fracture morphology control the fracture hydraulic conductivity. r

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“…To quantify the fluctuations in the crack morphology as a function of the sample thickness, we follow the multiscaling analysis commonly employed to study fracture fronts [27,[38][39][40] and compute the q moments of the correlation function,…”

Section: Crack Front Roughness and Avalanchesmentioning

confidence: 99%

Role of the sample thickness in planar crack propagation

et al. 2013

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We study the effect of the sample thickness in planar crack front propagation in a disordered elastic medium using the random fuse model. We employ different loading conditions and we test their stability with respect to crack growth. We show that the thickness induces characteristic lengths in the stress enhancement factor in front of the crack and in the stress transfer function parallel to the crack. This is reflected by a thickness-dependent crossover scale in the crack front morphology that goes from from multiscaling to self-affine with exponents, in agreement with line depinning models and experiments. Finally, we compute the distribution of crack avalanches, which is shown to depend on the thickness and the loading mode.

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Statistics of fracture surfaces

Cited by 96 publications

References 31 publications

Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

Fracture morphology and viscous transport

Role of the sample thickness in planar crack propagation

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