Hydrothermal coupling in a rough fracture

Heat exchange during laminar flow is studied at the fracture scale on the basis of the Stokes equation. We used a synthetic aperture model (a self-affine model) that has been shown to be a realistic geometrical description of the fracture morphology. We developed a numerical modelling using a finite difference scheme of the hydrodynamic flow and its coupling with an advection/conduction description of the fluid heat. As a first step, temperature within the surrounding rock is supposed to be constant. Influence of the fracture roughness on the heat flux through the wall, is estimated and a thermalization length is shown to emerge. Implications for the Soultz-sous-For\^{e}ts geothermal project are discussed

Dynamics and structure of interfacial crack fronts

The propagation of an interfacial crack front through a weak plane of a transparent Plexiglas block has been studied experimentally. A stable crack in mode I was generated by loading the system by an imposed displacement. The local velocities of the fracture front line have been measured by using an high speed CCD camera. The distribution of the velocities exhibits a power law behavior for velocities larger than the average front velocity with a crossover to a slowly increasing function for velocities lower than . The fluctuations in the velocities reflect an underlying irregular bursts activity with a power law distribution of the bursts. We further found that the size of the local bursts scales differently in the direction parallel to and perpendicular to the fracture front

Roughness of stylolites: a stress-induced instability with non local interactions

We study the roughness of stylolite surfaces (i.e. natural pressure-dissolution surfaces in sedimentary rocks) from profiler measurements at laboratory scales. The roughness is shown to be nicely described by a self-affine scaling invariance. At large scales, the roughness exponent is $\zeta_1 \approx 0.5$ and very different from that at small scales where $\zeta_2 \approx 1.1$. A cross-over length scale at around $\lambda_c =1$mm is well characterized and interpreted as a possible fossil stress measurement if related to the Asaro-Tiller-Grinfeld stress-induced instability. Measurements are consistent with a Langevin equation that describes the growth of stylolite surfaces in a quenched disordered material with long range elastic correlations.Comment: 4 pages, 5 figure

Reply to Comment on "Roughness of Interfacial Crack Fronts: Stress-Weighted Percolation in the Damage Zone"

This is the reply to a Comment by Alava and Zapperi (cond-mat/0401568) on Schmittbuhl, Hansen and Batrouni, PRL, 90, 045505 (2003)

Dynamical stability of the crack front line

Dynamical stability of the crack front line that propagates between two plates is studied numerically using the simple two-dimensional mass-spring model. It is demonstrated that the straight front line is unstable for low speed while it becomes stable for high speed. For the uniform model, the roughness exponent in the slower speed region is fairly constant around 0.4 and there seems to be a rough-smooth transition at a certain speed. For the inhomogeneous case with quenched randomness, the transition is gradual.Comment: 14 pages, 7 figure

High resolution 3D laser scanner measurements of a strike-slip fault quantify its morphological anisotropy at all scales

The surface roughness of a recently exhumed strikeslip fault plane has been measured by three independent 3D portable laser scanners. Digital elevation models of several fault surface areas, from 1 m2 to 600 m2, have been measured at a resolution ranging from 5 mm to 80 mm. Out of plane height fluctuations are described by non-Gaussian distribution with exponential long range tails. Statistical scaling analyses show that the striated fault surface exhibits self-affine scaling invariance with a small but significant directional morphological anisotropy that can be described by two scaling roughness exponents, H1 = 0.7 in the direction of slip and H2 = 0.8 perpendicular to the direction of slip

Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces: Correlated Percolation in the Damage Zone

We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture process being a correlated percolation process in a self-generated quadratic damage gradient. We use the quasi-static two-dimensional fuse model as a paradigm of a fracture model. We measure for this model, that exhibits a correlated percolation process, the correlation length exponent nu approximately equal to 1.35 and conjecture it to be equal to that of uncorrelated percolation, 4/3. We then show that the roughness exponent in the fuse model is zeta = 2 nu/(1+2 nu)= 8/11. This is in accordance with the numerical value zeta=0.75. As for three-dimensional brittle fractures, a mean-field theory gives nu=2, leading to zeta=4/5 in full accordance with the universally observed value zeta =0.80.Comment: 4 pages RevTeX