Roughness of Crack Interfaces in Two-Dimensional Beam Lattices

The roughness of crack interfaces is reported in quasistatic fracture, using an elastic network of beams with random breaking thresholds. For strong disorders we obtain 0.86(3) for the roughness exponent, a result which is very different from the minimum energy surface exponent, i.e., the value 2/3. A cross-over to lower values is observed as the disorder is reduced, the exponent in these cases being strongly dependent on the disorder.Comment: 9 pages, RevTeX, 3 figure

Statistical Physics of Fracture Surfaces Morphology

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, succeeding to reproduce the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up with the proposition of new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.Comment: A review paper submitted to J. Stat. Phy

Transport in rough self-affine fractures

Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium approximation predicts the right scaling behavior of the permeability and of the velocity fluctuations, in terms of the aperture of the fracture, the roughness exponent and the characteristic length of the fracture surfaces, in the limit of small separation between surfaces. The permeability of the fractures is also investigated as a function of the normal and lateral relative displacements between surfaces, and is shown that it can be bounded by the permeability of two-dimensional fractures. The development of channel-like structures in the velocity field is also numerically investigated for different relative displacements between surfaces. Finally, the dispersion of tracer particles in the velocity field of the fractures is investigated by analytic and numerical methods. The asymptotic dominant role of the geometric dispersion, due to velocity fluctuations and their spatial correlations, is shown in the limit of very small separation between fracture surfaces.Comment: submitted to PR

HIGH-VELOCITY PRESSURE LOSS IN SANDSTONE FRACTURES: MODELING AND EXPERIMENTS

ABSTRACT High-velocity pressure loss in Berea sandstone fractures was measured and analyzed with a new model. The Berea fracture geometry was measured, and modeled as two identical impermeable self-affine surfaces spaced by a fixed width normal to the average fracture plane. High-velocity pressure loss in a self-affine rough channel was assumed to be proportional to the force of centripetal acceleration as the flow impinges on and bends around obstructions. The modeled pressure loss is square in velocity, and a power law in fracture width, and the power is given by the roughness exponent. We argue that the model may be valid for three-dimensional self-affine rough fractures. Gas flow experiments on fractures with varying widths were performed. High-velocity pressure loss was described by a sum of a linear and a square term in velocity with the Forchheimer equation. The dominating square term was a power law in fracture width, and the power was close to the power predicted by the model. For some of the greater fracture widths, the linear term was negative. For low velocities the Forchheimer equation was not valid. This is in accordance with theory, which states that the Darcy and Forchheimer flow regimes are separated by a weak inertial flow regime