Eur. Phys. J. B 67, 121-131 (2009)
https://doi.org/10.1140/epjb/e2009-00002-2

Does roughening of rock-fluid-rock interfaces emerge from a stress-induced instability?

¹ Laboratoire Jean Kuntzmann, Université Joseph Fourier and CNRS, B.P. 53, 38041 Grenoble Cedex 9, France
² Laboratoire de Spectrométrie Physique, 140 avenue de la physique, Université Joseph Fourier, and CNRS, 38402, Saint Martin d'Hères, France
³ Laboratoire de Géodynamique des Chaines Alpines, CNRS-OSUG, Université Joseph Fourier, B.P. 53, 38041 Grenoble, France
⁴ Physics of Geological Processes, University of Oslo, 0316 Oslo, Norway
⁵ Institut de Physique du Globe de Strasbourg, UMR CNRS 7516, 5 rue Descartes, 67084 Strasbourg Cedex, France
⁶ EOST, Université de Strasbourg, Strasbourg, France

Corresponding author: ^a chaouqi.misbah@ujf-grenoble.fr

Received: 20 October 2008
Revised: 24 November 2008
Published online: 9 January 2009

Abstract

Non-planar solid-fluid-solid interfaces under stress are very common in many industrial and natural materials. For example, in the Earth's crust, many rough and wavy interfaces can be observed in rocks in a wide range of spatial scales, from undulate grain boundaries at the micrometer scale, to stylolite dissolution planes at the meter scale. It is proposed here that these initially flat solid-fluid-solid interfaces become rough by a morphological instability triggered by elastic stress. A model for the formation of these unstable patterns at all scales is thus presented. It is shown that such instability is inherently present due to the uniaxial stress that promotes them, owing to the gain in the total elastic energy: the intrinsic elastic energy plus the work of the external forces. This is shown explicitly by solving the elastic problem in a linear stability analysis, and proved more generally without having resort to the computation of the elastic field.