Normal Stress Distribution of Rough Surfaces in Contact

We study numerically the stress distribution on the interface between two thick elastic media bounded by interfaces that include spatially correlated asperities. The interface roughness is described using the self-affine topography that is observed over a very wide range of scales from fractures to faults. We analyse the correlation properties of the normal stress distribution when the rough surfaces have been brought into full contact. The self affinity of the rough surfaces is described by a Hurst exponent H . We find that the normal stress field is also self affine, but with a Hurst exponent H − 1. Fluctations of the normal stress are shown to be important, especially at local scales with anti-persistent correlations. Theories describing the elastic properties of two media in contact through rough surfaces have important applications in a wide range of geophysical problems, such as earthquakes, fracture, fluid permeability or rock friction [Scholz, 1990]. Asperities exist at all scales: grain roughness is relevant for closure of rock joints [Brown and Scholz, 1986] and seamounts might induce large scale stress fluctuations along subduction slabs [Dmowska et al., 1996]. Whatever the scale of the asperities in contact is, when they are attached to an elastic medium and are loaded, they interact and concentrate high stresses. Friction properties of an interface are very dependent on the heterogeneities of the normal stresses [Dieterich and Kilgore, 1996]. At fault scale, residual stresses resulting from asperity squeeze might be responsible for heterogeneities of the dynamic stress field and influence the earthquake propagation [Bouchon et al., 1998]. Figure 1. We consider in this letter the normal component of the stress field σN that appears on the interface between two elastic media with rough surfaces (see Figure 1) [Sayles, 1996]. We assume that possible local plastic Present address: NORDITA, Blegdamsvej 17, DK-2100 Copenhagen, Denmark Permanent address: Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Permanent address: Laboratoire de Géologie, UMR CNRS 8538, Ecole Normale Supérieure, 24, rue Lhomond, F–75231 Paris Cédex 05, France Permanent address: Institut Non-Linéaire de Nice, UMR CNRS 6618, Université de Nice–Sophia Antipolis, 1361 Route des Lucioles, F–06560 Valbonne, France