Frustration and disorder in granular media and tectonic blocks: implications for earthquake complexity

Abstract. We present exploratory analogies and speculations on the mechanisms underlying the organization of faulting and earthquake in the earth crust. The mechanical properties of the brittle lithosphere at scales of the order or larger than a few kilometers are proposed to be analogous to those of non-cohesive granular media, since both systems present stress amplitudes controlled by gravity, and shear band (faulting) localization is determined by a type of friction Mohr-Coulomb rupture criterion. here, we explore the implications of this correspondence with respect to the origin of tectonic and earthquake complexity, on the basis of the existing experimental data on granular media available in the mechanical literature. An important observation is that motions and deformations of non-cohesive granular media are characterized by important fluctuations both in time (sudden breaks, avalanches, which are analogous to earthquakes) and space (strain localizations, yield surfaces forming sometimes complex patterns). This is in apparent contradiction with the conventional wisdom in mechanics, based on the standard tendency to homogenize, which has led to dismiss fluctuations as experimental noise. On the basis of a second analogy with spinglasses and neural networks, based on the existence of block and grain packing disorder and block rotation "frustration", we suggest that these fluctuations observed both at large scales and at the block scale constitute an intrinsic signature of the mechanics of granular media. The space-time complexity observed in faulting and earthquake phenomenology is thus proposed to result form the special properties of the mechanics of granular media, dominated by the "frustration" of the kinematic deformations of its constitutive blocks.