Friction memory in the stick-slip of a sheared granular bed Fabio Leoni a , Andrea Baldassarri b,c , Fergal Dalton d , Alberto Petri c,d, ⁎, Giorgio Pontuale d , Stefano Zapperi e a CEA, IRAMIS, SPEC, Grp. Ins¡tability & Turbulence, F-91191 Gif Sur Yvette, France b Istituto dei Sistemi Complessi del CNR, via dei Taurini 19, I-00185, Roma, Italy c Dipartimento di Fisica, Sapienza Universitá, P.le A. Moro 5, I-00185 Roma, Italy d Istituto dei Sistemi Complessi del CNR, via Fosso del Cavaliere 100, I-00133, Roma, Italy e Istituto per l'Energetica e le Interfasi del CNR, Via R. Cozzi 53, I-20125, Milano, Italy abstract article info Article history: Received 14 July 2010 Available online 19 August 2010 Keywords: Granular media; Friction; Shear; Noise; Ageing We investigate friction memory effects in the chaotic stick-slip motion of a plate shearing a granular bed. By analyzing separately trajectories' portions having increasing or decreasing instantaneous velocity, it is found that there are two quantitatively distinct granular friction–velocity curves for positive or negative acceleration, which cross one another in the weakening region. Interpreting acceleration dependence as an indirect consequence of contact ageing, we try to explain these effects by including rate-and-state (RS) friction equations in the stochastic model describing the plate motion. Preliminary results on a study case show that the main experimental features can be reproduced in this way, although quantitative agreement is partial. From the value obtained for the RS parameters we conclude that sliding friction decorrelation takes place at the length-scale of the solid-on-solid micro-contacts between grains and plate. In addition, the contemporary presence of noise and RS effects influences the average friction curve at large shear rate. © 2010 Elsevier B.V. All rights reserved. 1. Introduction The physics of Granular Systems (GS) offers very rich opportuni- ties to expand the understanding of many types of non-equilibrium and complex systems. At the simplest level a (dry) GS is composed of a large number of massive athermal particles interacting through elastic and frictional forces. As interactions are dissipative, energy is effectively removed from the system and one must therefore continuously inject additional energy to observe any kind of long term dynamics. These few ingredients are sufficient for the system to generate a wide variety of behaviours. As yet there exists no consistent physical framework representing the dynamic evolution of a GS from a general point of view such as the Navier–Stokes equation for fluids. The state of the grains themselves can sometimes be described as either gaseous, liquid or solid, depending on the system parameters and the applied excitation, and much existing research focuses on describing the granular material in a single experimental context though important progress have been made in recent years towards unifying different views (see e.g. [1]). One typical situation is that of a horizontal densely packed bed of granular medium subject to a horizontal shear force exerted by an upper plate. Besides being interesting both in itself and for industrial applications, this kind of system can also be considered to some extent a very simplified model for a low-pressure earthquake fault zone, where the granular material plays the role of the fault gouge (see e.g. [2,3] and refs. therein). One major item in this context concerns the response force that the medium exerts on the shearing plate. It has recently been shown [4] that the dynamics of the plate shearing the top of a granular channel can be well described by a stochastic equation of motion, where the reaction force of the medium to the shear stress is decomposed into two independent contributions: one random and one deterministic. In analogy with usual viscous forces the latter can be taken to be a function of velocity, while the former depends on the position of the plate. Comparison with experimental data [4,5] showed that this assumption allows a good quantitative description of the dynamics. Nevertheless it is known that GS can display hysteretic behaviour with respect to shear [6], which is not considered by the friction law adopted in [4]. Such behaviour can be ascribed to memory and/or ageing of the medium, and has been observed and investigated in both solid-on-solid experiments and gouge system friction [7–11] (see e.g. [2,3] and [12] for reviews). In the present article we investigate the effective stress response of a granular bed on a top shearing plate performing chaotic stick-slip motion, with large and intermittent velocity fluctuations. We find that the average effective stress dependence on the instantaneous shear velocity for positive and negative instantaneous acceleration is described by two distinct friction laws, which cross each other at low share rate. We ascribe this behaviour to memory and ageing and attempt to reproduce it by adopting a suitable rate-and-state friction law (instead of the simple velocity dependent law of ref. [4]) in the Journal of Non-Crystalline Solids 357 (2011) 749–753 ⁎ Corresponding author. Istituto dei Sistemi Complessi del CNR via Fosso del Cavaliere 100 I-00133 Rome Italy. E-mail address: alberto.petri@isc.cnr.it (A. Petri). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.07.046 Contents lists available at ScienceDirect Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol