Unjamming Dynamics: The Micromechanics of a Seismic Fault Model

Abstract

The unjamming transition of granular systems is investigated in a seismic fault model via three dimensional Molecular Dynamics simulations. A two-time force-force correlation function, and a susceptibility related to the system response to pressure changes, allow to characterize the stick-slip dynamics, consisting in large slips and microslips leading to creep motion. The correlation function unveils the micromechanical changes occurring both during microslips and slips. The susceptibility encodes the magnitude of the incoming microslip.PACS numbers: 46.55.+d; 45.70.Ht; 91.30.Px In a number of industrial processes and natural phenomena, such as earthquakes or landslides, disordered solid granular systems start to flow. This solid-to-liquid transition, known as unjamming, occurs either on decreasing the confining pressure P , or increasing the applied shear stress σ. Understanding the properties of this transition is a big challenge due to the absence of an established theoretical framework for granular materials. A proposed analogy with the glass transition [1] of thermal systems has recently triggered the study of the jamming transition via numerical investigations of systems of soft frictionless particles at zero applied shear stress [2], where the only control parameter is the pressure (or the density). As the unjamming transition is approached by decreasing the confining pressure, the vibrational spectrum develops an excess of low frequency modes, known as soft-modes, leading to the identification of a length scale which diverges on unjamming [3]. This length scale is related to the emergence of an increasingly heterogeneous response as the system moves towards the transition [3]. A different approach to the study of the unjamming transition has been followed in a two dimensional numerical study [4] and in a number of experiments [5][6][7][8], where the applied shear stress is controlled via a spring mechanism, as the one in Fig. 1a. A stick-slip motion characterized by a complex slip size statistics [7] is recovered at high confining pressures P and small driving velocities V d . This stick-slip dynamics is altered by the presence of noise [9]. Analogous results have been found at fixed strain rate [10,11].

Micromechanics and statistics of slipping events in a granular seismic fault model

“…According to the above observations, since k m varies in a small range, k m ∈ [10,20], ∆ is roughly constant and we can expect a scaling with k m /L. Fig.…”

“…1 (left panel), slips of different size typically involve the entire top plate. It could be therefore surprising that this and similar granular models of faults have been shown to reproduce the GR distribution experimentally [5,6,7] and numerically [20,13]. However, it is not clear what is the role of the granular media in the overall dynamics, and how the slip size probability distribution is affected by the model parameters.…”

“…In fact, the non linear behaviour could be explained considering that small perturbations applied to a granular system modify the contact force network, setting up a memory mechanisms which could be responsible of the spatio-temporal correlations between earthquakes. Numerical simulations of granular models for seismic faults allow to investigate the mechanical properties of the system at a level of spatial and temporal resolution not accessible experimentally [13,19,14,15,16,17,18,20]. Some studies investigate the effect of fragmentation of the gouge [19,14,15], others focus on the mechanisms at the basis of the unjamming transition [16,17,18,20].…”

“…Numerical simulations of granular models for seismic faults allow to investigate the mechanical properties of the system at a level of spatial and temporal resolution not accessible experimentally [13,19,14,15,16,17,18,20]. Some studies investigate the effect of fragmentation of the gouge [19,14,15], others focus on the mechanisms at the basis of the unjamming transition [16,17,18,20]. An important open question concerns the ability of granular fault models to reproduce fundamental phenomenological laws for seismic occurrence, as for instance the Gutenberg-Richter (GR) law [21].…”

Synchronized oscillations and acoustic fluidization in confined granular materials

“…Model parameters are chosen according to ref. [25,27] in order to have long stick phases interrupted by rapid plate displacements, i.e. the slips.…”