Role of visco-elastic rheologies in the persistence of heterogeneous stress distributions in dynamic rupture models.

Understanding how past ruptures will affect the propagation of the following ruptures is fundamental to a better comprehension of earthquake behavior. In that sense, numerical simulations provide a useful tool to study the dynamics of slip. In this study, we model a setup similar to laboratory friction experiments [Rubinstein et al., 2007; Ben-David et al. 2010], consisting of a 2D block of viscoelastic material in contact with a rigid body, with slip-weakening friction at the interface. As in the experiments, the block is loaded from the side, which results in a high concentration of shear stresses close to one edge, where slip will initiate. We observe a sequence of precursory slip, which initiate at shear levels well below the global static friction threshold. These precursory slip stop before propagating over the entire interface, and their length increase with increasing loading. High stress concentrations are generated at the tip of the arrested rupture. We analyze the evolution of these stress concentrations when the following slip events take place. Due to the viscous properties of the material, the stress concentrations created by the arrest of precursory slip are not erased by the propagation of the following rupture, but reappear with the relaxation of the material, with a smaller amplitude. This leads to perturbation in the rupture velocities, with accelerations of the front at the location of these stress concentrations. The amplitude of the stress concentrations follows an exponential decrease rate with successive ruptures. We show that this decrease rate is controlled by the material properties, in particular the ratio of the viscous over instantaneous Young’s moduli. Our formulation gives a good agreement to the behavior observed in the simulations, and implies that about five slip fronts are necessary to erase all stress concentrations. These results highlight the importance of viscous relaxation mechanisms in the persistence of heterogeneous stress state along a frictional interface. This study also provides a mechanism to explain how previous slip history will influence the propagation of the next rupture.

Evolution of heterogeneous stress distributions created by slip precursors in numerical simulations of frictional interfaces

David Simon Kammer, Jean-François Molinari, Mathilde Edmée Lucette Radiguet de la Bastaie

Understanding how a frictional interface fails, and how past ruptures will affect the propagation of the following ruptures is fundamental to a better comprehension of earthquake behavior. In that sense, numerical simulations provide a useful tool to study the dynamics of slip. In this study, we model a setup similar to laboratory friction experiments [Rubinstein et al., 2007 ; Ben-David et al. 2010] using the finite-element method. We model a 2D block of viscoelastic material in contact with a rigid body. A slip-weakening friction law controls the friction at the interface. Special care is taken to apply appropriate regularization and viscosity in the simulation. Our model allows to investigate the onset and evolution of sliding at a frictional interface. The block is loaded by applying shear loading on the trailing edge, which results in a high concentration of shear stresses close to that edge, where slip will initiate. The simulated slip events are consistent with experimental observations [Rubinstein et al., 2007]: we observe a sequence of slip precursors, which initiate at shear levels well below the global static friction threshold. These precursors stop before propagating over the entire interface, and their length increase with increasing shear force. Such precursors to global sliding significantly modify interface stresses, and affect the onset and propagation of global sliding. We analyze in details the changes affecting interface stresses. In particular, we evaluate how the stress concentration created by the arrest of one precursor event evolves when the following events take place. We show that each slip event does not renew the interface, but that stress heterogeneities are maintained after several slip events. Each slip event thus propagates in a highly heterogeneous stress field, which leads to important variations in the propagation velocity of the slip front.

2013

Dynamics of Slip Fronts at Frictional Interfaces: Analysis of Slip Precursors

David Simon Kammer, Jean-François Molinari, Mathilde Edmée Lucette Radiguet de la Bastaie

The transition from sticking to sliding of frictional interfaces is a phenomenon of importance for many physical systems in nature as well as in engineering. This transition is marked by the occurrence of local slip events, often called precursors, which appear before the global sliding is observed. Such precursors to global sliding may occur on segments of geophysical faults subject to non uniform shear loading, for example a fault segment located between a locked and steadily slipping region. Sequences of small earthquakes (foreshocks) of identical seismic characteristics have been observed preceding large earthquakes in several regions. The links between the occurrence of these foreshocks and the nucleation process of large earthquakes remains elusive, but has large implications for earthquake prediction and risk assessment. These precursors have been studied experimentally by Rubinstein et al. [2007]. However, the experimental study of interfaces is challenging due to difficulties to access information at the interface. Therefore, numerical simulations are needed in order to give additional information for accurate analysis. First attempts have been undertaken using simple spring-block systems [Maegawa et al. 2010, Tromborg et al. 2011]. In this study however, we use the finite-element method, which allows us to represent accurately the continuum character of the system, and to investigate the onset and evolution of sliding at a frictional interface. The studied setup is similar to the experimental setup used by Ben-David et al. [2010]. It consists of a block of viscoelastic material in contact with a rigid body. A velocity-weakening friction law controls the friction at the interface. Special care is taken to apply appropriate regularization and viscosity in the simulation. We apply a shear load to the block, either on the top surface of the block or on one side. In both cases, the resulting shear tractions at the interface are non-uniform. The stress distribution presents a high concentration close to the edge when the load is applied on the side. Applying a non-uniform shear loading, we observe a sequence of slip precursors, which initiate at shear levels well below the global static friction threshold. These precursors stop before propagating over the entire interface, and their length increase with increasing shear force. Our results are consistent with previous experimental observations [Rubinstein et al., 2007]. We analyze the relation between the applied load, the precursors length, and the evolution of stresses at the interface.

2012

The role of viscoelasticity on heterogeneous stress fields at frictional interfaces

David Simon Kammer, Jean-François Molinari, Mathilde Edmée Lucette Radiguet de la Bastaie

We investigate the evolution of heterogeneous stress states along frictional in- terfaces. Using finite-element simulations, we model the occurrence of precur- sory slip sequences on a deformable-deformable as well as a deformable-rigid interface between two solids. Every interface rupture creates a stress concen- tration at its arrest position and erases the stress concentrations produced by previous slip events. While the interface is sticking perfectly between two slip events, erased stress concentrations reappear and survive several cycles of ruptures. Such reestablished stress concentrations are smaller than they were before the rupture. We show that the decrease rate of these stress concentrations is exponential with respect to the number of subsequent events and that the bulk viscoelasticity is at the origin of this history effect. During a slip event, the friction tractions at the interface change almost instantaneously, which leads, between two ruptures, to a relaxation-resembling viscous effect that restores the stress concentration. We describe the decrease rate analytically and highlight that it is proportional to the ratio of the viscous over the instantaneous Young’s moduli, and illustrate it by varying the material properties in our simulations.

Elsevier2015

Evolution of heterogeneous stress distributions created by slip precursors in numerical simulations of frictional interfaces

David Simon Kammer, Jean-François Molinari, Mathilde Edmée Lucette Radiguet de la Bastaie

2013

Dynamics of Slip Fronts at Frictional Interfaces: Analysis of Slip Precursors

David Simon Kammer, Jean-François Molinari, Mathilde Edmée Lucette Radiguet de la Bastaie

2012