The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations [1]. Analytical methods and sophisticated 'dislocation-dynamics' simulations have proved very effective in the study of dislocation patterning, and have led to macroscopic constitutive laws of plastic deformation [2][3][4][5][6][7][8][9]. Yet, a statistical analysis of the dynamics of an assembly of interacting dislocations has not hitherto been performed. Here we report acoustic emission measurements on stressed ice single crystals, the results of which indicate that dislocations move in a scale-free intermittent fashion. This result is confirmed by numerical simulations of a model of interacting dislocations that successfully reproduces the main features of the experiment. We find that dislocations generate a slowly evolving configuration landscape which coexists with rapid collective rearrangements. These rearrangements involve a comparatively small fraction of the dislocations and lead to an intermittent behavior of the net plastic response. This basic dynamical picture appears to be a generic feature in the deformation of many other materials [10][11][12]. Moreover, it should provide a framework for discussing fundamental aspects of plasticity, that goes beyond standard mean-field approaches that see plastic deformation as a smooth laminar flow.Whenever dislocation glide is the dominant plastic deformation mechanism in a crystalline material, we observe a constant strain-rate regime usually described by Orowan's relationγ ∼ ρ m bv. Here, the plastic strain-rate of the materialγ is simply related to average quantities such as ρ m , the density of mobile dislocations, and v, their average velocity along the slip direction (parallel to the Burgers vector b) [1]. Transmission electron micrographs of plastically deformed materials display, on the other hand, complex features such as cellular structures and fractal patterns [2,3], which are the fingerprint of a complex multiscale dynamics not appropriately accounted for by the mean-field character of Orowan's relation. In addition, rapid slip events [10] have been observed in the plastic deformation of various metals and alloys [11,12], and in the Portevin-LeChatelier effect [13]. We believe that formulating plastic deformation as a nonequilibrium statistical mechanics problem [14] requires a substantial understanding of basic collective dislocation dynamics.Experimentally, the complex character of collective dislocation dynamics can be revealed by acoustic emission measurements. The acoustic waves recorded in a piezoelectric transducer disclose the pulse-like changes of the local displacements in the material during plastic deformation, whereas a smooth plastic flow would not be detected [15].Thus, this method is particularly useful for inspecting possible fluctuations in the dislocation velocities and densities.Ice single crystals can be used as a model material to study glide dislocation dynamics by acoustic emis...

We analyze the volume distribution of natural rockfalls on different geological settings (i.e., calcareous cliffs in the French Alps, Grenoble area, and granite Yosemite cliffs, California Sierra) and different volume ranges (i.e., regional and worldwide catalogs). Contrary to previous studies that included several types of landslides, we restrict our analysis to rockfall sources which originated on subvertical cliffs. For the three data sets, we find that the rockfall volumes follow a power law distribution with a similar exponent value, within error bars. This power law distribution was also proposed for rockfall volumes that occurred along road cuts. All these results argue for a recurrent power law distribution of rockfall volumes on subvertical cliffs, for a large range of rockfall sizes (102–1010 m3), regardless of the geological settings and of the preexisting geometry of fracture patterns that are drastically different on the three studied areas. The power law distribution for rockfall volumes could emerge from two types of processes. First, the observed power law distribution of rockfall volumes is similar to the one reported for both fragmentation experiments and fragmentation models. This argues for the geometry of rock mass fragment sizes to possibly control the rockfall volumes. This way neither cascade nor avalanche processes would influence the rockfall volume distribution. Second, without any requirement of scale‐invariant quenched heterogeneity patterns, the rock mass dynamics can arise from avalanche processes driven by fluctuations of the rock mass properties, e.g., cohesion or friction angle. This model may also explain the power law distribution reported for landslides involving unconsolidated materials. We find that the exponent values of rockfall volume on subvertical cliffs, 0.5 ± 0.2, is significantly smaller than the 1.2 ± 0.3 value reported for mixed landslide types. This change of exponents can be driven by the material strength, which controls the in situ topographic slope values, as simulated in numerical models of landslides [Densmore et al., 1998; Champel et al., 2002].

Hundreds of shallow, small to moderate earthquakes have occurred near the Lacq deep gas field in southwestern France since 1969. These earthquakes are clearly separated from tectonic seismicity occurring in the Pyrenees, 25 km to the southwest. The induced seismicity began when the reservoir pressure had declined by ∼30 MPa. Repeated leveling over the field shows localized subsidence reaching a maximum of 60 mm in 1989. Segall (1989) suggested that poroelastic stressing, associated with volumetric contraction of the reservoir rocks, is responsible for induced seismicity associated with fluid extraction. To test this model, we compare the observed subsidence and hypocentral distributions with the predicted displacement and stress fields. We find that the relationship between average reservoir pressure drop and subsidence is remarkably linear, lending support to the linear poroelastic model. Displacements and stresses are computed based on a priori knowledge of the reservoir geometry, material properties, and reservoir pressure changes. The computed vertical displacements are found to be in excellent agreement with the subsidence observed from leveling. Stress perturbations accompanying gas extraction, computed using the same parameters, are found to be ∼0.2 MPa or less. Changes in Coulomb failure stress are computed assuming that slip occurs on optimally oriented planes. The predicted failure zones correlate very well with the spatial distribution of earthquakes if the perturbing stresses are small in comparison to the ambient regional deviatoric stresses and if the minimum regional compressive stress axis is vertical. Accurate determination of focal mechanisms of the induced events would allow a more rigorous test of the poroelastic model and could lead to important inferences about the crustal stress state.

The inverse Omori law for foreshocks discovered in the 1970s states that the rate of earthquakes prior to a mainshock increases on average as a power law ∝ 1/(t c − t) p ′ of the time to the mainshock occurring at t c . Here, we show that this law results from the direct Omori law for aftershocks describing the power law decay ∼ 1/(t − t c ) p of seismicity after an earthquake, provided that any earthquake can trigger its suit of aftershocks. In this picture, the seismic activity at any time is the sum of the spontaneous tectonic loading and of the activity triggered by all preceding events weighted by their corresponding Omori law. The inverse Omori law then emerges as the expected (in a statistical sense) trajectory of seismicity, conditioned on the fact that it leads to the burst of seismic activity accompanying the mainshock. In particular, we predict and verify by numerical simulations on the Epidemic-Type-Aftershock Sequence (ETAS) model that p ′ is always smaller than or equal to p and a function of p, of the b-value of the Gutenberg-Richter law (GR) and of a parameter quantifying the number of direct aftershocks as a function of the magnitude of the mainshock. The often documented apparent decrease of the b-value of the GR law at the approach to the main shock results straightforwardly from the conditioning of the path of seismic activity culminating at the mainshock. However, we predict that the GR law is not modified simply by a change of b-value but that a more accurate statement is that the GR law gets an additive (or deviatoric) power law contribution with exponent smaller than b and with an amplitude growing as a power law of the time to the mainshock. In the space domain, we predict that the phenomenon of aftershock diffusion must have its mirror process reflected into an inward migration of foreshocks towards the mainshock. In this model, foreshock sequences are special aftershock sequences which are modified by the condition to end up in a burst of seismicity associated with the mainshock. Foreshocks are not 2 just statistical creatures, they are genuine forerunners of large shocks as shown by the large prediction gains obtained using several of their qualifiers.

The dislocation dynamics during the creep deformation of single crystals of ice Ih was studied using acoustic emission (AE) measurements. The AE activity was recorded during uniaxial compression and torsion creep tests. The results were interpreted in terms of dislocation dynamics with the help of an AE source model relating the amplitude of an acoustic event to the number of dislocations involved in the event and to their velocity. This model was first validated by a comparison between the global AE activity and the global strain rate. Then, it was possible to evaluate the density of moving dislocations during creep deformation. Two regimes were revealed. Without significant polygonization, the density of mobile dislocations, deduced from AE, was proportional to the stress, but increased much faster after polygonization, in agreement with theoretical arguments. Finally, the power law distributions observed for AE amplitudes, the slow driving process, the very large number of interacting dislocations involved, argued for the dislocation dynamics to be a new example of a class of nonlinear dynamics defined as a self-organized critical state (SOC). It would imply that, from a global point of view, the creep of ice single crystals is a marginally stable state rather than a steady-stable state.