Stick-slip behavior in a continuum-granular experiment

Predicting fault slip via transfer learning

Data-driven machine-learning for predicting instantaneous and future fault-slip in laboratory experiments has recently progressed markedly, primarily due to large training data sets. In Earth however, earthquake interevent times range from 10's-100's of years and geophysical data typically exist for only a portion of an earthquake cycle. Sparse data presents a serious challenge to training machine learning models for predicting fault slip in Earth. Here we describe a transfer learning approach using numerical simulations to train a convolutional encoder-decoder that predicts fault-slip behavior in laboratory experiments. The model learns a mapping between acoustic emission and fault friction histories from numerical simulations, and generalizes to produce accurate predictions of laboratory fault friction. Notably, the predictions improve by further training the model latent space using only a portion of data from a single laboratory earthquake-cycle. The transfer learning results elucidate the potential of using models trained on numerical simulations and fine-tuned with small geophysical data sets for potential applications to faults in Earth.

Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media

The behavior of granular media under quasistatic loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regime traditionally linked to a self-organized critical state. This, together with the nonuniqueness and the nonmonotony of macroscopic deformation curves, suggests that the statistical avalanche properties and the susceptibilities of the system cannot be reduced to a function of the macromechanical state. The associated scaling exponents are nonuniversal and depend on the interactions between particles. For stiffer particles (or samples at low confining pressure) we find distributions of avalanche properties compatible with the predictions of mean-field theory. The scaling exponents decrease below the mean-field values for softer interactions between particles. These lower exponents are consistent with observations for amorphous solids at their critical point. We specifically discuss the relationship between microscopic and macroscopic variables, including the relation between the external stress drop and the internal potential energy released during kinetic avalanches.

The role of friction in statistics and scaling laws of avalanches

We investigate statistics and scaling laws of avalanches in two-dimensional frictional particles by numerical simulations. We find that the critical exponent for avalanche size distributions is governed by microscopic friction between the particles in contact, where the exponent is larger and closer to mean-field predictions if the friction coefficient is finite. We reveal that microscopic "slips" between frictional particles induce numerous small avalanches which increase the slope, as well as the power-law exponent, of avalanche size distributions. We also analyze statistics and scaling laws of the avalanche duration and maximum stress drop rates, and examine power spectra of stress drop rates. Our numerical results suggest that the microscopic friction is a key ingredient of mean-field descriptions and plays a crucial role in avalanches observed in real materials.

A heavy intruder in a locally-shaken granular solid

We experimentally investigate the gravitational-driven motion of a heavy object inside a vertical 2D assembly of identical, plastic cylinders arranged in a regular, triangular lattice. The bottom of the assembly is in contact with a rough plate whose horizontal, sinusoidal motion induces the formation of shear bands in the granular solid, aligned with the edges of the lattice. The intruder sinks when the width of the shear band is as large as its size and halts once the regular configuration of the grains is recovered. The resulting vertical motion of the intruder is random and intermittent, as in disordered granular or colloidal systems near jamming, with alternate flows and blockades. We show, in analogy with earthquakes, that the relation between the size and the duration of the flowing events follows a power-law with an exponent larger than one, and that the statistics of their size is compatible with the Gutenberg-Richter law. We also show that the probability density function of times between flowing events is similar to the Omori law governing the distribution of aftershock sequences following large earthquakes. Finally, the analysis of the velocity fluctuations of the intruder points to a transition from a strong to a weak contact network in the ordered granular assembly, similar to the transition from jammed to fragile states in disordered systems.

Breakdown of Scaling and Friction Weakening in Intermittent Granular Flow

Many materials are produced, processed and stored as grains, while granularity of matter can be crucial in triggering potentially catastrophic geological events like landslides, avalanches and earthquakes. The response of grain assemblies to shear stress is therefore of utmost relevance to both human and natural environment. At low shear rate a granular system flows intermittently by distinct avalanches. In such state the avalanche velocity in time is expected to follow a symmetrical and universal average behavior, whose dependence on the slip size reduces to a scale factor. Analyzing data from long lasting experiments, we observe a breakdown of this scaling: While in short slips velocity shows indeed a self-similar and symmetric profile, it does not in long slips. The investigation of frictional response in these different regimes evidences that this breakdown can be traced back to the onset of a friction weakening, which is of dynamical origin and can amplify instabilities exactly in this critical state, the most frequent state for natural hazards.

From Stress Chains to Acoustic Emission

A numerical scheme using the combined finite-discrete element method is employed to study a model of an earthquake system comprising a granular layer embedded in a formation. When the formation is driven so as to shear the granular layer, a system of stress chains emerges. The stress chains endow the layer with resistance to shear and on failure launch broadcasts into the formation. These broadcasts, received as acoustic emission, provide a remote monitor of the state of the granular layer of the earthquake system.

Transition rates for slip-avalanches in soft athermal disks under quasi-static simple shear deformations

We study slip-avalanches in two-dimensional soft athermal disks by quasi-static simulations of simple shear deformations. Sharp drops in shear stress, or slip-avalanches, are observed intermittently during steady state. Such stress drops are caused by restructuring of the contact networks, accompanied by drastic changes of the interaction forces, Δf. The changes of the forces happen heterogeneously in space, indicating that collective non-affine motions of the disks are most pronounced when slip-avalanches occur. We analyze and predict the statistics for the force changes, Δf, by transition rates of the contact forces and angles, where slip-avalanches are characterized by wide power-law tails. We find that the transition rates are described by a q-Gaussian distribution regardless of the area fraction of the disks. Because the transition rates quantify structural changes of the force-chains, our findings are an important step towards linking macroscopic observations to a microscopic theory of slip-avalanches in the experimentally accessible quasi-static regime.

Two sides of a fault: Grain-scale analysis of pore pressure control on fault slip

Pore fluid pressure in a fault zone can be altered by natural processes (e.g., mineral dehydration and thermal pressurization) and industrial operations involving subsurface fluid injection and extraction for the development of energy and water resources. However, the effect of pore pressure change on the stability and slip motion of a preexisting geologic fault remains poorly understood; yet, it is critical for the assessment of seismic hazard. Here, we develop a micromechanical model to investigate the effect of pore pressure on fault slip behavior. The model couples fluid flow on the network of pores with mechanical deformation of the skeleton of solid grains. Pore fluid exerts pressure force onto the grains, the motion of which is solved using the discrete element method. We conceptualize the fault zone as a gouge layer sandwiched between two blocks. We study fault stability in the presence of a pressure discontinuity across the gouge layer and compare it with the case of continuous (homogeneous) pore pressure. We focus on the onset of shear failure in the gouge layer and reproduce conditions where the failure plane is parallel to the fault. We show that when the pressure is discontinuous across the fault, the onset of slip occurs on the side with the higher pore pressure, and that this onset is controlled by the maximum pressure on both sides of the fault. The results shed new light on the use of the effective stress principle and the Coulomb failure criterion in evaluating the stability of a complex fault zone.

Universal slip dynamics in metallic glasses and granular matter - linking frictional weakening with inertial effects

Slowly strained solids deform via intermittent slips that exhibit a material-independent critical size distribution. Here, by comparing two disparate systems - granular materials and bulk metallic glasses - we show evidence that not only the statistics of slips but also their dynamics are remarkably similar, i.e. independent of the microscopic details of the material. By resolving and comparing the full time evolution of avalanches in bulk metallic glasses and granular materials, we uncover a regime of universal deformation dynamics. We experimentally verify the predicted universal scaling functions for the dynamics of individual avalanches in both systems, and show that both the slip statistics and dynamics are independent of the scale and details of the material structure and interactions, thus settling a long-standing debate as to whether or not the claim of universality includes only the slip statistics or also the slip dynamics. The results imply that the frictional weakening in granular materials and the interplay of damping, weakening and inertial effects in bulk metallic glasses have strikingly similar effects on the slip dynamics. These results are important for transferring experimental results across scales and material structures in a single theory of deformation dynamics.

Inertia and universality of avalanche statistics: The case of slowly deformed amorphous solids

By means of a finite elements technique we solve numerically the dynamics of an amorphous solid under deformation in the quasistatic driving limit. We study the noise statistics of the stress-strain signal in the steady-state plastic flow, focusing on systems with low internal dissipation. We analyze the distributions of avalanche sizes and durations and the density of shear transformations when varying the damping strength. In contrast to avalanches in the overdamped case, dominated by the yielding point universal exponents, inertial avalanches are controlled by a nonuniversal damping-dependent feedback mechanism, eventually turning negligible the role of correlations. Still, some general properties of avalanches persist and new scaling relations can be proposed.