Sheared Granular Systems Research Articles

Predicting Stick-Slips in Sheared Granular Fault Using Machine Learning Optimized Dense Fault Dynamics Data

Predicting earthquakes through reasonable methods can significantly reduce the damage caused by secondary disasters such as tsunamis. Recently, machine learning (ML) approaches have been employed to predict laboratory earthquakes using stick-slip dynamics data obtained from sheared granular fault experiments. Here, we adopt the combined finite-discrete element method (FDEM) to simulate a two-dimensional sheared granular fault system, from which abundant fault dynamics data (i.e., displacement and velocity) during stick-slip cycles are collected at 2203 “sensor” points densely placed along and inside the gouge. We use the simulated data to train LightGBM (Light Gradient Boosting Machine) models and predict the gouge-plate friction coefficient (an indicator of stick-slips and the friction state of the fault). To optimize the data, we build the importance ranking of input features and select those with top feature importance for prediction. We then use the optimized data and their statistics for training and finally reach a LightGBM model with an acceptable prediction accuracy (R2 = 0.94). The SHAP (SHapley Additive exPlanations) values of input features are also calculated to quantify their contributions to the prediction. We show that when sufficient fault dynamics data are available, LightGBM, together with the SHAP value approach, is capable of accurately predicting the friction state of laboratory faults and can also help pinpoint the most critical input features for laboratory earthquake prediction. This work may shed light on natural earthquake prediction and open new possibilities to explore useful earthquake precursors using artificial intelligence.

Stochastic methods for slip prediction in a sheared granular system.

We consider a sheared granular system experiencing intermittent dynamics of stick-slip type via discrete element simulations. The considered setup consists of a two-dimensional system of soft frictional particles sandwiched between solid walls, one of which is exposed to a shearing force. The slip events are detected using stochastic state space models applied to various measures describing the system. The amplitudes of the events spread over more than four decades and present two distinctive peaks, one for the microslips and the other for the slips. We show that the measures describing the forces between the particles provide earlier detection of an upcoming slip event than the measures based solely on the wall movement. By comparing the detection times obtained from the considered measures, we observe that a typical slip event starts with a local change in the force network. However, some local changes do not spread globally over the force network. For the changes that become global, we find that their size strongly influences the further behavior of the system. If the size of a global change is large enough, then it triggers a slip event; if it is not, then a much weaker microslip follows. Quantification of the changes in the force network is made possible by formulating clear and precise measures describing their static and dynamic properties.

Equivalence of Fluctuation-Dissipation and Edwards' Temperature in Cyclically Sheared Granular Systems.

Using particle trajectory data obtained from x-ray tomography, we determine two kinds of effective temperatures in a cyclically sheared granular system. The first one is obtained from the fluctuation-dissipation theorem which relates the diffusion and mobility of lighter tracer particles immersed in the system. The second is the Edwards compactivity defined via the packing volume fluctuations. We find robust agreement between these two temperatures, independent of the type of the tracers, cyclic shear amplitudes, and particle surface roughness, giving therefore the first experimental evidence that the concept of effective temperature is valid in driven frictional granular systems.

On intermittency in sheared granular systems.

We consider a system of granular particles, modeled by two dimensional frictional soft elastic disks, that is exposed to externally applied time-dependent shear stress in a planar Couette geometry. We concentrate on the external forcing that produces intermittent dynamics of stick-slip type. In this regime, the top wall remains almost at rest until the applied stress becomes sufficiently large, and then it slips. We focus on the evolution of the system as it approaches a slip event. Our main finding is that there are two distinct groups of measures describing system behavior before a slip event. The first group consists of global measures defined as system-wide averages at a fixed time. Typical examples of measures in this group are averages of the normal or tangent forces acting between the particles, system size and number of contacts between the particles. These measures do not seem to be sensitive to an approaching slip event. On average, they tend to increase linearly with the force pulling the spring. The second group consists of the time-dependent measures that quantify the evolution of the system on a micro (particle) or mesoscale. Measures in this group first quantify the temporal differences between two states and only then aggregate them to a single number. For example, Wasserstein distance quantitatively measures the changes of the force network as it evolves in time while the number of broken contacts quantifies the evolution of the contact network. The behavior of the measures in the second group changes dramatically before a slip event starts. They increase rapidly as a slip event approaches, indicating a significant increase in fluctuations of the system before a slip event is triggered.

Flow characteristics and mechanical mechanism analysis in a dense sheared granular system

Flow characteristics and the mechanical theory of granular flows in dense sheared granular systems have yet to be fundamentally understood because of the complexities and discreteness of these systems. This study derives the appropriate equations and effects of mechanical parameters on fluctuation velocity, and investigates the solid volume fraction for a dense granular assembly sheared between two parallel plates. Theoretical results are verified via a discrete element method simulation. Thereafter, the mechanical mechanisms of the granular flows in this dense sheared granular system are investigated using this simulation method. Results show that the fluctuation velocity of granules at the boundaries is larger than that in the middle of the clearance, which is opposite the variation tendency of solid volume fraction. A change in the mechanical parameters can directly influence fluctuation velocity, thereby inducing the variation of the solid volume fraction. Moreover, studies on the mechanical mechanisms of granular flows indicate that inertial number has more significant effects on shear dilatancy, micro-contact structures, and coordination coefficient than contact stiffness coefficient. That is, shear dilatancy amplitude, strong force chains, and coordination coefficient decrease with the increased inertial number.

Estimating Contact Force Chains Using Artificial Neural Network

The inhomogeneous distribution of contact force chains (CFC) in quasi-statically sheared granular materials dominates their bulk mechanical properties. Although previous micromechanical investigations have gained significant insights into the statistical and spatial distribution of CFC, they still lack the capacity to quantitatively estimate CFC evolution in a sheared granular system. In this paper, an artificial neural network (ANN) based on discrete element method (DEM) simulation data is developed and applied to predict the anisotropy of CFC in an assembly of spherical grains undergoing a biaxial test. Five particle-scale features including particle size, coordination number, x- and y-velocity (i.e., x and y-components of the particle velocity), and spin, which all contain predictive information about the CFC, are used to establish the ANN. The results of the model prediction show that the combined features of particle size and coordination number have a dominating influence on the CFC’s estimation. An excellent model performance manifested in a close match between the rose diagrams of the CFC from the ANN predictions and DEM simulations is obtained with a mean accuracy of about 0.85. This study has shown that machine learning is a promising tool for studying the complex mechanical behaviors of granular materials.

X-Ray Tomography Investigation of Cyclically Sheared Granular Materials.

We perform combined x-ray tomography and shear force measurements on a cyclically sheared granular system with highly transient behaviors, and obtain the evolution of microscopic structures and macroscopic shear force during the shear cycle. We explain the macroscopic behaviors of the system based on microscopic processes, including particle level structural rearrangement and frictional contact variation. Specifically, we show how contact friction can induce large structural fluctuations and cause significant shear dilatancy effect for granular materials, and we also construct an empirical constitutive relationship for the macroscopic shear force.

Effects of interparticle friction on the response of 3D cyclically compressed granular material

We numerically study the effect of inter-particle friction coefficient on the response to cyclical pure shear of spherical particles in three dimensions. We focus on the rotations and translations of grains and look at the spatial distribution of these displacements as well as their probability distribution functions. We find that with increasing friction, the shear band becomes thinner and more pronounced. At low friction, the amplitude of particle rotations is homogeneously distributed in the system and is therefore mostly independent from both the affine and non-affine particle translations. In contrast, at high friction, the rotations are strongly localized in the shear zone. This work shows the importance of studying the effects of inter-particle friction on the response of granular materials to cyclic forcing, both for a better understanding of how rotations correlate to translations in sheared granular systems, and due to the relevance of cyclic forcing for most real-world applications in planetary science and industry.

Plate motion in sheared granular fault system

Plate motion near the fault gouge layer, and the elastic interplay between the gouge layer and the plate under stick-slip conditions, is key to understanding the dynamics of sheared granular fault systems. Here, a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), is used to explicitly simulate a sheared granular gouge fault system. We focus on investigating the influence of normal load, driving shear velocity and plate stiffness on the velocities and displacements in the direction parallel to the shear direction (x-direction) measured at locations on the upper and lower plates just adjacent to the gouge. The simulations show that during slip phases the magnitudes of the measured velocities on the upper and lower plates are proportional to the normal load and may be inversely proportional to the square root of the plate's shear modulus. Whereas, the driving shear velocity does not show distinct influence on the measured velocities. Additionally, large slip velocities are generally associated with large macroscopic friction coefficient drops. For the models subjected to smaller normal loads, larger shear velocities and with stiffer shear plates, the same magnitude of slip velocity could cause a larger drop of macroscopic friction coefficient. During stick phases, the velocities of the upper and lower plates are respectively slightly greater and slightly smaller than half of the driving shear velocity and are both in the same direction of shear. The shear strain rate of the gouge is calculated from this velocity difference between the upper and lower plate during stick phases and thus the gouge effective shear modulus can be calculated. The results show that the gouge effective shear modulus increases proportionally with normal load, while the influence of shear velocity and plate stiffness on gouge effective shear modulus is minor. The simulations address the dynamics of a laboratory-scale fault gouge system and may aid in revealing the complexities of earthquake frictional dynamics.

Fluctuation and self-diffusion research about dry granular materials under shearing

Flow and self-diffusion behaviors of granules in sheared granular systems are a typical study field but still not yet fully grasped because of the complexities and discreteness of granular matter systems. This paper presents a discrete element method-based simulation research of the fluctuation and self-diffusion characteristics of granules in a dense sheared granular system. Simulation results show that the average velocity of granules decreases with the altitude location, which is reverse to the variation of fluctuation velocity. It is noted that the model channel can be classified into “solid-like,” “oscillating” and “fluid-like” region according to the magnitude of shear rate and fluctuation velocity of granules. The self-diffusion of granules is greater in the “solid-like” region, but smaller in the “fluid-like” region. These findings emphasize the importance of research on macroscopic dynamics of granules, such as re-arrangement and self-diffusion of granular matter systems.

Modeling of Stick‐Slip Behavior in Sheared Granular Fault Gouge Using the Combined Finite‐Discrete Element Method

AbstractSheared granular layers undergoing stick‐slip behavior are broadly employed to study the physics and dynamics of earthquakes. Here a two‐dimensional implementation of the combined finite‐discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), is used to explicitly simulate a sheared granular fault system including both gouge and plate, and to investigate the influence of different normal loads on seismic moment, macroscopic friction coefficient, kinetic energy, gouge layer thickness, and recurrence time between slips. In the FDEM model, the deformation of plates and particles is simulated using the FEM formulation while particle‐particle and particle‐plate interactions are modeled using DEM‐derived techniques. The simulated seismic moment distributions are generally consistent with those obtained from the laboratory experiments. In addition, the simulation results demonstrate that with increasing normal load, (i) the kinetic energy of the granular fault system increases, (ii) the gouge layer thickness shows a decreasing trend, and (iii) the macroscopic friction coefficient does not experience much change. Analyses of the slip events reveal that, as the normal load increases, more slip events with large kinetic energy release and longer recurrence time occur, and the magnitude of gouge layer thickness decrease also tends to be larger; while the macroscopic friction coefficient drop decreases. The simulations not only reveal the influence of normal loads on the dynamics of sheared granular fault gouge but also demonstrate the capabilities of FDEM for studying stick‐slip dynamic behavior of granular fault systems.

On continuum modelling of dense inelastic granular flows of relevance for high shear granulation

This article investigates a number of possible formulations of a continuum description for modelling dense inelastic granular flows. The revised Enskog theory (RET) for expressing the granular temperature and formulation of transport coefficients has been used within the continuum framework. The framework assumes particles as inelastic spheres and can describe a granular system at a wide range of volume fractions. The transport coefficients depend on the volume fraction through a modified expression for the radial distribution function. The proposed radial distribution function is based on previous studies on the behaviour of the shear viscosity in which an earlier divergence of the latter compared to the other transport coefficients has been demonstrated for sheared dense granular systems. Our results show that the newly developed radial distribution function maintains the ability of RET to predict the occurrence of instabilities in a homogeneous cooling granular gas. The introduced function also improves predictions for the velocity and volume fraction profiles in a Couette cell dense shear flow. Thus the proposed expression shows promising features in terms of improving predictions for volume fractions relevant in high shear granulators. We have also observed that a different expression may be needed for the densest regions.

Reynolds Pressure and Relaxation in a Sheared Granular System

Reynolds Pressure and Relaxation in a Sheared Granular System

Reynolds Pressure and Relaxation in a Sheared Granular System

We describe experiments that probe the evolution of shear jammed states, occurring for packing fractions [symbol: see text](S) ≤ [symbol: see text] ≤ [symbol: see text] J, for frictional granular disks, where above [symbol: see text]J there are no stress-free static states. We use a novel shear apparatus that avoids the formation of inhomogeneities known as shear bands. This fixed [symbol: see text] system exhibits coupling between the shear strain, γ, and the pressure, P, which we characterize by the "Reynolds pressure" and a "Reynolds coefficient," R([symbol: see text]) = (∂(2)P/∂γ(2))/2. R depends only on [symbol: see text] and diverges as R ~ ([symbol: see text])c - )(α), where [symbol: see text](c) ~/= [symbol: see text](J) and α ~/= -3.3. Under cyclic shear, this system evolves logarithmically slowly towards limit cycle dynamics, which we characterize in terms of pressure relaxation at cycle n: ΔP ~/= -βln (n/n(0)). β depends only on the shear cycle amplitude, suggesting an activated process where β plays a temperaturelike role.

Jet-induced jammed states of granular jet impacts

The impacts of granular jets for both frictional and frictionless grains in two dimensions are numerically investigated. A dense flow with a dead zone emerges during the impact. From our two-dimensional simulation, we evaluate the equations of state and the con- stitutive equations of the flow. The asymptotic divergences of pressure and shear stress similar to the situation near the jamming transition appear for the frictionless case, while their exponents are smaller than those of the sheared granular systems, and are close to the extrapolation from the kinetic theoretical regime. In a similar manner to the jam- ming for frictional grains, the critical density decreases as the friction constant of grains increases. For bi-disperse systems, the effective friction constant defined as the ratio of shear stress to normal stress, monotonically increases from near zero, as the strain rate increases. On the other hand, the effective friction constant has two metastable branches for mono-disperse systems because of the coexistence of a crystallized state and a liquid state.

Granular pressure—temperature relation during regime change in a simple shear state

In a recent study, a regime chart was established for sheared granular systems. For a soft particle system under simple shear, the internal stress showed a range of rate dependency. As the particle concentration increased, the system transitioned from a kinetic gas to a plastic solid. This transition was gradual for low stiffness systems but became more abrupt as the stiffness increased. In this study, the relationship between the granular temperature and pressure is investigated for the same system of particles. The granular temperature is defined as the average kinetic energy per unit volume and the pressure is defined as the trace of the stress tensor. It is found that this pressure-temperature (P-T curve depicts a sharp turn when the system moves away from the kinetic gas regime. However, no signature is found in the P-T relationship in other regimes.

Generalized Green-Kubo relation and integral fluctuation theorem for driven dissipative systems without microscopic time reversibility

We derive the generalized Green-Kubo relation and an integral form of the fluctuation theorem that apply to driven dissipative systems, in which time-reversal symmetry or local detailed balance is broken. Uniformly sheared granular systems and driven inelastic Lorentz-gas model are considered as examples. It is discussed how statistical mechanical theory dealing with nonequilibrium steady-state properties can be constructed for such systems for which equilibrium state does not exist.

Visualization of displacement fields in a sheared granular system

We study experimentally the motion of particles in a wet granular system at the onset of flow. The suspension is density matched and subjected to a uniform confining pressure and uniform shear. Trajectories of the individual particles are visualized in three dimensions using laser sheet imaging. These trajectories reveal a flow field with pressure-dependent dilation and superdiffusive motions around the mean flow. Correlations in the particle displacements are analyzed as a function of applied confining pressure and applied shear. We find correlations with a pressure-dependant correlation length at small strains.

Representation of the Nonequilibrium Steady-State Distribution Function for Sheared Granular Systems

We derive the representation of the nonequilibrium steady-state distribution function which is expressed in terms of the excess free energy production. This representation resembles the one derived recently by Komatsu and Nakagawa [Phys. Rev. Lett. 100 (2008), 030601] resting on the use of microscopic time-reversal symmetry, but our representation applies also to sheared granular systems in which such a symmetry is broken.

Physical test of a particle simulation model in a sheared granular system

We report a detailed comparison of a slow gravity-driven sheared granular flow with a discrete-element simulation performed in the same geometry. In the experiments, grains flow inside a silo with a rectangular cross section and are sheared by a rough boundary on one side and smooth boundaries on the other sides. Individual grain position and motion are measured using a particle index-matching imaging technique where a fluorescent dye is added to the interstitial liquid which has the same refractive index as the glass beads. The simulations use a Cundall-Strack contact model between the grains using contact parameters that have been used in many other previous studies and ignore the hydrodynamic effects of the interstitial liquid. Computations are performed to understand the effect of particle coefficient of friction, elasticity, contact model, and polydispersity on mean flow properties. We then perform a detailed comparison of the particle fluctuation properties as measured by the displacement probability distribution function and the mean square displacement. All in all, our study suggests a high level of quantitative agreement between the simulations and experiments.