We investigate the scaling properties of the sources of crackling noise in a fully dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly sized spherical particles that are then connected by breakable beams. Loading at a constant strain rate the cohesive elements fail, and the resulting stress transfer produces sudden bursts of correlated failures, directly analogous to the sources of acoustic emissions in real experiments. The source size, energy, and duration can all be quantified for an individual event, and the population can be analyzed for its scaling properties, including the distribution of waiting times between consecutive events. Despite the nonstationary loading, the results are all characterized by power-law distributions over a broad range of scales in agreement with experiments. As failure is approached, temporal correlation of events emerges accompanied by spatial clustering. DOI: 10.1103/PhysRevLett.112.065501 PACS numbers: 61.43.Gt, 46.50.+a, 89.75.Da, 91.60.Ba Understanding the processes that lead to catastrophic failure of porous granular media is an important problem in a wide variety of applications, notably in Earth science and engineering [1][2][3][4][5][6][7][8]. Such failure is often preceded by detectable changes in mechanical properties (stress and strain) and in geophysical signals (elastic wave velocity, electrical conductivity, and acoustic emissions) measured remotely at the sample boundary [9]. In particular, acoustic emissions result from sources of internal damage due to sudden local dislocations in the form of tensile or shear microcracks whose origin time, location, orientation, duration, and magnitude can all be inferred from the radiated wave train [10]. Typically, only a very small proportion of the microcracks revealed by destructive thin sectioning after the test result in detectable acoustic emissions [11]. As a consequence, experimental data provide only limited insight into the complexity of the microscopic processes at work prior to failure, notably the probability distributions of the relevant parameters, their scaling properties, and their population dynamics.Theoretical approaches to the dynamics and statistics of rupture cascades have typically been based on stochastic fracture models comprising lattices of springs [12], beams [13,14], fuses [15,16], or fibers [17][18][19]. However, such lattice models involve a strong simplification of the material microstructure and the inhomogeneous stress field. For example, macroscopic laws of damage for cohesive elements are often implemented at the mesoscopic scale on a regular two-dimensional grid, avoiding the truly threedimensional microstructure of real porous media, and often using power-law rheology as an input. Here, we adopt a discrete element modeling (DEM) approach that relaxes all of these restrictions and allows a realistic investigation of the emergent properties of the dynamics, including the temporal and spatial...

We investigate the approach to catastrophic failure in a model porous granular material undergoing uniaxial compression. A discrete element computational model is used to simulate both the microstructure of the material and the complex dynamics and feedbacks involved in local fracturing and the production of crackling noise. Under strain-controlled loading, microcracks initially nucleate in an uncorrelated way all over the sample. As loading proceeds the damage localizes into a narrow damage band inclined at 30°-45° to the load direction. Inside the damage band the material is crushed into a poorly sorted mixture of mainly fine powder hosting some larger fragments. The mass probability density distribution of particles in the damage zone is a power law of exponent 2.1, similar to a value of 1.87 inferred from observations of the length distribution of wear products (gouge) in natural and laboratory faults. Dynamic bursts of radiated energy, analogous to acoustic emissions observed in laboratory experiments on porous sedimentary rocks, are identified as correlated trails or cascades of local ruptures that emerge from the stress redistribution process. As the system approaches macroscopic failure consecutive bursts become progressively more correlated. Their size distribution is also a power law, with an equivalent Gutenberg-Richter b value of 1.22 averaged over the whole test, ranging from 3 to 0.5 at the time of failure, all similar to those observed in laboratory tests on granular sandstone samples. The formation of the damage band itself is marked by a decrease in the average distance between consecutive bursts and an emergent power-law correlation integral of event locations with a correlation dimension of 2.55, also similar to those observed in the laboratory (between 2.75 and 2.25).

Catastrophic failure of natural and engineered materials is often preceded by an acceleration and localization of damage that can be observed indirectly from acoustic emissions (AE) generated by the nucleation and growth of microcracks. In this paper we present a detailed investigation of the statistical properties and spatiotemporal characteristics of AE signals generated during triaxial compression of a sandstone sample. We demonstrate that the AE event amplitudes and interevent times are characterized by scaling distributions with shapes that remain invariant during most of the loading sequence. Localization of the AE activity on an incipient fault plane is associated with growth in AE rate in the form of a time-reversed Omori law with an exponent near 1. The experimental findings are interpreted using a model that assumes scale-invariant growth of the dominating crack or fault zone, consistent with the Dugdale-Barenblatt "process zone" model. We determine formal relationships between fault size, fault growth rate, and AE event rate, which are found to be consistent with the experimental observations. From these relations, we conclude that relatively slow growth of a subcritical fault may be associated with a significantly more rapid increase of the AE rate and that monitoring AE rate may therefore provide more reliable predictors of incipient failure than direct monitoring of the growing fault.