Record-breaking events during the compressive failure of porous materials

Abstract

An accurate understanding of the interplay between random and deterministic processes in generating extreme events is of critical importance in many fields, from forecasting extreme meteorological events to the catastrophic failure of materials and in the Earth. Here we investigate the statistics of record-breaking events in the time series of crackling noise generated by local rupture events during the compressive failure of porous materials. The events are generated by computer simulations of the uniaxial compression of cylindrical samples in a discrete element model of sedimentary rocks that closely resemble those of real experiments. The number of records grows initially as a decelerating power law of the number of events, followed by an acceleration immediately prior to failure. The distribution of the size and lifetime of records are power laws with relatively low exponents. We demonstrate the existence of a characteristic record rank k * , which separates the two regimes of the time evolution. Up to this rank deceleration occurs due to the effect of random disorder. Record breaking then accelerates towards macroscopic failure, when physical interactions leading to spatial and temporal correlations dominate the location and timing of local ruptures. The size distribution of records of different ranks has a universal form independent of the record rank. Subsequences of events that occur between consecutive records are characterized by a power-law size distribution, with an exponent which decreases as failure is approached. High-rank records are preceded by smaller events of increasing size and waiting time between consecutive events and they are followed by a relaxation process. As a reference, surrogate time series are generated by reshuffling the event times. The record statistics of the uncorrelated surrogates agrees very well with the corresponding predictions of independent identically distributed random variables, which confirms that temporal and spatial correlation in the crackling noise is responsible for the observed unique behavior. In principle the results could be used to improve forecasting of catastrophic failure events, if they can be observed reliably in real time.

Fragmentation and shear band formation by slow compression of brittle porous media

“…The model proved to be very successful in reproducing the observed power law statistics of burst sizes, energies, durations, and of the waiting times between consecutive events [18,19]. Most recently we have also analyzed the details of the time series of bursts of the model searching for the record breaking events [20].…”

“…The fault itself develops as a localized shear band formed by multiple fracturing and refracturing both prior to and during slip. To study this problem, recently we have introduced a discrete element model of porous sedimentary rocks which captures the essential ingredients of the materials' microstructure and of the dynamics of breaking [18][19][20].…”

Record statistics of bursts signals the onset of acceleration towards failure

“…The record statistics (RS) of stochastic time series has attracted a great attention due to its relevance for weather, climate and earthquake research [50][51][52][53][54][55] . The RS analysis has proven very successful to reveal trends, correlations, and spatio-temporal clustering of events in complex evolving systems [50][51][52][53][54][55][56][57][58][59] . For fracture processes, here we demonstrate that the waiting time between consecutive record breakings, i.e.…”

Effect of disorder on the spatial structure of damage in slowly compressed porous rocks

“…In our previous studies, the model was used to investigate the uniaxial compression of cylindrical samples focusing on both the time evolution of the fracture process [14,15,20] and on the spatial structure of the emerging damage [21]. We demonstrated that the gradual cracking proceeds in bursts of beam breakings, analogous to sources of acoustic emissions or crackling noise of real experiments.…”