Rupture cascades in a discrete element model of a porous sedimentary rock

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 which 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 analyzed for their scaling properties, including the distribution of waiting times between consecutive events. Despite the non-stationary 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 emerge accompanied by spatial clustering.Comment: 5 pages, 4 figure

Do climate models reproduce complexity of observed sea level changes ?

International audienceThe ability of Atmosphere–Ocean General Circulation Models (AOGCMs) to capture the statistical behavior of sea level (SL) fluctuations has been assessed at the local scale. To do so, we have compared scaling behavior of the SL fluctuations simulated in the historical runs of 36 CMIP5 AOGCMs to that in the longest (>100 years) SL records from 23 tides gauges around the globe. The observed SL fluctuations are known to manifest a power-law scaling. We have checked if the SL changes simulated in the AOGCM exhibit the same scaling properties and the long-term correlations as observed in the tide gauge records. We find that the majority of AOGCMs overestimates the scaling of SL fluctuations, particularly in the North Atlantic. Consequently, AOGCMs, routinely used to project regional SL rise, may underestimate the part of the externally driven SL rise, in particular the anthropogenic footprint, in the projections for the 21 st century. AOGCMs overestimate long-term correlations in sea level fluctuations in the North Atlantic The NCAR CESM1-CAM5-historical run gives the best fit to observed sea level scaling CMIP5 AOGCM can mask the part of sea level trend driven by external forcing

Acceleration and localization of subcritical crack growth in a natural composite material

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

Avalanche precursors of failure in hierarchical fuse networks

We study precursors of failure in hierarchical random fuse network models which can be considered as idealizations of hierarchical (bio)materials where fibrous assemblies are held together by multi-level (hierarchical) cross-links. When such structures are loaded towards failure, the patterns of precursory avalanche activity exhibit generic scale invariance: Irrespective of load, precursor activity is characterized by power-law avalanche size distributions without apparent cut-off, with power-law exponents that decrease continuously with increasing load. This failure behavior and the ensuing super-rough crack morphology differ significantly from the findings in non-hierarchical structures

Crack phantoms: localized damage correlations and failure in network models of disordered materials

We study the initiation of failure in network models of disordered materials such as random fuse and spring models, which serve as idealized representations of fracture processes in quasi-two-dimensional, disordered material systems. We consider two different geometries, namely rupture of thin sheets and delamination of thin films, and demonstrate that irrespective of geometry and implementation of the disorder (random failure thresholds versus dilution disorder) failure initiation is associated with the emergence of typical localized correlation structures in the damage patterns. These structures ('crack phantoms') exhibit well-defined characteristic lengths, which relate to the failure stress by scaling relations that are typical for critical crack nuclei in disorder-free materials. We discuss our findings in view of the fundamental nature of failure processes in materials with random microstructural heterogeneity

Impact of internal climate memory on future sea level rise

International audienceEstimating the magnitude of sea level rise (SLR) for the end of 21st century is among the primary goals of current climate research. An important practical aspect of this problem is that any projection of the SLR is obtained with uncertainty, which is partly due to internal variability of the Earth climate system. This internal variability is due to complex non-linear interactions within the Earth climate system and can induce diverse quasi-periodic oscillatory modes and a long-term memory behavior. It has been demonstrated that the interplay of long-term memory fluctuations in sea level changes can be modeled by a power-law process. Therefore, this makes possible the uncertainty estimations in sea level trends caused by the internal variability. The obvious question is whether the long-memory of the internal variability is correctly simulated in climate models. In this study, we (1) analyze the scaling behaviour of the sea level fluctuations projected for the 21st century by the National Center for Atmospheric Research Community Climate System Model (NCAR-CCSM) and (2) compare the uncertainties in predicated sea level changes obtained from a NCAR-CCSM multi-member ensemble simulations with estimates derived from the Lennartz-Bunde statistics for the power-law processes

Time evolution of damage due to environmentally assisted aging in a fiber bundle model

Damage growth in composite materials is a complex process which is of interest in many fields of science and engineering. We consider this problem in a fiber bundle model where fibers undergo an aging process due to the accumulation of damage driven by the locally acting stress in a chemically active environment. By subjecting the bundle to a constant external load, fibers fail either when the load on them exceeds their individual intrinsic strength or when the accumulated internal damage exceeds a random threshold. We analyze the time evolution of the breaking process under low external loads where aging of fibers dominates. In the mean field limit, we show analytically that the aging system continuously accelerates in a way which can be characterized by an inverse power law of the event rate with a singularity that defines a failure time. The exponent is not universal; it depends on the details of the aging process. For localized load sharing, a more complex damage process emerges which is dominated by distinct spatial regions of the system with different degrees of stress concentration. Analytical calculations revealed that the final acceleration to global failure is preceded by a stationary accumulation of damage. When the disorder is strong, the accelerating phase has the same functional behavior as in the mean field limit. The analytical results are verified by computer simulations

Uncertainties in Future Regional Sea Level Trends: How to Deal with the Internal Climate Variability?

International audienceToday, the Climate models (CM) are the main tools for forecasting sea level rise (SLR) at global and regional scales. The CM forecasts are accompanied by inherent uncertainties. Understanding and reducing these uncertainties is becoming a matter of increasing urgency in order to provide robust estimates of SLR impact on coastal societies, which need sustainable choices of climate adaptation strategy. These CM uncertainties are linked to structural model formulation, initial conditions, emission scenario and internal variability. The internal variability is due to complex non-linear interactions within the Earth Climate System and can induce diverse quasi-periodic oscillatory modes and long-term persistences. To quantify the effects of internal variability, most studies used multi-model ensembles or sea level projections from a single model ran with perturbed initial conditions. However, large ensembles are not generally available, or too small, and computationally expensive. In this study, we use a power-law scaling of sea level fluctuations, as observed in many other geophysical signals and natural systems, which can be used to characterize the internal climate variability. From this specific statistical framework, we (1) use the pre-industrial control run of the National Center for Atmospheric Research Community Climate System Model (NCAR-CCSM) to test the robustness of the power-law scaling hypothesis; (2) employ the power-law statistics as a tool for assessing the spread of regional sea level projections due to the internal climate variability for the 21st century NCAR-CCSM; (3) compare the uncertainties in predicted sea level changes obtained from a NCAR-CCSM multi-member ensemble simulations with estimates derived for power-law processes, and (4) explore the sensitivity of spatial patterns of the internal variability and its effects on regional sea level projections