Variability in the power-law distributions of rupture events
Variability in the power-law distributions of rupture events
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DOI：
10.1140/epjst/e2012-01571-9
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发表时间：
2012-05-01
影响因子：
2.8
通讯作者：
Amitrano, D.
中科院分区：
文献类型：
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作者：
Amitrano, D.
观察到与脆性材料变形相关的破裂事件（如裂纹扩展或沿断层滑动）服从幂律分布。这在从实验室样品到地壳的各种尺度、各种材料和各种加载模式下得到了验证。除了声称这是异质介质变形的普遍特征之外，还在指数和尾部形状中观察到空间和时间变化。这些对于通过小事件预测大事件的能力和可靠性具有相当大的影响。人们越来越有兴趣确定造成这些变化的因素。在这项工作中，我们首先提出了不同尺度的观测结果（实验室测试、现场实验、滑坡、采矿诱发的地震活动、地壳地震），表明破裂事件大小分布的斜率和尾部形状都存在很大的变化。这次审查使我们能够确定这些变化的潜在解释（不正确的统计方法、异质性、应力、脆性/延性转变、有限尺寸效应、接近失效）。还绘制了与临界点理论的可能联系，表明考虑到临界点的距离，它能够解释部分观察到的变化。通过渐进式失效的数值模拟，我们研究了机械性能对幂律分布的作用。模拟结果与从延展性到脆性的各种宏观行为的临界点理论一致，为理解破裂现象中观察到的幂律变异性提供了统一的框架。
Rupture events, as the propagation of cracks or the sliding along faults, associated with the deformation of brittle materials are observed to obey power-law distributions. This is verified at scales ranging from laboratory samples to the Earth's crust, for various materials and under various loading modes. Besides the claim that this is a universal characteristic of the deformation of heterogeneous media, spatial and temporal variations are observed in the exponent and tail-shape. These have considerable implications for the ability and the reliability of forecasting large events from smaller ones. There is a growing interest in identifying the factors responsible for these variations. In this work, we first present observations at various scales (laboratory tests, field experiments, landslides, mining induced seismicity, crustal Earthquakes) showing that substantial variations exist in both the slope and the tail-shape of the rupture event size distribution. This review allows us to identify potential explanations for these variations (incorrect statistical methods, heterogeneity, stress, brittle/ductile transition, finite size effects, proximity to the failure). A possible link with the critical point theory is also drawn showing that it is able to explain a part of the observed variations considering the distance to the critical point. Using numerical simulations of progressive failure we investigate the role of mechanical properties on the power-law distributions. The results of simulations agree with the critical point theory for various macroscopic behaviors ranging from ductility to brittleness providing a unified framework for the understanding of power-law variability observed in rupture phenomena.