Abstract

Doppler laser interferometry is used to measure the transient time between the slow quasi-stationary stage of damage accumulation in rock samples to the ultrafast catastrophic stage of failure as well as the duration of the autocatalytic stage of macroscopic fracture. Small rock samples are tested for compression and three-point bending, and the velocity of displacement of their lateral surfaces is measured up to macroscopic fracture. The surface velocity at the catastrophic stage proves to be three orders of magnitude higher than the average surface velocity at the quasi-stationary stage of damage accumulation. The transient time to catastrophic failure is estimated at 60–100 ms, and the duration of the ultrafast catastrophic failure stage is 15–20 ms for small marble samples. The transient stage is the process of self-organization of individual acts of fracture into the state of self-organized criticality. At this stage, the distribution of individual acts of fracture evolves into power-law distributions. A simple fracture model with power laws is proposed, which is in full agreement with the experimental data. The developed mathematical model is used to calculate fracture of small rock samples, reproducing uniaxial compression and three-point bending tests, as well as fracture in rock masses with mine openings. We also model the process of faulting and fracturing in the mountains of Central Altai, including the foreshock process, main event (the Chuya earthquake of September 27, 2003) and aftershock process. The calculated seismic process fully corresponds to the Gutenberg–Richter recurrence law, and the calculated aftershock process conforms to the Omori law.

中文翻译：

---

从岩样到煤矿不同尺度的灾难性破坏阶段的实验和数值研究

摘要

多普勒激光干涉仪用于测量岩石样品中损伤积累的缓慢准平稳阶段到超快灾难性破坏阶段之间的瞬态时间以及宏观断裂自催化阶段的持续时间。对小岩石样品进行压缩和三点弯曲测试，并测量其侧面的位移速度，直至宏观断裂。灾难阶段的地表速度被证明比损伤积累准静止阶段的平均地表速度高三个数量级。灾难性破坏的瞬态时间估计为 60-100 毫秒，对于小大理石样品，超快灾难性破坏阶段的持续时间为 15-20 毫秒。瞬态阶段是个体行为断裂到自组织临界状态的自组织过程。在这个阶段，个体断裂行为的分布演化为幂律分布。提出了一种具有幂律的简单断裂模型，与实验数据完全吻合。开发的数学模型用于计算小岩样的断裂，再现单轴压缩和三点弯曲试验，以及具有矿井开口的岩体的断裂。我们还模拟了阿尔泰中部山区的断层和压裂过程，包括前震过程、主要事件（2003 年 9 月 27 日楚雅地震）和余震过程。计算出的地震过程完全符合 Gutenberg-Richter 递推定律，