Abstract The heterogeneity of natural rock affects its fracture behaviour resulting in a variation of rock strength. To investigate the sensitivity of damage response and failure strength across rock samples numerical simulations are performed with random realizations of the Young’s modulus. As a test case, we consider a rock specimen with a pre-existing 3-D surface flaw under uniaxial compression. To test the sensitivity of the damage response due to material heterogeneity for specific geometrical configurations Young’s modulus is varied at the mesoscale using different randomized distributions while keeping the bulk material properties constant at the macroscale. The study shows that in general, the standard deviation is independent from geometrical parameters of initial fracture, but deviation increases when the orientations of the initial flaw and of the external loading are more aligned. In all cases, the exact fracture path displays some variability and in particular for cases with a high degree of heterogeneity some caution must be used when interpreting fracture patterns from a limited number of samples. As a consequence deviation of damage patterns generated from numerical models when compared to experimental results can confidently be attributed to the particular realizations of the heterogeneity present in the real and numerical sample.

中文翻译：

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单轴加载下包含预先存在的 3-D 表面缺陷的砂岩试样中存在的材料异质性的损伤响应和断裂路径的敏感性

摘要 天然岩石的非均质性影响其断裂行为，导致岩石强度发生变化。为了研究岩石样品的损伤响应和破坏强度的敏感性，通过杨氏模量的随机实现进行数值模拟。作为测试案例，我们考虑在单轴压缩下具有预先存在的 3-D 表面缺陷的岩石试样。为了测试由于特定几何配置的材料异质性引起的损伤响应的敏感性，杨氏模量在中尺度上使用不同的随机分布而变化，同时在宏观尺度上保持体材料特性不变。研究表明，一般情况下，标准偏差与初始断裂的几何参数无关，但是当初始缺陷的方向和外部载荷的方向更加一致时，偏差会增加。在所有情况下，确切的裂缝路径都显示出一些可变性，特别是对于具有高度异质性的情况，在从有限数量的样本中解释裂缝模式时必须谨慎。因此，与实验结果相比，数值模型产生的损伤模式的偏差可以自信地归因于真实和数值样本中存在的异质性的特定实现。