Modeling of Rock Inhomogeneity and Anisotropy by Explicit and Implicit Representation of Microcracks
Modeling of Rock Inhomogeneity and Anisotropy by Explicit and Implicit Representation of Microcracks
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发表时间：
2018-08
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通讯作者：
R. Abedi;P. Clarke
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作者：
R. Abedi;P. Clarke
岩石在动态单轴压缩载荷作用下，由于其脆性和缺乏宏观应力集中点，其断裂模式对微观结构缺陷高度敏感。我们提出了两种不同的方法来模拟岩石微观结构缺陷和不均匀性。在显式实现方法中，将具有一定统计量的微裂纹纳入计算域。在隐式实现方法中，断裂强度值使用威布尔概率分布进行采样。我们使用Mohr-Coulomb破坏准则来定义界面损伤模型中的有效应力。该模型预测的裂纹扩展角度为±φch =±（45−φ/2），相对于压缩载荷方向，其中φ为摩擦角。通过适当的断裂强度各向异性模型，我们证明了岩石最弱面与φch的相互作用。数值结果表明，当采用显式方法时，强度各向异性对断裂模式的影响更大。当最弱面夹角接近±φch时，裂缝密度增大。断裂模拟采用h-自适应异步时空不连续伽辽金（aSDG）方法进行，该方法可以适应任意方向的裂纹扩展。致谢：作者感谢美国国家科学基金会（NSF）、CMMI材料与结构力学（mom）项目资助号1538332和CCF极限可扩展并行（SPX）项目资助号1725555对这项工作的部分支持。
Fracture patterns experienced under a dynamic uniaxial compressive load are highly sensitive to rock microstructural defects due to its brittleness and the absence of macroscopic stress concentration points. We propose two different approaches for modeling rock microstructural defects and inhomogeneity. In the explicit realization approach, microcracks with certain statistics are incorporated in the computational domain. In the implicit realization approach, fracture strength values are sampled using a Weibull probability distribution. We use the Mohr-Coulomb failure criterion to define an effective stress in the context of an interfacial damage model. This model predicts crack propagation at angles ±φch = ±(45 − φ/2) relative to the direction of compressive load, where φ is the friction angle. By using appropriate models for fracture strength anisotropy, we demonstrate the interaction of rock weakest plane and φch. Numerical results demonstrate the greater effect of strength anisotropy on fracture pattern when an explicit approach is employed. In addition, the density of fractures increases as the angle of the weakest planes approaches ±φch. The fracture simulations are performed by an h-adaptive asynchronous spacetime discontinuous Galerkin (aSDG) method that can accommodate crack propagation in any directions. Acknowledgments: The authors gratefully acknowledge partial support for this work via the U.S. National Science Foundation (NSF), CMMI Mechanics of Materials and Structures (MoMS) program grant number 1538332 and CCF Scalable Parallelism in the Extreme (SPX) program grant number 1725555.