This study presents a phase field model for brittle fracture in fluid-infiltrating vuggy porous media. While the state-of-the-art in hydraulic phase field fracture considers Darcian fracture flow with enhanced permeability along the crack, in this study, the phase field not only acts as a damage variable that provides diffuse representation of cracks or cavities, but also acts as an indicator function that separates the domain into two regions where fluid flows are governed by Stokes and Darcy equations, respectively. Since the phase field and its gradient can be respectively regarded as smooth approximations of the Heaviside function and Dirac delta function, our new approach is capable of imposing interfacial transmissibility conditions without explicit interface parametrizations. In addition, the interaction between solid and fluid constituents is modeled by adopting the concept of mixture theory, where the fluid velocities in Stokes and Darcy regions are considered as relative measures compared to the solid motion. This model is particularly attractive for coupled flow analysis in geological materials with complex microstructures undergoing brittle fracture often encountered in energy geotechnics problems, since it completely eliminates the needs to generate specific enrichment function, integration scheme, or meshing algorithm tailored for complex geological features.

中文翻译：

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具有演化 Beavers-Joseph-Saffman 条件的流体渗透多孔介质的浸入相场破裂模型

本研究提出了流体渗透多孔多孔介质中脆性断裂的相场模型。虽然水力相场压裂的最新技术考虑了沿裂缝渗透率增强的达西裂缝流，但在本研究中，相场不仅充当提供裂缝或空洞的扩散表示的损伤变量，而且作为一个指示函数，将域分为两个区域，其中流体流动分别由 Stokes 和 Darcy 方程控制。由于相场及其梯度可以分别被视为 Heaviside 函数和 Dirac delta 函数的平滑近似，我们的新方法能够在没有明确界面参数化的情况下施加界面传输条件。此外，固体和流体成分之间的相互作用通过采用混合理论的概念进行建模，其中斯托克斯和达西区域的流体速度被视为与固体运动相比的相对量度。该模型对于能量岩土工程中经常遇到的具有脆性断裂的复杂微观结构的地质材料的耦合流分析特别有吸引力，因为它完全消除了生成特定富集函数、集成方案或为复杂地质特征量身定制的网格算法的需要。