An accurate and reliable mathematical model for water inrush can help ensure operational safety in coal mines. In this study, a numerical model for water inrush caused by collapsed columns that couples mechanical rock deformation with flow in porous media based on a fractal treelike fracture network was developed. In particular, the proposed model considers collapsed columns and mining damage zones as fractal dual-porosity media. The model incorporates Darcy’s law, the Brinkman equation, and the Navier–Stokes equation to govern the groundwater flow. The Brinkman equation was adopted to simulate the groundwater flow in collapsed columns, for which the non-Darcy coefficient can be derived based on damage criteria for the fracture zone. To simulate the dynamics of water inrush in collapsed columns, the finite element method was used to solve the governing equations for the groundwater flow, solid mechanics, and rock damage. The proposed model was validated against two sets of field data, and the results showed that dynamic changes in the non-Darcy coefficient could be used to identify the occurrence of water inrush, which can be employed to improve mining safety.

中文翻译：

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分形树状裂缝网络模型，用于在矿井水从塌陷柱涌入过程中水力和机械引起的非达西系数动态变化

准确可靠的突水数学模型有助于保障煤矿安全运行。在这项研究中，基于分形树状裂缝网络，开发了一种由倒塌柱引起的突水数值模型，该模型将机械岩石变形与多孔介质中的流动耦合。特别是，所提出的模型将倒塌柱和采矿损伤区视为分形双孔隙度介质。该模型结合了达西定律、布林克曼方程和纳维-斯托克斯方程来控制地下水流。采用布林克曼方程模拟倒塌柱中的地下水流动，根据断裂带的破坏准则可以推导出非达西系数。为了模拟倒塌柱中的突水动力学，有限元法用于求解地下水流动、固体力学和岩石损伤的控制方程。该模型通过两组现场数据进行了验证，结果表明，非达西系数的动态变化可用于识别突水的发生，可用于提高采矿安全性。