Abstract This paper presents a model to reveal the heat transfer mechanism and simulate the heat-flow coupling process in fractured rock masses. Specifically, effects of fracture density, roughness, and percolation on heat-flow coupling are investigated systematically. The fractured rock masses are composed of a discrete fracture network and a rock matrix. Regarding the mesh discretisation for finite element analysis, the rock matrix is discretised into three-dimensional (3D) solid elements, whereas the discrete fractures are modelled by zero-thickness elements. Fracture and matrix elements share the same nodes. Considering the effect of temperature on fluid density and dynamic viscosity, a heat-flow coupled model of fractured rock masses is established with an embedded 3D fracture network. The reliability of the model is verified by comparing it with the analytical solution of a two-dimensional single-fracture heat-flow coupling problem. The effects of fracture density and diameter on percolation probability are studied based on Monte-Carlo tests with each group for 10,000 times. Finally, numerical samples of the 3D discrete fracture network with different geometric parameters are generated to characterise fractured rock masses, and heat-flow coupling numerical simulation is conducted simultaneously. Results show that the percolation of the fracture network is the decisive factor affecting heat-flow coupling. The average outlet flow rate of the percolation network under the same fracture density is much larger than that of the nonpercolation fracture network, which results in a more rapid decrease in the outlet temperature. Other factors such as fracture roughness are also investigated. It is discovered that the effect of fracture roughness on heat-flow coupling is almost negligible for the nonpercolation fracture network model.

中文翻译：

---

裂缝密度、粗糙度和裂缝网络渗流对嵌入三维裂缝网络的热岩体热流耦合的影响

摘要 本文提出了一个模型来揭示裂隙岩体中的传热机制并模拟热流耦合过程。具体而言，系统研究了裂缝密度、粗糙度和渗流对热流耦合的影响。裂隙岩体由离散的裂隙网络和岩石基质组成。关于有限元分析的网格离散化，岩石矩阵被离散化为三维 (3D) 实体元素，而离散裂缝则由零厚度元素建模。断裂和矩阵元素共享相同的节点。考虑温度对流体密度和动力粘度的影响，利用嵌入的3D裂缝网络建立了裂隙岩体的热流耦合模型。通过与二维单裂缝热流耦合问题解析解的对比验证了模型的可靠性。对每组进行10000次蒙特卡罗试验，研究裂缝密度和直径对渗流概率的影响。最后，生成具有不同几何参数的三维离散裂缝网络的数值样本来表征裂缝岩体，同时进行热流耦合数值模拟。结果表明，裂缝网络的渗流是影响热流耦合的决定性因素。相同裂缝密度下渗流网络的平均出口流量远大于非渗流裂缝网络，导致出口温度下降更快。还研究了其他因素，例如断裂粗糙度。结果表明，对于非渗流裂缝网络模型，裂缝粗糙度对热流耦合的影响几乎可以忽略不计。