On the basis of the one-dimensional heat conduction–convection equation, a thermal effect model for vertical groundwater migration in the stratified rock mass was established, the equations for temperature distribution in layered strata were deduced, and the impacts of the vertical seepage velocity of groundwater and the thermal conductivity of surrounding rocks on the temperature field distribution in layered strata were analyzed. The proposed model was employed to identify the thermal convection and conduction regions at two temperature-measuring boreholes in coal mines, and the vertical migration velocity of groundwater was obtained through reverse calculation. The results show that the vertical temperature distribution of the layered rock mass is subject to the migration of the geothermal water; the temperature curve of the layered formation is convex when the geothermal water travels upward, but concave when the water moves downward. The temperature distribution in the stratified rock mass is also subject to the thermal conductivity of the rock mass; greater thermal conductivity of the rock mass leads to a larger temperature difference among regions of the rock mass, while weaker thermal conductivity results in a smaller temperature difference. A greater velocity of the vertical migration of geothermal water within the surrounding rock leads to a larger curvature of the temperature curve. The model was applied to a study case, which showed that the model could appropriately describe the variation pattern of the ground temperature in the stratified rock mass, and a comparison between the modeling result and the measured ground temperature distribution revealed a high goodness of fit of the model with the actual situation.

中文翻译：

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地下水垂直迁移对层状岩体温度分布影响的热效应模型及其应用

基于一维热传导-对流方程，建立了层状岩体中地下水垂向运移的热效应模型，推导了层状地层中温度分布的方程，并对垂直渗流速度的影响进行了研究。分析了地下水和围岩的热导率对层状地层温度场分布的影响。利用该模型确定了煤矿两个测温井的热对流和传导区域，并通过反算得到了地下水的垂直运移速度。结果表明，层状岩体的垂直温度分布受地热水迁移的影响。当地热水向上移动时，层状地层的温度曲线呈凸形；当水向下移动时，层状地层的温度曲线呈凹形。分层岩体中的温度分布也受岩体的热导率的影响。岩体的较大的热导率导致岩体各区域之间的温度差较大，而较低的热导率导致较小的温度差。地热水在围岩中的垂直迁移速度越大，温度曲线的曲率越大。将该模型应用于某研究案例，结果表明该模型可以恰当地描述层状岩体中地温的变化规律，