Simulation of Groundwater Flow Field of Coal Mine Based on Subdomain-Analytic Element Method
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摘要: 为了分析将子域解析元素法应用于煤矿地下水流场模拟的可行性，并探究如何提高此方法的模拟精度，首先推导出了强度非线性变化的高阶线汇的复势表达式，分析了其流量势与流函数的空间分布特征，在此基础上应用python语言构建了基于子域解析元素法的煤矿地下水流场模型并应用于求解某煤矿放水试验后水位分布问题.模拟结果显示，模拟水位与观测孔水位偏差绝对值范围为1.36~5.27 m，模型外边界（实际定水头边界）上的水位接近实际值（900 m），且通过模型外边界（实际隔水边界）的流量近似为零.对模拟原理及模拟结果的分析表明，基于子域解析元素法的煤矿地下水流场模型在全域上满足质量守恒及达西流梯度场，在全域内任意一点的水位可通过该点所处的子域所对应的流量势函数求得，因此应用子域解析元素法进行煤矿地下水流场模拟是可行的，而且将代表模型边界的非线性强度线汇剖分为更短的长度可进一步提高模拟精度.Abstract: In order to analyze the feasibility of applying the subdomain-analytic element method to the simulation of coal mine groundwater flow field, and to explore how to improve the simulation accuracy of this method, complex potential expression of nonlinear density distribution high-order line-sink of analytic element method was derived independently here, and spatial distribution characteristics of values of discharge potential and stream function on line-sink were analyzed. On the basis of that, the flow field model of coal mine was constructed with python language based on subdomains-analytic element method which was used for solving a problem concerning the distribution of head in a coal mine after drainage test. According to the simulation results, the absolute value of the deviation between the simulated heads and the heads of the observation holes ranges from 1.36 m to 5.27 m, and the heads on the outer boundaries of the model (actual constant head boundaries) are close to the actual value (900 m), and the flow rates passing through the outer boundaries of the model (actual impermeable boundaries) approximate zero. The analysis of the simulation principle and simulation results show that the coal mine groundwater flow field model based on the subdomain-analytic element method satisfies the conservation of mass and the gradient field of Darcy flow in the whole area, and the head at any point in the whole area can be determined using the discharge potential function of the subdomain where the point is located in. Therefore, it is feasible to apply the subdomain-analytic element method to simulate the groundwater flow field of coal mine; and the nonlinear density distribution line-sinks representing the model boundaries can be divided into shorter lengths to further improve the accuracy of the simulation.
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图 1 奥灰含水层水流场模型平面图
K为渗透系数；H为含水层厚度；h0为初始平均水位
Fig. 1. Plan view of flow field model in Ordovician limestone aquifer
图 4 子域内边界线汇上流函数值分布
Fig. 4. Values of stream function on inter-domain boundary represented by line-sink
图 5 通过子域内边界线汇各段流量
Fig. 5. Discharge across segments of inter-domain boundary represented by line-sink
图 7 定流量边界线汇上流函数值分布
Fig. 7. Values of stream function on normal flux-specified boundary represented by line-sink
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