南水北调中线工程穿越多个煤矿采空区，对工程的安全施工与运行造成了严重威胁，因此对煤矿采空区进行注浆加固处理已成为工程迫切需要解决的问题。本文根据注浆浆液的宾汉姆流体特性，建立宾汉姆流体本构模型方程。基于采空区三维几何地质信息模型，提出三维宾汉姆流体k-ε紊流数学模型。针对注浆工程中岩层、断裂带、冒落区、采空区、煤层底板等地质层采用不同的地质参数、孔隙率和阻力系数，对宾汉姆流体浆液在采空区中的紊流扩散进行模拟，实现了宾汉姆流体浆液的采空区多孔分序注浆模拟，并分析了浆液的扩散规律。结果表明：在一定时间范围内，浆液扩散半径和采空区的充填率随时间的增加而增加，但其变化率呈逐渐减少的趋势，并最终趋于零，数值模拟的注浆量与实际注浆量相比误差为11.8%。研究可为采空区注浆的设计与优化提供理论依据与技术支持，对确保南水北调渠道长期安全稳定运行具有重要的理论意义和实践价值。%Multiple coal mine goaf under the South-to-North Water Transfer Project have brought serious threat to the safety of its construction and operation. It becomes an urgent engineering problem to reinforce the coal mine goaf by grouting reinforcement process. According to the Bingham fluid properties, the Bing-ham constitutive equation was established in this paper. Based on the 3-D geometry model with geological information of coal mine goaf, a three-dimensional k-ε turbulence mathematical model considering Bingham liquid character was presented. Different geological parameters, porosity, resistance coefficient are adopted for the different geological layers, such as strata, fault, collapsed zone, goaf, coal floor, and then turbu-lent diffusion law of Bingham fluid in goaf was simulated. According to the grouting hole sequence,sub-se-quence grouting was achieved and the diffusion law of slurry was analyzed. The results show that within a certain time range, diffusion radius and filling rate of goaf increased over time, but a decreasing trend of the change rate was demonstrated and finally the change rate approached to zero. The error of grouting amount between the numerical simulation and the actual situation was 11.8%. The research can provide a theoretical basis and technical support for the goaf grouting design and optimization, which has an impor-tant theoretical and practical value to ensure the long-term security and stability run for the South-to-North Water Transfer Channel.
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