大规模高强度回采和深部开采常导致顶部裂隙煤岩体失稳、漏风及其次生灾害。钻孔注浆是封堵裂隙和加固煤岩体的主要手段之一。由于煤岩裂隙高位注浆研究相对滞后，井下高位注浆施工设计缺少足够的依据。为探究煤岩裂隙高位注浆浆液扩散规律，以任意倾斜有限边界的光滑平板裂隙和宾汉流体为研究对象，建立裂隙高位注浆扩散数学模型并进行数值模拟求解，分析不同裂隙倾角和注浆速率下浆液在裂隙流动过程中的扩散锋面、流量分配及压力场变化规律；在此基础上，建立浆液高位流动数学模型，并推导恒定注浆速率工况下的解析解。研究结果表明：根据扩散锋面的演变规律，浆液流动过程可分为自由扩散阶段、过渡阶段和受限堆积阶段3个阶段。裂隙倾角对高位扩散距离的影响程度随着流动阶段的演化逐渐减小，注浆流速对高位扩散距离的影响程度随着流动阶段的演化逐渐增大。过大的裂隙倾角加大了高位流量的损耗并加快了流动阶段的转变，而过大的注浆速率减缓了高位流量的损耗并加快了流动阶段的转变。注浆速率和裂隙倾角的增大均会导致注浆压力增加，且在浆液进入受限堆积阶段后注浆压力发生突变。以高位流动扩散形态的等效圆半径临界状态为界，高位流动可划分为扩散阶段与堆积阶段，不同阶段内反演得出的等效圆心角与注浆速率、裂隙倾角和注浆时间具有较好的相关性。根据对比分析结果，浆液高位流动数学模型中相对误差低于20％的样本占97％，相对误差低于10％的样本占78.4％，表明浆液高位流动数学模型具有一定的合理性。浆液在不同时间段内向高位裂隙深部扩散的范围受到裂隙边界影响，只有当底部裂隙空间被填充完毕后浆液才会在裂隙边界的支撑下向深部堆积，因此在现场高位注浆设计时应先探明裂隙区域的边界范围。针对上覆煤岩表层区域范围的裂隙封堵时可采用较低的注浆速率以延长自由扩散阶段时长，实现底部裂隙空间的快速封堵。对煤岩裂隙深部区域进行注浆充填时可先使用较高的注浆速率进行注浆，当压力表发生突变后表明浆液已进入受限堆积阶段，此时可降低注浆速率，使注浆压力控制在安全可控范围内。

The safety risk of top fractured coal and rock mass is caused by large-scale and high-intensity mining and deep mining.Drilling grouting is one of the main methods used to seal fractures and strengthen coal and rock mass.Due to the relatively less research on the theory of high-position grouting for fractures, the design of high-position grouting lacks sufficient theoretical basis.In order to explore the diffusion law of high-position grouting slurry in coal and rock fractures, the smooth plate fractures with arbitrarily inclined finite boundaries and Bingham fluids were taken as the research objects, and the mathematical model of high-position grouting diffusion in fractures was established.The ANSYS FLUENT numerical software was used to numerically solve the mathematical model.The diffusion front, flow distribution and pressure field variation of slurry in the process of fracture flow under different fracture inclination angles and grouting rates were studied.Based on this, the mathematical model of slurry high-position flow was established, and the analytical solution under the condition of constant grouting rate was derived.The research shows that based on the evolution law of the diffusion front, the flow process can be divided into three stages: the free diffusion stage, the transition stage and the restricted accumulation stage.The influence of the fracture dip angle on the high-position diffusion distance gradually decreases with the evolution of the flow stage, and the influence of the grouting flow rate on the high-position diffusion distance gradually increases with the evolution of the flow stage.Excessive fracture inclination increases the loss of high-position flow and accelerates the transition of flow stage, while excessive grouting rate slows down the loss of high-position flow and accelerates the transition of flow stage.The increase of grouting rate and fracture inclination will lead to the increase of grouting pressure, and the grouting pressure changes abruptly after the slurry enters the restricted accumulation stage.The high-position flow can be divided into the diffusion stage and the accumulation stage based on the critical state of the equivalent circle radius of the high-position flow diffusion form.The equivalent central angle obtained by inversion in different stages has an excellent correlation with the grouting rate, crack inclination angle and grouting time.After comparing with the calculation results of the numerical model, it is concluded that the samples with a relative error of less than 20% in the mathematical model of slurry high-position flow accounts for 97%, and the samples with a relative error of less than 10% accounts for 78.4%.The mathematical model of slurry high-position flow has been proved to have certain rationality.The scope of the slurry spreading to the deep part of high-position fractures in different time periods is affected by the fracture boundary.Only when the bottom fracture space is filled will the slurry accumulate to the deep part under the support of the fracture boundary.Therefore, when designing high-position grouting on site, the boundary extent of the fractured area should be identified.A lower grouting rate can be used to extend the duration of the free diffusion stage when plugging the cracks in the surface area of the overlying coal and rock to achieve rapid sealing of the bottom crack space.When grouting and filling the deep area of coal-rock fracture, a higher grouting rate can be used first.When the pressure gauge changes abruptly, it indicates that the grout has entered the limited accumulation stage.At this time, the grouting rate can be reduced to control the grouting pressure within a safe and controllable range.

1 煤岩裂隙高位注浆理论

   1.1 注浆工艺

   1.2 浆液流变方程

2 裂隙高位注浆数值模拟

   2.1 数值模型建立

   2.2 模拟结果及分析

3 浆液高位流动数学模型

   3.1 模型求解

   3.2 模型验证

   3.3 工程意义

4 结论