本文以垮落带注浆充填应用为研究核心，深入探究了采动覆岩空隙的分布特性、演化机理，以及充填浆体在破碎岩石空隙内的流动与扩散规律。运用理论分析对采空区空间分区长度进行了精确量化，并构建了采空区空隙率分布模型；采用相似模拟试验和数值模拟，进一步揭示了开采过程中覆岩垮落规律与采空区空隙率分布的紧密关联；通过注浆模拟试验研究了垮落带空隙率分布对浆液扩散范围的影响机制；根据现场情况，研究了垮落带邻位注浆充填技术，提出了钻孔布置方式及注浆方案。主要结论如下：

（1）利用理论分析的方法，量化了自然堆积区、载荷影响区和压实稳定区宽度范围；采用薄板理论及“砌体梁”结构将弯曲下沉带至裂隙带未失稳关键层简化为多层叠合的薄板，裂隙带至垮落带破断关键层走向和倾向形成“砌体梁”结构，建立了基于采动覆岩关键层“板-梁”结构的下沉曲面模型。根据该曲面模型计算关键层层间碎胀系数及空隙率分布情况，得到垮落带和裂隙带空隙率分布模型。在球形注浆理论的基础上，基于空隙率分布情况，分析垮落带注浆充填浆液扩散机制。考虑重力影响，使用宾汉流体求解浆液扩散速度，对浆液扩散速度和路径进行了分析。

（2）工作面采空区空间对覆岩的“砌体梁”结构形成影响较大。初次来压时，采空区空间较大，直接顶和基本顶回转空间大，从而导致开切眼侧上覆岩层破断为破碎岩块。由于岩石的碎胀作用，采空区空间被破碎岩石逐渐填满，基本顶以上关键层允许下沉空间相对较小，易形成“砌体梁”结构。

（3）覆岩关键层形成的砌体梁结构影响着采空区空隙。开切眼及工作面附近覆岩离层裂隙发育，空隙率较大，约为7~15%；采空区中部离层裂隙被重新压实，空隙率较小，约为3~5%。采动过程中裂隙带上方空隙空隙率最高达到40%左右；所以注浆充填的主要区域应集中在裂隙带上方形成的离层区域。垮落带开切眼侧自然堆积区岩石破碎程度较高，空隙率从18%被压缩到12%；载荷影响区未完全压实，空隙率为14~10%；工作面侧空隙率受开采影响动态变化，开采结束后，自然堆积区和载荷影响区还未被充分压实，空隙率高达25%；中部压实稳定区碎胀系数较小。开采结束后，注浆充填的主要区域应集中在采空区两侧空隙率较大的区域，优先充填工作面侧。

（4）在煤层回采的过程中，上覆岩层破断下沉，在这个过程中形成了强力链拱，逐步向上拓展，并随着岩层断裂，下方破碎岩石堆积区域重新发育出强力链。在外部载荷的影响下，岩块间的挤压作用和接触力加强，导致上部破碎岩石中强力链的数量和配位数从下至上显著增加后逐渐稳定，同时空隙率显著降低后缓慢减小。开采结束后，模型中部强力链集中的位置，空隙率较低，约为6%~15%；模型两侧强力链较少，空隙率较高，达到35%。

（5）开采结束后的三维物理相似模型中，采空区空隙率分区情况明显，整体呈四周高中间低的盆地型。垮落带开切眼自然堆积区侧最高空隙率达到29.2%，工作面侧约为17%；载荷影响区空隙率约为10%，压实稳定区为7%左右。开展注浆模拟试验。提出了一种基于AHFO的浆液扩散范围监测方法，依据浆液温度与AHFO温度的差异，反演了浆液扩散形态。试验结果表明：采空区浆液扩散半径为椭圆形，采空区自然堆积区的扩散半径大于压实稳定区。使用浆液扩散理论计算浆液在采空区内的扩散半径，通过与注浆模型试验实测结果对比，最大相对误差为19.40%，验证了理论公式的可行性。

（6）以龙王沟煤矿61601工作面为背景，通过理论分析确定了充填关键参数，对注浆钻孔位置进行优化设计，预测了垮落带邻位注浆渗流扩散范围和单孔充填量，得出垮落带高度为72m，走向方向上浆体扩散距离为103m，确定邻位注浆充填的钻孔步距为50m，预测浆体单孔充填量为2.0×10⁵m³。

This dissertation focuses on the application of grouting in goaf areas, delving into the distribution characteristics and evolution mechanisms of overlying rock voids during mining, as well as the flow and diffusion rules of the grout in the voids of fractured rocks. By comprehensively applying theoretical analysis, similar simulation experiments, numerical simulations, grouting simulation tests, and field measurements, it accurately quantifies the spatial zoning length of goaf areas and constructs a model for the distribution of void ratio in goaf areas. The study further reveals the close correlation between the collapse pattern of overlying rocks during mining and the distribution of void ratio in the goaf area, as well as the influence mechanism of the void ratio distribution in the collapse zone on the diffusion of grout. The main conclusions are as follows:

(1) By using theoretical analysis, the widths of natural accumulation areas, load-affected areas, and compaction-stable areas were quantified. The plate theory and "masonry beam" structure were employed to simplify the curved sinking zone to the unsteady key layer of the fracture zone into multilayer composite thin plates, and the direction and inclination of the fracture zone to the breaking key layer of the collapse zone formed a "masonry beam" structure. A sink surface model based on the "plate-beam" structure of key layers affected by mining was established. The bulking coefficient and void ratio distribution between key layers were calculated according to this surface model, leading to the development of void ratio distribution models for the collapse zone and fracture zone. Based on the spherical grouting theory and the void ratio distribution, the diffusion mechanism of grouting in the collapse zone was analyzed. Considering the impact of gravity, the Bingham fluid was used to solve the grout diffusion speed and analyze the diffusion speed and path of the grout.

(2) The "masonry beam" structure of overlying rocks is significantly influenced by the spatial space of the mining face. At the initial pressure, the space in the goaf area is large, allowing the basic roof space to exceed the limit squeezing permissible subsidence between broken blocks, causing the basic roof rock layer on the side of the starting cut to break into fractured rock blocks, becoming a non-articulated roof structure acting on the fallen rock blocks in the goaf area. Due to the bulking action of the rocks, the space in the goaf area is gradually filled with broken rocks. The allowed subsidence space above the basic roof is relatively small, making it easy to form a hinged structure. Hence, the upper overlying rock breakage presents an alternating structure of "cantilever beam - masonry beam".

(3) The development of the fracture zone is primarily controlled by the position of the overlying rock key layers and the deformation, breaking, and unstable patterns of the masonry beam structure formed by them. Lamination fractures near the open-off cut and work face develop with a large void ratio, about 7~15%; the lamination fractures in the middle of the goaf area are re-compacted, with a smaller void ratio, about 3~5%. During mining, the void ratio above the fracture zone can reach up to 40%; therefore, the main area for grouting should be concentrated in the delamination area formed above the fracture zone. The degree of rock fragmentation in the natural accumulation area on the side of the collapse zone's open-off cut is high, with the void ratio being compressed from 18% to 12%; the load-affected area is not fully compacted, with a void ratio of 14~10%; the void ratio on the side of the work face changes dynamically due to mining, and after mining ends, the natural accumulation area and load-affected area are not fully compacted, with a void ratio reaching up to 25%; the bulking coefficient in the middle compaction stable area is smaller. After mining ends, the main area for grouting should be concentrated in areas with higher void ratios on both sides of the goaf area, giving priority to filling the side of the work face.

(4) As the coal seam is recovered, the force chain within the surrounding rock of the mining field will continue to evolve, and the overlying rock layer undergoes a dynamic evolution process of "strong force chain arch formation—expansion—stabilization—breaking". As the overlying rock layer breaks and subsides, the strong force chain redevelops in the area below where broken rocks accumulate. Under external load, the squeezing effect between rock blocks is enhanced, leading to an increase in contact force between rocks. The number of strong force chains on top of the broken rocks increases, with the rock coordination number increasing sharply from bottom to top, then slowly. The void ratio decreases sharply from bottom to top, then slowly. After mining ends, the middle part of the model, where strong force chains are concentrated, has a lower void ratio, about 6%~15%; the sides of the model with fewer strong force chains have a higher void ratio, reaching up to 35%.

(5) After mining ends, the void ratio zoning situation in the three-dimensional physical similar model is obvious, with an overall basin shape with high periphery and low middle. The highest void ratio on the side of the natural accumulation area at the cut eye of the collapse zone reaches 29.2%, and about 17% on the side of the work face; the load-affected area has a void ratio of about 10%, and the compaction-stable area is about 7%. Grouting simulation experiments were conducted. A monitoring method for the grout diffusion range based on AHFO was proposed, and the grout diffusion shape was inferred based on the temperature difference between the grout and AHFO. The experimental results show that the grout diffusion radius in the goaf area is elliptical, with the diffusion radius in the natural accumulation area of the goaf area being larger than that in the compaction-stable area. The grout diffusion radius in the goaf area was calculated using grout diffusion theory, and the maximum relative error compared to the measured results of the grouting model test was 19.40%, verifying the feasibility of the theoretical formula.

(6) Taking the 61601 working face of Longwanggou coal mine as the background, the key filling parameters were determined through theoretical analysis, and the grouting drilling position was optimized and designed. The diffusion range and single hole filling amount of adjacent grouting in the collapse zone were predicted. The height of the collapse zone was 72m, and the diffusion distance of the slurry in the direction of the strike was 103m. The drilling step distance for adjacent grouting filling was determined to be 50m, and the predicted single hole filling amount of the slurry was 2.0×10⁵m³.

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