为研究底板加固中浆液充填套管对底板岩层变形影响，以套管为主要研究对象，建立采动作用下浆液充填套管在底板岩层中的力学作用模型，理论分析浆液充填套管的应力分布和作用机制并进行验证。将采空区四周支承压力分区，根据集中力作用下半空间体内应力解，通过角点法积分得到矩形基底三角形分布支承压力角点下的一点应力状态，并运用辅助线法和叠加法得到了采空区下方底板岩层中任一点的空间应力分布。然后，基于浆液充填套管破断形态和抗弯刚度，结合采动作用下底板岩层变形破坏特征及套管布置方式，建立以浆液充填套管为中心的套管与岩层耦合作用力学模型，阐明了弹塑性极限平衡条件下浆液充填套管的空间受力特征及对底板岩层变形影响机制，得到了浆液充填套管在准破坏区界点处的弯矩公式和基于抗弯刚度和许用应力的套管容许最大变形公式。最后，根据工程实例建立数值模型，计算结果表明轴向上套管垂向位移形态以破坏区为界分为2段，破坏区内套管位移较大，套管位移形态阐明套管发生弯曲变形过程。施加套管时监测点位移变形量小于未施加套管时的变形量，且套管长度越大变形量越小，验证了浆液充填套管具有抵抗岩层变形的作用。数值计算结果与理论分析相符，组合浆液充填套管能够提高底板岩层抵抗变形的性能。

In order to study the influence mechanism of casing pipes filled with slurry on the deformation of rock strata in coal seam floor,the spatial stress model of grouting reinforced casing pipes in floor rock under distributed abutment pressure is established,and the influence mechanism of casing pipes filled with slurry on surrounding rock is theoretically deduced,and the numerical verification is carried out.According to the stress solution in half space under concentrated force,the stress state of any point under the corner of the abutment pressure zone is obtained by integration and corner method.The spatial stress state of any point of the casing pipes in the floor rock below the goaf is obtained by superposition method.Based on the bending rigidity and fracture form of casing pipes,combined with the deformation characteristics of floor strata and casing pipes layout under mining conditions,the stress model centered on casing pipes filled with slurry is established.The deformation characteristics of strata and casing pipes stress characteristics under elastic plastic limit equilibrium conditions are analyzed,and the influence mechanism of casing pipes on the deformation of strata in the failure zone is clarified.The theoretical formula of bending moment and the allowable deformation formula are obtained based on the bending stiffness and allowable stress of casing pipes.Finally,the numerical model is established according to the example of grouting engineering in the floor.The results show that the vertical displacement form of the casing pipes along the axis can be divided into two sections with the failure area as the boundary,and the casing pipes displacement in the failure section is larger.The distribution law of the axial displacement of the casing pipe is consistent with the theoretical analysis,and the process of the casing pipe bending deformation is clarified.When the casing pipes is applied,the displacement and deformation of the monitoring point is less than that when the casing pipes is not applied,and the larger the casing pipes length,the smaller the deformation.The numerical results are consistent with the theoretical analysis,and the group of slurry filling casing pipes can improve the deformation resistance of floor rock.

1 浆液充填套管抗弯性能与破断形态

   1.1 抗弯性能分析

   1.2 套管布置与破断形态

2 分布支承压力作用下套管的空间应力求解

   2.1 分布支承压力与套管受力模型

   2.2 空间应力求解

   2.3 空间中套管上点N正应力和切应力

   2.4 浆液充填套管力学作用机制

3 套管对煤层底板岩体变形影响的数值分析

   3.1 数值模型

   3.2 模拟结果分析

4 注浆工程应用

5 结论