This paper is aimed at the inverted arch support instability of track roadway with mining level +1100 m in Liuyuanzi Coal Mine. By means of field investigation, theoretical analysis, numerical calculation, and engineering practice, the instability reasons of inverted arch structure are expounded, the mechanical mechanism of instability of inverted arch structure is revealed, and the “sliding-rotating beam” for the instability of inverted arch structure is put forward. Based on Fenner’s formula and mechanics principle, the equilibrium equation of “sliding-rotating beam” is given. The results show the following: Firstly, the insufficient stiffness at the joint of the inverted arch structure and the U-shaped steel support on the floor is the key reason for the floor instability. Secondly, when the action stress of the “sliding-rotating beam” is less than the critical value, three kinds of instability modes of the inverted arch structure may occur, that is, sliding upward, rotating upward, or sliding-rotating upward. Each instability criterion and critical value are also different. Considering the axisymmetric condition, the critical value calculation formula of the three modes can be simplified into one formula. Thirdly, the equivalent friction factor restricts the stability of the “sliding-rotating beam,” and there is a “breaking point.” The relationship between the equivalent friction factor and the action stress of the “sliding-rotating beam” is “class hyperbola.” When the equivalent friction factor is greater than the “breaking point value,” the “sliding-rotating beam” may remain stable. Moreover, with the increase of equivalent friction factor, the action stress required for the stability of the “sliding-rotating beam” is smaller, and it tends to be more stable. The breaking point value of equivalent friction factor is 18.6. Finally, 36U-shaped steel round frame with bolt-mesh-shotcrete-combined support is applied to improve the equivalent friction factor and the foot stiffness of U-shaped support in roadway. After two months of on-site implementation, the floor heave was reduced by 69.1%. In conclusion, the theoretical analysis is correct and the control method is effective.

中文翻译：

---

软底板巷道U形钢反拱支护的稳定机理及修复方法

本文针对柳园子煤矿+1100 m采空区轨道巷道拱拱支护失稳问题。通过现场调查，理论分析，数值计算和工程实践，阐述了倒拱结构失稳的原因，揭示了倒拱结构失稳的力学机理，并为倒拱结构的失稳提供了“旋转旋转梁”。提出了倒拱结构。根据芬纳公式和力学原理，给出了“旋转梁”的平衡方程。结果表明：首先，倒拱结构与地板U型钢支撑处的结合处刚度不足是导致地板失稳的主要原因。其次，当“滑动旋转梁”的作用应力小于临界值时，会发生倒拱结构的三种失稳模式，即向上滑动，向上旋转或向上滑动旋转。每个不稳定标准和临界值也不同。考虑轴对称条件，可以将三种模式的临界值计算公式简化为一个公式。第三，等效摩擦系数限制了“滑动旋转梁”的稳定性，并且存在“断裂点”。等效摩擦系数与“滑动旋转梁”的作用应力之间的关系为“双曲线”。当等效摩擦系数大于“断裂点值”时，“滑动旋转梁”可能保持稳定。此外，随着等效摩擦系数的增加，“旋转旋转梁”的稳定性所需的作用应力较小，并且趋于更稳定。当量摩擦因数的折点值为18.6。最后，采用36U型钢网架结合螺栓-喷浆混凝土组合支护，以提高巷道U形支护的等效摩擦系数和支脚刚度。经过两个月的现场实施，地面起伏减少了69.1％。总之，理论分析是正确的，控制方法是有效的。采用36U型钢网架结合螺栓-喷混凝土组合支架，提高巷道U形支架的当量摩擦系数和支脚刚度。经过两个月的现场实施，地面起伏减少了69.1％。总之，理论分析是正确的，控制方法是有效的。采用36U型钢网架结合螺栓-喷混凝土组合支架，提高巷道U形支架的当量摩擦系数和支脚刚度。经过两个月的现场实施，地面起伏减少了69.1％。总之，理论分析是正确的，控制方法是有效的。