以东升庙矿孤立大型采空区围岩大面积垮落引发动力冲击灾害隐患为研究背景,应用空气动力学理论、能量守恒理论建立了特大型垮落岩体-空气-围岩耦合冲击力学模型,应用冲击基础理论建立了垫层厚度指数型冲击力计算公式,应用材料力学理论导出矿柱在冲击载荷下内部最大拉应力、最大剪应力、最大挠度计算公式,从经济节约、安全有效角度出发,进一步基于理论导出公式量化研究了东升庙铜矿采空区缓冲垫层合理厚度,并应用FLAC3D数值模拟计算结果对理论结果的正确性加以验证。结果表明:(1)考虑压缩空气做功、围岩摩擦力做功的影响,东升庙矿采空区发生大面积垮落冒落体滚动到采空区底部的最大冲击速度为30.99 m·s-1;(2)冲击力与矿柱内应力均随垫层厚度增加而减小,垫层随其厚度增加缓冲效应逐渐减弱,即垫层厚度增大到一定值,几乎不产生缓冲效应;(3)矿柱简化为简支梁相比固支梁而言,其内部最大拉应力、最大剪应力、最大挠度与数值模拟求解结果比较接近,综合分析最佳垫层厚度为18 m。
The research background is the hidden danger of dynamic impact disaster caused by large-scale collapse of surrounding rock in the isolated large goaf area of Dongshengmiao Mine, a coupled impacting mechanical model related to a caving rock-air-surrounding rock system is established by using the aerodynamic theory and the energy conservation theory. An exponential relationship between cushion thickness and impacting force is formed by applying several theoretical methods. Under the impacting load, the calculating formulas of maximum tensile stress, shear stress and deflection are derived by applying the material mechanics theory. Furthermore, based on the theoretical derivation formula, the reasonable thickness of cushion is studied quantitatively in the super-large goal and the correctness of the theoretical results is verified by FLAC3D numerical simulation. The results show that: (1) Considering the influence of compressed air and surrounding rock friction on the motion of caving rock mass, the maximum impacting velocity of falling body rolling to bottom of goaf is solved as a result of 30.99 m·s-1. (2) The buffering effect gradually decreases with the increasing cushion thickness, namely it hardly produces cushioning effect when the thickness of cushion increases to a certain value. (3) Compared with the fixed beam, the maximum tensile stress, maximum shear stress and maximum deflection solved by simply supported beam are closer to the numerical simulation results from the ore pillar, and the optimum cushion thickness is 18 m.
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