顶板-锚拉支架系统稳定性的突变理论分析

对裂纹顶板系统的稳定性运用突变理论分析，其失稳模式可归结为突变理论中的尖点突变模型，并由该模型的分叉集方程导得顶板大面积冒落的临界条件。从几何上分析系统参数变化对顶板稳定性的影响，发现顶板岩体的流变特性和裂纹顶板应力集中部位的局部破碎累积量是导致顶板冒落的主要因素。锚拉支架的补强作用充分的条件下，由系统参数决定的控制点路径无法达到分叉集右分枝，顶板冒落的临界条件得不到满足，相应顶板处于稳定状态。

Analysis of the Stability of Roof-truss System by Catastrophic Theory

The stability of cracky roof system is analyzed by catastrophic theory and its instability model belongs to cusp catastrophic model of catastrophic theory. The critical condition for roof falling in large area is induced by bifurcation set equation of this model. The effect of the change of system parameters on the roof stability is analyzed geometrically and the rheological property of roof rockmass and local crack accumulation in the stress concentrated part of cracky roof are found to be the main factors leading to roof falling. When the compensation of the truss is enough, the changing route of reference point can't arrive at right divarication of bifurcation set. As a result, the critical condition of roof falling isn't satisfied and correspondently, the roof is in steady state.