顶板-锚拉支架系统稳定性的突变理论分析

本文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。对照分叉集方程的图形，从几何上分析系统参数变化对顶板稳定性的影响。形象地观察到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。在文中图2所示锚拉支架的补强充分的条件下，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。

STUDY ON STABILITY OF ROOF-TRUSS SYSTEM BY CATASTROPHE THEORY

The paper analyzes the stability of cracky roof system by catastrophe theory.Its destabilizing model belongs to the cusp catastrophe model of catastrophe theory.The critical condition for roof falling is educed by bifurcation set equation of this model.With reference to the figures of bifurcation set eauation,the paper analyzes the impact on roof stability imposed by the change of system parameters and observes that the rheological property of rock mass in the roof and the accumulation volume of local fragmentation are the main factors causing the roof falling.As shown in Fig 2 below,if the compensation of the truss is enough,the route of control point which is determined by the system parameters can not reach the right ramification of bifurcation set and critical conditions of roof falling can not be satisfied,the roof is therefore stable.