邻近爆破对矩形岩柱稳定性影响的突变理论分析

Stability analysis of rectangular rock pillars influenced by vicinal blasting with catastrophe theory

运用突变理论,建立了邻近爆破扰动诱发矩形岩柱失稳的非线性动力学模型,导出了岩柱发生动力失稳的充分必要条件。根据建立的尖点突变模型,分析了竖向压力、爆破扰动强度及频率对矩形岩柱失稳机理的影响。结果表明:(1)借助突变理论分析邻近爆破扰动诱发岩柱失稳机理是可行的;(2)邻近爆破扰动强度越大,岩柱越容易发生失稳破坏;(3)竖向荷载越大,满足岩柱失稳条件所对应的爆破扰动强度越小,岩柱发生失稳的可能性越大;(4)岩柱发生动力失稳破坏,爆破扰动频率必须满足一定条件。

By using the catastrophe theory,a nonlinear dynamic model was proposed to describe the rectangular rock pillar instability induced by vicinal blasting.And sufficient and necessary conditions were worked out for the pillar dynamic instability.The proposed catastrophe models were used to analyze the influences of the vertical press,the blasting disturbing strength and its frequency on the instability mechanism of the rectangular rock pillars.Results show as follows.It is feasible to analyze the instability mechanism of the rectangular rock pillars induced by vicinal blasting by using the catastrophe theory.The higher the vicinal blasting disturbing strength,the more easily the rock pillar instability occurs.The blasting disturbing strength responding to the instability conditions of rock pillars will be less with the increasing of the vertical press,and the instability of rock pillars becomes more possible.If the dynamic instability of rock pillars happens,the blasting disturbing frequency must meet certain conditions.