水平采空区群动力响应的类非线性振动模型

摘要

在线性多自由度振动模型的基础上,考虑到围岩对水平采空区群的水平地应力作用及能量耗散影响,引入水平地应力因子a和类非线性因子p,建立适用于水平采空区群的类非线性多自由度振动模型.基于单个间柱微差爆破及间隔间柱单段爆破2个算例,对类非线性多自由度振动模型的合理性进行验证.研究结果表明:水平地应力未对水平采空区群的动力响应造成明显的影响,可忽略水平地应力的作用(α=0);采用标准动载荷S(t)计算水平采空区群各岩体的类非线性因子p是可行的,对于同一矿山,只需计算1次p,便可应用到类似工况,节省了p的取值时间;对比线性模型,类非线性振动模型结果与数值模拟结果更加吻合,较好地揭示了水平采空区群各岩体的动力响应规律.%On the basis of linear multi-degree of freedom (MDOF) vibration model,considering the effect of horizontal geostatic stress and energy dissipation caused by surrounding rocks,a similar nonlinear vibration model for horizontal goaf group was established by introducing horizontal geostatic stress factor a and similar nonlinear factor p.Similar nonlinear vibration model was investigated and verified based on two cases of millisecond blasting in single barrier pillar and single deck blasting in interval barrier pillars.The results show that the dynamic response results are not obviously affected by horizontal geostatic stress,and the effect of horizontal geostatic stress could be ignored (a=0).It is feasible to use the standard dynamic load S(t) to calculate the similar nonlinear factor p of each rock mass in horizontal goaf group,andp could be applied to similar conditions by calculating only once for the same mine,which saves the selecting time of p;compared with linear model,similar nonlinear vibration model result is more consistent with numerical simulation result,which effectively reveals the dynamic response law of horizontal goaf group.