基于固有频率的错断式坠落危岩体稳定系数计算模型  

A CALCULATION MODEL OF SAFETY FACTOR OF SHEAR FRACTURED FALLING DANGEROUS ROCK MASS BASED ON NATURAL FREQUENCY

作　　者：张晓勇 谢谟文[1,2] 张磊 杜岩[1] 高世崇 李双全[1] ZHANG Xiao-yong;XIE Mo-wen;ZHANG Lei;DU Yan;GAO Shi-chong;LI Shuang-quan(School of Civil and Environmental Engineering,University of Science&Technology,Beijing 100083,China;Beijing Zhongguancun Insititute of Safety Sscience Co.,Ltd,Beijing 100083,China)

机构地区：[1]北京科技大学土木与资源工程学院,北京100083 [2]北京中关村智连安全科学研究院有限公司,北京100083

出　　处：《工程力学》2024年第4期1-10,共10页Engineering Mechanics

基　　金：崩塌组合式传感智能监测预警仪器研发项目(2019YFC1509602);国家自然科学基金项目(41572274)。

摘　　要：错断式坠落危岩体的安全稳定程度受后缘裂缝深度控制,基于静力学的稳定系数计算可得到后缘裂隙深度临界值,但静力学计算方法无法得到裂隙深度的实时变化。基于修正Timoshenko梁建立岩梁动力学方程,结合动力基础半空间理论对岩梁的约束刚度及边界条件做深入分析,得到不同裂缝深度条件下危岩体固有频率理论解析。基于数值计算验证固有频率算法的正确性,并得出结论:随裂隙深度增大,固有频率不断降低,固有频率对危岩体后缘裂隙深度变化较为敏感,根据危岩体的固有频率值可反算危岩体后缘裂隙深度。基于固有频率与危岩体后缘裂隙深度之间的关系建立错断式坠落危岩体稳定系数计算模型,并采用室内试验进行验证,得出结论:危岩体固有频率与其后缘裂隙深度近似为负线性相关。基于固有频率的错断式坠落危岩体稳定系数计算模型可为危岩体自动化监测提供有益借鉴。The safety and stability of shear fractured falling dangerous rock mass is controlled by the depth of trailing edge fracture.The critical value of the depth of trailing edge fracture can be obtained by calculating the stability factor based on statics,but the statics calculation method cannot obtain the real-time change of the fracture depth.Based on the modified Timoshenko Beam theory,the dynamic equation of rock beam was established.Combined with the half-space theory of dynamic foundation,the constraint stiffness and boundary conditions of rock beam were analyzed in depth,and theoretical analysis of natural frequency of dangerous rock mass under different fracture depths was conducted.The correctness of the natural frequency algorithm was verified through numerical calculation.It was concluded that the natural frequency decreases with the increase of crack depth,and the natural frequency is sensitive to the change of fracture depth at trailing edge of dangerous rock mass.According to the natural frequency value of dangerous rock mass,the fracture depth at trailing edge of dangerous rock mass can be inversely calculated.Based on the relationship between the natural frequency and the fracture depth of the trailing edge of dangerous rock mass,the calculation model of the stability coefficient of the dangerous rock mass was established,and the indoor test was used to verify it.It was concluded that the natural frequency of the dangerous rock mass is approximately negative-linearly correlated with the crack depth of the trailing edge.The calculation model of stability factor of shear fractured falling dangerous rock mass based on natural frequency can provide useful reference for automatic monitoring of dangerous rock mass.

关 键 词：错断式坠落危岩体 稳定系数 修正Timoshenko梁理论 动力基础半空间理论 固有频率 

分 类 号：TU45[建筑科学—岩土工程]