悬臂式危岩体振动特征研究

Research on Vibration Characteristics of Cantilevered Dangerous Rock Mass

悬臂式危岩体的稳定程度受后缘裂隙深度控制,危岩后缘裂隙深度的判定是静力学无法解决的问题。将悬臂式危岩体概化为悬臂梁模型,基于修正的Timoshenko梁理论建立岩梁动力学方程,结合动力基础半空间理论对岩梁的边界约束条件及阻尼条件做深入分析,得到不同裂隙深度条件下危岩体固有频率的解析算法。通过室内试验对算法合理性进行验证,得出结论:(1)危岩体固有频率与其后缘裂隙深度呈非线性负相关,二者呈一一对应关系,可根据固有频率值对裂隙深度进行反算;(2)理论计算结果与室内试验结果吻合度较高,充分说明所提出的算法的合理性,该算法可实现危岩体不同裂缝深度的固有频率定量计算,为实现边坡崩塌监测预警提供了理论依据.

The stability of cantilevered dangerous rock mass is controlled by the rear edge crack depth.The determination of the rear edge crack depth of dangerous rock mass is a problem that statics cannot solve.The cantilevered dangerous rock mass was generalized as a cantilevered beam model,and the dynamic equation of the rock beam was established based on the modified Timoshenko beam theory.Combined with the half-space theory of dynamic foundation,the boundary constraint conditions and damping conditions of the rock beam were analyzed in depth,and an analytical algorithm for the fixed frequency of the dangerous rock mass under different crack depth conditions was obtained.Through indoor experiments,the rationality of the algorithm was verified.The conclusions are drawn as follows.Firstly,the natural frequency of the dangerous rock mass is nonlinear and negatively correlated with the depth of its rear edge cracks,and the two are in a one-to-one correspondence relationship.The crack depth can be backcalculated based on the natural frequency value.Secondly,the theoretical calculation results are in good agreement with the indoor test results,fully demonstrating the rationality of the proposed algorithm.This algorithm can achieve quantitative calculation of the natural frequencies of different crack depths in dangerous rock masses,providing a theoretical basis for monitoring and warning of slope collapse.