基于固有频率的坠落危岩体稳定系数计算模型研究

doi:10.13722/j.cnki.jrme.2022.0361

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摘要坠落危岩体的稳定系数受后缘裂隙深度控制，而常规的静力学计算方法无法实时追踪裂隙深度的动态变化，如何实现实时获取当前危岩稳定系数仍是亟需解决的问题。基于修正Timoshenko梁理论建立岩梁动力学方程，将基岩与危岩体之间的关系比拟为半无限空间地基与基础的关系，进而基于动力基础半空间理论得到基岩对危岩体的动力学约束边界，结合约束边界条件及动力学方程通解推导得到危岩体固有频率解析解，建立固有频率与危岩体后缘裂隙深度之间的定量关系。基于固有频率与危岩体后缘裂隙深度关系，建立基于固有频率的动力学稳定系数计算模型。为验证算法正确性，将理论计算值与室内试验值进行对比，不同裂隙深度条件下一阶固有频率误差最大为3.3%，充分说明了危岩体固有频率算法的合理性与有效性。算法应用于宝泉抽水蓄电站，通过对常时微动的测量成功获取危岩体固有频率值，经过计算获得当前危岩体后缘裂隙深度，并计算得到当前危岩体稳定系数，实践证明，危岩体的固有频率具有可测性，为实现崩塌自动化监测提供理论借鉴，具有理论及市场前景。

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	张晓勇1
	2
	谢谟文1
	2
	张磊1
	2
	杜岩1
	刘卫南1
	高世崇1

关键词 ：岩石力学, 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, 常时微动

Abstract：The stability coefficient of the falling dangerous rock mass is controlled by the depth of the trailing edge crack，and the conventional static calculation method cannot track the dynamic change of the crack depth in real time. How to obtain the current stability coefficient of the dangerous rock in real time is still an urgent problem to be solved. The dynamic equation of a rock beam is established based on the modified Timoshenko beam theory，and the relationship between the bedrock and the dangerous rock mass is compared to the relationship between the Semi-infinite space foundation bed and the foundation. The dynamic constraint boundary of the bedrock to the dangerous rock mass was obtained based on the semi-space theory of the dynamic foundation. Combined with the constraint boundary conditions and the general solution of the dynamic equation，the analytical solution of the natural frequency of the dangerous rock mass is derived，and the quantitative relationship between the natural frequency and the fracture depth of the trailing edge of the dangerous rock mass is established. In order to verify the correctness of the algorithm，the theoretical calculation value is compared with the laboratory test value. The maximum error of the first-order natural frequency under different crack depths is 3.3%，which fully demonstrates the rationality and effectiveness of the natural frequency algorithm of dangerous rock mass. The algorithm is applied to Baoquan Pumped Storage Power Station，and the natural frequency of the dangerous rock mass is successfully obtained through the measurement of constant time fretting. After calculation，the fracture depth of the rear edge of the current dangerous rock mass is obtained，and the stability coefficient of the current dangerous rock mass is calculated. Practice has proved that the natural frequency of the dangerous rock mass is measurable，which provides a theoretical reference for the realization of automatic monitoring of collapse and has theoretical and market prospective.

Key words： rock mechanics dangerous rock mass stability coefficient modified Timoshenko beam theory the semi-space theory of dynamic foundation natural frequency constant time fretting

引用本文:

张晓勇1，2，谢谟文1，2，张磊1，2，杜岩1，刘卫南1，高世崇1. 基于固有频率的坠落危岩体稳定系数计算模型研究[J]. 岩石力学与工程学报, 2023, 42(3): 585-593.
ZHANG Xiaoyong1，2，XIE Mowen1，2，ZHANG Lei1，2，DU Yan1，LIU Weinan1，GAO Shichong1. Study on calculation model of stability coefficient of falling dangerous rock mass based on natural frequency. , 2023, 42(3): 585-593.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2022.0361 或 http://rockmech.whrsm.ac.cn/CN/Y2023/V42/I3/585

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