基于悬臂梁理论的倒悬危岩体地震弯折崩塌评价方法研究

Evaluation Method of Earthquake-induced Bending Collapse of the Upside-down Dangerous Rock-Mass Based on Cantilever Beam Theory

倒悬危岩体是常见的一种危岩形式,在地震荷载作用下极易发生弯折崩塌事故,因此,研究地震诱发其崩塌失稳的评价方法对于评估该类型危岩体在地震作用下的安全性具有重要的意义。基于悬臂梁计算理论,首先推导了任意形状的倒悬危岩体在水平地震荷载和自身重力作用下最危险截面的最大拉应力计算公式,建立了最大拉应力的地震时程曲线,同时,把最大拉应力强度准则作为危岩体裂缝扩展的判据,并结合弹性应变能与裂缝扩展能量密度之间的关系,建立了裂缝扩展深度的计算方法,进而研究危岩体裂缝扩展随时间变化的演化过程。其次,针对实际工程中常见的危岩体形态,把倒悬危岩体简化为两种特殊形状:等截面长方体和等截面圆柱体,提出了此两类危岩体发生弯折破坏的裂缝临界深度计算公式,并建立了其在地震作用下安全系数的计算方法,即安全系数等于裂缝临界深度与地震后危岩体裂缝深度的比值。最后,以某高速公路隧道进口的倒悬危岩体为研究对象,采用本文的计算方法探讨了其在地震作用下不同时间步的裂缝深度演化规律,结果表明,在8级地震作用下,此处危岩体在14 s时的裂缝总深度(0.175 9 m)超过了满足自稳条件的裂缝临界深度(0.167 m),即在14 s时发生弯折崩塌,从而说明本文计算方法的可行性。

The cantilever beam type is a common form of the upside-down dangerous rock-mass,and it is easily to collapse under earthquake ac- tion.Thus,the study on the evaluation method of earthquake-induced bending collapse of the upside-down dangerous rock-mass have great signi- ficance on evaluating its security degree.On basis of the calculation theory of the cantilever beam,firstly,the calculating formula for the maximum tensile stress of the cantilever beam type dangerous rock-mass with arbitrary shape under the action of seismic loading and its own gravity has been proposed,and the time-history curve of the maximum tensile stress has been established.At the same time,the tensile failure criterion is con- sidered as the criterion of crack propagation,combined with the relationship between the elastic strain energy and fracture propagation energy, and an approach for calculating the depth of crack has been established to study the crack depth along with the earthquake time.Secondly,according to the shapes of dangerous rocks in real engineering,they are simplified into two special forms：rectangular parallelepiped and cylinder,and has pro- posed a calculation formula for the critical depth of crack to define the safety factor of dangerous rock under the action of earthquake.At last,a dangerous rock-mass located at the entrance of a tunnel is taken as an example to illustrate the application of the proposed method in this paper.The results show that,under the action of 8.0 magnitude earthquake,the total depth of crack induced by earthquake of this dangerous rock- mass at 14 s is 0.1759 m,which is greater than the critical depth of crack （0.167 m）,implying that this dangerous rock-mass would collapse at 14 s.