双向地震动的随机性对倾倒式危岩模糊可靠度的影响  

Effects of Randomness of Bidirectional Ground Motion on the Fuzzy Reliability of Toppling Perilous Rock Mass

作　　者：张继旭 王林峰[1] 黄晓明[2] 谭国金[3] ZHANG Jixu;WANG Linfeng;HUANG Xiaoming;TAN Guojin(Key Lab.of Geological Hazards Mitigation for Mountainous Highway and Waterway,Chongqing Jiaotong Univ.,Chongqing 400074,China;School of Transportation,Southeast Univ.,Nanjing 211189,China;College of Transportation,Jilin Univ.,Changchun 130012,China)

机构地区：[1]重庆交通大学山区公路水运交通地质减灾重庆市高校市级重点实验室,重庆400074 [2]东南大学交通学院,江苏南京211189 [3]吉林大学交通学院,吉林长春130012

出　　处：《工程科学与技术》2023年第6期161-171,共11页Advanced Engineering Sciences

基　　金：国家重点研发计划项目(2021YFB2600604,2021YFB2600600);国家自然科学基金联合基金项目(U22A20600);重庆市研究生导师团队建设项目(JDDSTD2022009);重庆市研究生联合培养基地建设项目(JDLHPYJD2022004)。

摘　　要：危岩体在地震作用下极易发生崩塌灾害,为计算倾倒式危岩在双向地震作用下的稳定性,并探究地震动随机性对倾倒式危岩动力模糊可靠度的影响,通过结构动力学和随机过程理论对倾倒式危岩的动力响应进行分析。首先,基于结构动力学理论建立了倾倒式危岩地震动力响应力学模型及其在两条主控面上的运动方程,并分别采用Wilson-θ法和虚拟激励法求解运动方程,建立倾倒式危岩在确定性地震波和随机地震激励下动力响应计算方法。然后,基于极限平衡理论推导了倾倒式危岩在确定性地震作用下的动力稳定系数计算公式,并将随机地震视为平稳随机过程,基于首次穿越破坏准则求解倾倒式危岩在随机地震激励下地震力峰值响应的均值和方差,从而建立了危岩随机动力稳定性计算方法。最后,将倾倒式危岩失稳事件视为模糊事件,引入模糊失效准则并采用改进的Monte-Carlo法计算危岩体的模糊可靠度,建立了动力模糊可靠度快速计算方法,并分析了地震动随机性对模糊可靠度的影响。将本文方法应用到工程实例中,结果表明:考虑地震动随机性后倾倒式危岩的动力稳定系数和模糊可靠度分别增加了6.34%和22.83%,降低了危岩体的失效概率,且采用模糊失效准则计算得到的模糊可靠度更偏于工程安全。考虑地震动的双向性和随机性较好地判断了倾倒式危岩的动力稳定性,为危岩随机地震动力稳定性评价提供参考。Perilous rock mass is highly susceptible to collapse disasters under seismic actions.To calculate the stability of toppling perilous rock mass under bidirectional ground motion and explore the influence of ground motion randomness on the dynamic fuzzy reliability of toppling perilous rock mass,the dynamic response of toppling perilous rock mass was analyzed by using structural dynamics and stochastic process theory.Firstly,based on the theory of structural dynamics,the mechanical model of the seismic dynamic response of toppling perilous rock mass and its motion equations on two main control surfaces were established.The Wilson-θmethod and the pseudo-excitation method were respectively employed to solve the motion equations,and the calculation methods for the dynamic response of toppling perilous rock mass under deterministic seismic waves and stochastic seismic excitations were established.Then,based on the limit equilibrium theory,the calculation formula of the dynamic stability coefficient for toppling perilous rock mass under deterministic seismic was derived.The stochastic ground motion was considered as a stationary stochastic process,and the mean and variance of seismic force peak response of toppling perilous rock mass under stochastic seismic excitations were solved based on the first-passage failure criterion.As a result,a method for calculating the random dynamic stability of perilous rock mass has been established.Finally,the instability event of toppling perilous rock mass was regarded as a fuzzy event.The fuzzy failure criterion was introduced,and the improved Monte Carlo method was used to calculate the fuzzy reliability of perilous rock mass.A rapid calculation method for the dynamic fuzzy reliability was established,and the influence of seismic randomness on the fuzzy reliability was analyzed.The application of our method to an engineering example shows that the dynamic stability coefficient and fuzzy reliability of toppling perilous rock mass respectively increase by 6.34%and 22.83%after consid

关 键 词：倾倒式危岩 双向随机地震 WILSON-Θ法 虚拟激励法 模糊可靠度 

分 类 号：P642.21[天文地球—工程地质学]