水平和竖向地震作用下顺层岩质边坡动力可靠性分析
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摘要
由于传统顺层岩质边坡地震可靠性分析往往是基于拟静力法,忽略了地震的动力特性,而基于数值模拟软件的地震时程分析法虽能考虑地震的动态性,却相对费时费力,该文同时考虑了地震的动力特性和强度参数随机性,提出顺层岩质边坡动力可靠性分析方法。运用Wilson-θ法和Matlab/Simulink工具建立了顺层岩质边坡地震响应简化计算方法。根据响应结果,运用Monte Carlo法计算了边坡的动力可靠度,并提出采用整体最小平均可靠度来评价边坡的地震整体可靠性。在此基础上,进一步分析了水平和竖向地震作用的叠加模式对顺层岩质边坡可靠性的影响。算例分析表明,提出的地震响应简化计算方法具有较高的计算精度和效率。该文可靠度分析方法低估了边坡的地震可靠性。与水平地震作用相比,竖向地震作用对顺层岩质边坡可靠性的影响也很明显。常用的水平和竖向地震作用的峰值叠加模式并不能充分地体现出双向地震的最大作用叠加效果,而采用双向地震的最大作用叠加模式更偏于工程安全。
As the traditional seismic reliability analysis of bedding rock slopes usually ignores the dynamic characteristics of earthquake and the existing seismic time-history analysis method is time-consuming and laborious, a dynamic reliability analysis method for bedding rock slopes considering the seismic dynamic characteristics and the randomness of strength parameters is proposed.A simplified calculation method for seismic response of bedding rock slopes is developed based on the Wilson-θ method and the Matlab/Simulink toolbox.The dynamic reliability of slopes is then calculated by the Monte Carlo method,and the evaluation index of overall minimum mean dynamic reliability is presented to assess the overall seismic reliability of slopes.Furthermore,the effects of superposition modes of horizontal and vertical earthquake actions on the reliability of bedding rock slopes are analyzed.Analyses of examples show that this proposed method for seismic response possesses high accuracy and efficiency.The reliability analysis method proposed in this work underestimates the seismic reliability of slope.Compared to the horizontal earthquake action,the effect of vertical earthquake action on the reliability of bedding rock slopes is also remarkable.It is also observed that the commonly used superposition mode of peak values of horizontal and vertical earthquake actions is incapable of fully reflecting the superposition effect of the maximum actions of bidirectional earthquake,but the application of the superposition mode is generally safer.
As the traditional seismic reliability analysis of bedding rock slopes usually ignores the dynamic characteristics of earthquake and the existing seismic time-history analysis method is time-consuming and laborious, a dynamic reliability analysis method for bedding rock slopes considering the seismic dynamic characteristics and the randomness of strength parameters is proposed.A simplified calculation method for seismic response of bedding rock slopes is developed based on the Wilson-θ method and the Matlab/Simulink toolbox.The dynamic reliability of slopes is then calculated by the Monte Carlo method,and the evaluation index of overall minimum mean dynamic reliability is presented to assess the overall seismic reliability of slopes.Furthermore,the effects of superposition modes of horizontal and vertical earthquake actions on the reliability of bedding rock slopes are analyzed.Analyses of examples show that this proposed method for seismic response possesses high accuracy and efficiency.The reliability analysis method proposed in this work underestimates the seismic reliability of slope.Compared to the horizontal earthquake action,the effect of vertical earthquake action on the reliability of bedding rock slopes is also remarkable.It is also observed that the commonly used superposition mode of peak values of horizontal and vertical earthquake actions is incapable of fully reflecting the superposition effect of the maximum actions of bidirectional earthquake,but the application of the superposition mode is generally safer.
引文
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[13]黄润秋.汶川8.0级地震触发崩滑灾害机制及其地质力学模式[J].岩石力学与工程学报,2009,28(6):1239-1249(Huang Runqiu.Mechanism and geomechanical modes of landslide hazards triggered by wenchuan 8.0earthquake[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(6):1239-1249(in Chinese))
[14]栾茂田,李湛,范庆林.土石坝拟静力稳定性分析与坝坡地震滑移量估算[J].岩土力学,2007,28(2):224-230(Luan Maotian,Li Zhan,Fan Qinglin.Analysis and evaluation of pseudo-static aseismic stability and seisminduced sliding movement of earth-rock dams[J].Rock and Soil Mechanics,2007,28(2):224-230(in Chinese))
[15]Ling H I,Leshchinsky D,Yoshiyuki M.Soil slopes under combined horizontal and vertical seismic accelerations[J].Earthquake Engineering and Structural Dynamics,1997,26(12):1231-1241
[16]黄诚,王安明,任伟中.水平向与竖向地震动的时间遇合模式对边坡动力安全系数的影响[J].岩土力学,2010,31(11):3404-3410(Huang Cheng,Wang Anming,Ren Weizhong.Influence of time combination pattern of horizontal and vertical ground motions on slope seismic safety factor[J].Rock and Soil Mechanics,2010,31(11):3404-3410(in Chinese))
[17]薛守义,王思敬,张镜剑.块状岩体振动模型与动力反应分析方法[C]//第二届全国岩石动力学学术会议.宜昌,1990(Xue Shouyi,Wang Sijing,Zhang Jingjian.The vibrating models of block rockmass and dynamic response analysis methods[C]//Proceedings of the 2nd Chinese academic conference on rock dynamic mechanics.Yichang,1990(in Chinese))
[18]Kontoe S,Zdravkovic L,Potts D M.An assessment of time integration schemes for dynamic geotechnical problems[J].Computers&Geotechnics,2008,35(2):253-264
[19]Taghipour R,Perez T,Moan T.Hybrid frequency time domain models for dynamic response analysis of marine structures[J].Ocean Engineering,2008,35(7):685-705
[20]谭晓慧,王建国,刘新荣,等.边坡稳定的有限元可靠度计算及敏感性分析[J].岩石力学与工程学报,2007,26(1):115-122(Tan Xiaohui,Wang Jianguo,Liu Xinrong,et al.Finite element reliability computation and sensitivity analysis of slope stability[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(1):115-122(in Chinese))
[21]Li D Q,Xiao T,Cao Z J,et al.Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation[J].Landslides,2016,13(2):293-303
[22]刘汉龙,费康,高玉峰.边坡地震稳定性时程分析方法[J].岩土力学,2003,24(4):553-556(Liu Hanlong,Fei Kang,Gao Yufeng.Time history analysis method of slope seismic stability[J].Rock and Soil Mechanics,2003,24(4):553-556(in Chinese))
[2]高荣雄,龚文惠,王元汉,等.顺层边坡稳定性及可靠度的随机有限元分析法[J].岩土力学,2009,30(4):1165-1169(Gao Rongxiong,Gong Wenhui,Wang Yuanhan,et al.Analysis of stability and reliability of bedding rock slope by stochastic finite element method[J].Rock and Soil Mechanics,2009,30(4):1165-1169(in Chinese))
[3]孙树林,朱杰.节理化岩质边坡的关键块体可靠度分析[J].岩石力学与工程学报,2007,26(1):131-136(Sun Shulin,Zhu Jie.Reliability analysis of key block for a jointed rock slope[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(1):131-136(in Chinese))
[4]Li D Q,Chen Y F,Lu W B,et al.Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables[J].Computers&Geotechnics,2011,38(1):58-68
[5]Low B K.Efficient probabilistic algorithm illustrated for a rock slope[J].Rock Mechanics&Rock Engineering,2008,41(5):715-734
[6]Shukha R,Baker R.Design implications of the vertical pseudo-static coefficient in slope analysis[J].Computers&Geotechnics,2008,35(1):86-96
[7]Pal Amir S,Kaynia A M,Bhasin R,et al.Earthquake stability analysis of rock slopes:a case study[J].Rock Mechanics&Rock Engineering,2012,45(2):205-215
[8]Chang K J,Taboada A,Lin M L,et al.Analysis of landsliding by earthquake shaking using a block-on-slope thermo-mechanical model:example of Jiufengershan landslide,central Taiwan[J].Engineering Geology,2005,80(1-2):151-163
[9]Refice A,Capolongo D.Probabilistic modeling of uncertainties in earthquake-induced landslide hazard assessment[J].Pergamon Press,Inc.,2002,28(6):735-749
[10]Zhou J W,Cui P,Yang X G.Dynamic process analysis for the initiation and movement of the Donghekou landslidedebris flow triggered by the Wenchuan earthquake[J].Journal of Asian Earth Sciences 2013,76(S1):70-84
[11]李海波,肖克强,刘亚群.地震荷载作用下顺层岩质边坡安全系数分析[J].岩石力学与工程学报,2007,26(12):2385-2394(Li Haibo,Xiao Keqiang,Liu Yaqun.Factor of safety analysis of bedding rock slope under seismic load[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(12):2385-2394(in Chinese))
[12]言志信,张森,张学东,等.顺层岩质边坡地震动力响应及地震动参数影响研究[J].岩石力学与工程学报,2011,30(S2):3522-3528(Yan Zhixin,Zhang Sen,Zhang Xuedong,et al.Study of dynamic response of bedding rock slope under earthquake and influence of ground motion parameters[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(S2):3522-3528(in Chinese))
[13]黄润秋.汶川8.0级地震触发崩滑灾害机制及其地质力学模式[J].岩石力学与工程学报,2009,28(6):1239-1249(Huang Runqiu.Mechanism and geomechanical modes of landslide hazards triggered by wenchuan 8.0earthquake[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(6):1239-1249(in Chinese))
[14]栾茂田,李湛,范庆林.土石坝拟静力稳定性分析与坝坡地震滑移量估算[J].岩土力学,2007,28(2):224-230(Luan Maotian,Li Zhan,Fan Qinglin.Analysis and evaluation of pseudo-static aseismic stability and seisminduced sliding movement of earth-rock dams[J].Rock and Soil Mechanics,2007,28(2):224-230(in Chinese))
[15]Ling H I,Leshchinsky D,Yoshiyuki M.Soil slopes under combined horizontal and vertical seismic accelerations[J].Earthquake Engineering and Structural Dynamics,1997,26(12):1231-1241
[16]黄诚,王安明,任伟中.水平向与竖向地震动的时间遇合模式对边坡动力安全系数的影响[J].岩土力学,2010,31(11):3404-3410(Huang Cheng,Wang Anming,Ren Weizhong.Influence of time combination pattern of horizontal and vertical ground motions on slope seismic safety factor[J].Rock and Soil Mechanics,2010,31(11):3404-3410(in Chinese))
[17]薛守义,王思敬,张镜剑.块状岩体振动模型与动力反应分析方法[C]//第二届全国岩石动力学学术会议.宜昌,1990(Xue Shouyi,Wang Sijing,Zhang Jingjian.The vibrating models of block rockmass and dynamic response analysis methods[C]//Proceedings of the 2nd Chinese academic conference on rock dynamic mechanics.Yichang,1990(in Chinese))
[18]Kontoe S,Zdravkovic L,Potts D M.An assessment of time integration schemes for dynamic geotechnical problems[J].Computers&Geotechnics,2008,35(2):253-264
[19]Taghipour R,Perez T,Moan T.Hybrid frequency time domain models for dynamic response analysis of marine structures[J].Ocean Engineering,2008,35(7):685-705
[20]谭晓慧,王建国,刘新荣,等.边坡稳定的有限元可靠度计算及敏感性分析[J].岩石力学与工程学报,2007,26(1):115-122(Tan Xiaohui,Wang Jianguo,Liu Xinrong,et al.Finite element reliability computation and sensitivity analysis of slope stability[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(1):115-122(in Chinese))
[21]Li D Q,Xiao T,Cao Z J,et al.Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation[J].Landslides,2016,13(2):293-303
[22]刘汉龙,费康,高玉峰.边坡地震稳定性时程分析方法[J].岩土力学,2003,24(4):553-556(Liu Hanlong,Fei Kang,Gao Yufeng.Time history analysis method of slope seismic stability[J].Rock and Soil Mechanics,2003,24(4):553-556(in Chinese))