低概率水平岩质边坡系统可靠度分析
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摘要
针对目前含多个相关失效模式的低概率水平岩质边坡系统可靠度分析的难题,提出了基于子集模拟的岩质边坡系统可靠度分析方法,推导了典型边坡系统失效概率计算表达式。为表征不同失效模式间的相关性,提出采用max和min函数构建边坡系统功能函数。并通过含多个相关失效模式的双滑块岩质边坡及锦屏一级左岸坝肩边坡系统可靠度分析验证了提出方法的有效性。结果表明:提出方法计算效率明显高于蒙特卡洛模拟方法,计算精度优于一阶等效近似方法、N维等效方法和Ditlevsen上下限方法,可为解决低概率水平复杂岩质边坡系统可靠度问题提供一个重要的工具。此外,通过max和min函数构建的边坡系统功能函数不仅可以准确地表征边坡不同失效模式间的相关性,而且可为边坡系统可靠度分析提供便利。
To effectively tackle system reliability problems of rock slopes involving multiple correlated potential failure modes at small probability levels, this paper aims to propose a subset simulation-based approach for system reliability analysis of rock slopes. The expressions for system failure probability calculation of typical slope systems are derived. To account for the correlations among multiple failure modes, the "max" and "min" functions are utilized to construct the system performance functions. A benchmark rock slope with two sliding blocks and the left abutment slope of Jinping I slope with multiple correlated failure modes are investigated to demonstrate the effectiveness of the proposed approach. The results indicate that the proposed approach is much more efficient than the Monte-Carlo simulation(MCS) and more accurate than the first order approximation, N-dimensional equivalent method and Ditlevsen's bounds method when solving the system reliability problems of rock slopes with small probabilities. In summary, it provides an effective means for tackling system reliability problems of complex rock slopes at small probability levels. In addition, the correlations among different failure modes can be effectively quantified with the aid of the "max" and "min" functions, which greatly facilitates the system reliability analysis of rock slopes.
To effectively tackle system reliability problems of rock slopes involving multiple correlated potential failure modes at small probability levels, this paper aims to propose a subset simulation-based approach for system reliability analysis of rock slopes. The expressions for system failure probability calculation of typical slope systems are derived. To account for the correlations among multiple failure modes, the "max" and "min" functions are utilized to construct the system performance functions. A benchmark rock slope with two sliding blocks and the left abutment slope of Jinping I slope with multiple correlated failure modes are investigated to demonstrate the effectiveness of the proposed approach. The results indicate that the proposed approach is much more efficient than the Monte-Carlo simulation(MCS) and more accurate than the first order approximation, N-dimensional equivalent method and Ditlevsen's bounds method when solving the system reliability problems of rock slopes with small probabilities. In summary, it provides an effective means for tackling system reliability problems of complex rock slopes at small probability levels. In addition, the correlations among different failure modes can be effectively quantified with the aid of the "max" and "min" functions, which greatly facilitates the system reliability analysis of rock slopes.
引文
[1]HOEK E,BRAY J.Rock slope engineering[M].3rd ed.London:Taylor&Francis,1981.
[2]宋胜武,向柏宇,杨静熙,等.锦屏一级水电站复杂地质条件下坝肩高陡边坡稳定性分析及其加固设计[J].岩石力学与工程学报,2010,29(3):442―458.SONG Sheng-wu,XIANG Bo-yu,YANG Jing-xi,et al.Stability analysis and reinforcement design of high and steep slopes with complex geology in abutment of Jinping I hydropower station[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(3):442―458.
[3]许湘华,曲广琇,方理刚.基于节理几何参数不确定性的边坡可靠度分析[J].中南大学学报(自然科学版),2010,41(3):336―342.XU Xiang-hua,QU Guang-xiu,FANG Li-gang.Reliability analysis of rock slope based on uncertainty of joint[J].Journal of Central South University(Science and Technology),2010,41(3):336―342.
[4]JIMENEZ-RODRIGUEZ R,SITAR N,CHACON J.System reliability approach to rock slope stability[J].International Journal of Rock Mechanics and Mining Sciences,2006,43(6):847―859.
[5]JIMENEZ-RODRIGUEZ R,SITAR N.Rock wedge stability analysis using system reliability methods[J].Rock Mechanics and Rock Engineering,2007,40(4):419―427.
[6]LOW B K.Reliability analysis of rock slopes involving correlated nonnormals[J].International Journal of Rock Mechanics and Mining Sciences,2007,44(6):922―935.
[7]李典庆,周创兵.考虑多失效模式相关的岩质边坡体系可靠度分析[J].岩石力学与工程学报,2009,28(3):541―551.LI Dian-qing,ZHOU Chuang-bing.System reliability analysis of rock slope considering multiple correlated failure modes[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(3):541―551.
[8]LI D Q,JIANG S H,CHEN Y F,et al.System reliability analysis of rock slope stability involving correlated failure modes[J].KSCE Journal of Civil Engineering,2011,15(8):1349―1359.
[9]陈昌富,成晓炜.双滑块边坡锚固系统时变可靠性分析[J].岩土力学,2012,33(1):197―203.CHEN Chang-fu,CHENG Xiao-wei.Time-varying reliability analysis of anchor system of rock slopes with double slide blocks[J].Rock and Soil Mechanics,2012,33(1):197―203.
[10]LEE Y F,CHI Y Y,JUANG C H,et al.Reliability analysis of rock wedge stability:knowledge-based clustered partitioning approach[J].Journal of Geotechnical and Geoenvironmental Engineering,2012,138(6):700―708.
[11]张道兵,杨小礼,朱川曲.多失效模式相关下的结构系统可靠度计算研究[J].采矿与安全工程学报,2013,30(1):100―106.ZHANG Dao-bing,YANG Xiao-li,ZHU Chuan-qu.Reliability calculation of structure system correlated with multiple failure modes[J].Chinese Journal of Mining&Safety Engineering,2013,30(1):100―106.
[12]JOHARI A,LARI A M.System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding method[J].International Journal of Rock Mechanics and Mining Sciences,2016,82(3):61―70.
[13]Department of the US Army.Engineering and design:Introduction to probability and reliability methods for use in geotechnical engineering[R].Washington DC:US Army Corps of Engineers,1997.
[14]赵国藩.工程结构可靠性理论与应用[M].大连:大连理工大学出版社,1996.ZHAO Guo-fan.Engineering structural reliability theory and application[M].Dalian:Dalian University of Technology Press,1996.
[15]蒋水华,祁小辉,曹子君,等.基于随机响应面法的边坡系统可靠度分析[J].岩土力学,2015,36(3):809―818.JIANG Shui-hua,QI Xiao-hui,CAO Zi-jun,et al.System reliability analysis of slope with stochastic response surface method[J].Rock and Soil Mechanics,2015,36(3):809―818.
[16]杨智勇,李典庆,曹子君,等.基于广义子集模拟的土坡系统可靠度分析[J].岩土力学,2018,39(3):957―966.YANG Zhi-yong,LI Dian-qing,CAO Zi-jun,et al.System reliability of soil slope using generalized subset simulation[J].Rock and Soil Mechanics,2018,39(3):957―966.
[17]AU S K,BECK J L.Estimation of small failure probabilities in high dimensions by subset simulation[J].Probabilistic Engineering Mechanics,2001,16(4):263―277.
[18]曹子君,王宇,区兆驹.基于子集模拟的边坡可靠度分析方法研究[J].地下空间与工程学报,2013,9(2):405―409.CAO Zi-jun,WANG Yu,AU Siu-kui.Probabilistic slope stability analysis using subset simulation[J].Chinese Journal of Underground Space and Engineering,2013,9(2):405―409.
[19]WANG Y,CAO Z J,AU S K.Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet[J].Canadian Geotechnical Journal,2010,48(1):162―172.
[20]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.
[21]LI D Q,XIAO T,CAO Z J,et al.Efficient and consistent reliability analysis of soil slope stability using both limit equilibrium analysis and finite element analysis[J].Applied Mathematical Modelling,2016,40(9―10):5216―5229.
[22]JIANG S H,HUANG J S.Efficient slope reliability analysis at low-probability levels in spatially variable soils[J].Computers and Geotechnics,2016,75:18―27.
[23]TANG X S,LI D Q,CHEN Y F,et al.Improved knowledge-based clustered partitioning approach and its application to slope reliability analysis[J].Computers and Geotechnics,2012,45(1):34―43.
[24]苏永华,杨红波.基于代理模型的边坡稳定可靠度算法[J].应用力学学报,2012,29(6):705―711.SU Yong-hua,YANG Hong-bo.Reliability algorithm of slope stability based on Kriging metamodel[J].Chinese Journal of Applied Mechanics,2012,29(6):705―711.
[25]YOUNG D S.A generalized probabilistic approach for slope analysis:practical application to an open pit iron ore mine[J].International Journal of Mining and Geological Engineering,1986,4(1):3―13.
[26]KROUNIS A,JOHAN F.The influence of correlation between cohesion and friction angle on the probability of failure for sliding of concrete dams[C]//Risk Analysis,Dam Safety,Dam Security and Critical Infrastructure Management.[S.l.]:CRC Press,2011:75―80.
[27]AHMADABADI M,POISEL R.Probabilistic analysis of rock slopes involving correlated non-normal variables using point estimate methods[J].Rock Mechanics and Rock Engineering,2016,49(3):909―925.
[28]DITLEVSEN O.Narrow reliability bounds for structural systems[J].Journal of Structural Mechanics,1979,7(4),453―472.
[29]周创兵,汪小刚,姜清辉,等.锦屏一级水电站工程区大坝左岸边坡变形与稳定性分析研究[R].武汉:武汉大学,2010.ZHOU Chuang-bing,WANG Xiao-gang,JIANG Qinghui,et al.Deformation and stability analysis of the slope in the left bank of the dam at Jinping I Hydropower Project Area[R].Wuhan:Wuhan University,2010.
[30]ALADEJARE A E,WANG Y.Evaluation of rock property variability[J].Georisk,2017,11(1):22―41.
[31]SARMA S K.Stability analysis of embankments and slopes[J].Journal of Geotechnical Engineering,1979,105(12):1511―1524.
[2]宋胜武,向柏宇,杨静熙,等.锦屏一级水电站复杂地质条件下坝肩高陡边坡稳定性分析及其加固设计[J].岩石力学与工程学报,2010,29(3):442―458.SONG Sheng-wu,XIANG Bo-yu,YANG Jing-xi,et al.Stability analysis and reinforcement design of high and steep slopes with complex geology in abutment of Jinping I hydropower station[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(3):442―458.
[3]许湘华,曲广琇,方理刚.基于节理几何参数不确定性的边坡可靠度分析[J].中南大学学报(自然科学版),2010,41(3):336―342.XU Xiang-hua,QU Guang-xiu,FANG Li-gang.Reliability analysis of rock slope based on uncertainty of joint[J].Journal of Central South University(Science and Technology),2010,41(3):336―342.
[4]JIMENEZ-RODRIGUEZ R,SITAR N,CHACON J.System reliability approach to rock slope stability[J].International Journal of Rock Mechanics and Mining Sciences,2006,43(6):847―859.
[5]JIMENEZ-RODRIGUEZ R,SITAR N.Rock wedge stability analysis using system reliability methods[J].Rock Mechanics and Rock Engineering,2007,40(4):419―427.
[6]LOW B K.Reliability analysis of rock slopes involving correlated nonnormals[J].International Journal of Rock Mechanics and Mining Sciences,2007,44(6):922―935.
[7]李典庆,周创兵.考虑多失效模式相关的岩质边坡体系可靠度分析[J].岩石力学与工程学报,2009,28(3):541―551.LI Dian-qing,ZHOU Chuang-bing.System reliability analysis of rock slope considering multiple correlated failure modes[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(3):541―551.
[8]LI D Q,JIANG S H,CHEN Y F,et al.System reliability analysis of rock slope stability involving correlated failure modes[J].KSCE Journal of Civil Engineering,2011,15(8):1349―1359.
[9]陈昌富,成晓炜.双滑块边坡锚固系统时变可靠性分析[J].岩土力学,2012,33(1):197―203.CHEN Chang-fu,CHENG Xiao-wei.Time-varying reliability analysis of anchor system of rock slopes with double slide blocks[J].Rock and Soil Mechanics,2012,33(1):197―203.
[10]LEE Y F,CHI Y Y,JUANG C H,et al.Reliability analysis of rock wedge stability:knowledge-based clustered partitioning approach[J].Journal of Geotechnical and Geoenvironmental Engineering,2012,138(6):700―708.
[11]张道兵,杨小礼,朱川曲.多失效模式相关下的结构系统可靠度计算研究[J].采矿与安全工程学报,2013,30(1):100―106.ZHANG Dao-bing,YANG Xiao-li,ZHU Chuan-qu.Reliability calculation of structure system correlated with multiple failure modes[J].Chinese Journal of Mining&Safety Engineering,2013,30(1):100―106.
[12]JOHARI A,LARI A M.System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding method[J].International Journal of Rock Mechanics and Mining Sciences,2016,82(3):61―70.
[13]Department of the US Army.Engineering and design:Introduction to probability and reliability methods for use in geotechnical engineering[R].Washington DC:US Army Corps of Engineers,1997.
[14]赵国藩.工程结构可靠性理论与应用[M].大连:大连理工大学出版社,1996.ZHAO Guo-fan.Engineering structural reliability theory and application[M].Dalian:Dalian University of Technology Press,1996.
[15]蒋水华,祁小辉,曹子君,等.基于随机响应面法的边坡系统可靠度分析[J].岩土力学,2015,36(3):809―818.JIANG Shui-hua,QI Xiao-hui,CAO Zi-jun,et al.System reliability analysis of slope with stochastic response surface method[J].Rock and Soil Mechanics,2015,36(3):809―818.
[16]杨智勇,李典庆,曹子君,等.基于广义子集模拟的土坡系统可靠度分析[J].岩土力学,2018,39(3):957―966.YANG Zhi-yong,LI Dian-qing,CAO Zi-jun,et al.System reliability of soil slope using generalized subset simulation[J].Rock and Soil Mechanics,2018,39(3):957―966.
[17]AU S K,BECK J L.Estimation of small failure probabilities in high dimensions by subset simulation[J].Probabilistic Engineering Mechanics,2001,16(4):263―277.
[18]曹子君,王宇,区兆驹.基于子集模拟的边坡可靠度分析方法研究[J].地下空间与工程学报,2013,9(2):405―409.CAO Zi-jun,WANG Yu,AU Siu-kui.Probabilistic slope stability analysis using subset simulation[J].Chinese Journal of Underground Space and Engineering,2013,9(2):405―409.
[19]WANG Y,CAO Z J,AU S K.Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet[J].Canadian Geotechnical Journal,2010,48(1):162―172.
[20]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.
[21]LI D Q,XIAO T,CAO Z J,et al.Efficient and consistent reliability analysis of soil slope stability using both limit equilibrium analysis and finite element analysis[J].Applied Mathematical Modelling,2016,40(9―10):5216―5229.
[22]JIANG S H,HUANG J S.Efficient slope reliability analysis at low-probability levels in spatially variable soils[J].Computers and Geotechnics,2016,75:18―27.
[23]TANG X S,LI D Q,CHEN Y F,et al.Improved knowledge-based clustered partitioning approach and its application to slope reliability analysis[J].Computers and Geotechnics,2012,45(1):34―43.
[24]苏永华,杨红波.基于代理模型的边坡稳定可靠度算法[J].应用力学学报,2012,29(6):705―711.SU Yong-hua,YANG Hong-bo.Reliability algorithm of slope stability based on Kriging metamodel[J].Chinese Journal of Applied Mechanics,2012,29(6):705―711.
[25]YOUNG D S.A generalized probabilistic approach for slope analysis:practical application to an open pit iron ore mine[J].International Journal of Mining and Geological Engineering,1986,4(1):3―13.
[26]KROUNIS A,JOHAN F.The influence of correlation between cohesion and friction angle on the probability of failure for sliding of concrete dams[C]//Risk Analysis,Dam Safety,Dam Security and Critical Infrastructure Management.[S.l.]:CRC Press,2011:75―80.
[27]AHMADABADI M,POISEL R.Probabilistic analysis of rock slopes involving correlated non-normal variables using point estimate methods[J].Rock Mechanics and Rock Engineering,2016,49(3):909―925.
[28]DITLEVSEN O.Narrow reliability bounds for structural systems[J].Journal of Structural Mechanics,1979,7(4),453―472.
[29]周创兵,汪小刚,姜清辉,等.锦屏一级水电站工程区大坝左岸边坡变形与稳定性分析研究[R].武汉:武汉大学,2010.ZHOU Chuang-bing,WANG Xiao-gang,JIANG Qinghui,et al.Deformation and stability analysis of the slope in the left bank of the dam at Jinping I Hydropower Project Area[R].Wuhan:Wuhan University,2010.
[30]ALADEJARE A E,WANG Y.Evaluation of rock property variability[J].Georisk,2017,11(1):22―41.
[31]SARMA S K.Stability analysis of embankments and slopes[J].Journal of Geotechnical Engineering,1979,105(12):1511―1524.