岩土强度参数空间中的极限状态面与系统可靠度分析
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摘要
采用FOSM,PEM和FORM等方法计算边坡可靠度时,随机参数空间中的极限状态面是对于某一固定滑面而言的,这种处理方式低估了滑动面不确定所带来的风险。为解决这一问题,提出参数空间中的系统极限状态面概念,将系统可靠度与与固定滑面可靠度做了区分。以边坡全局安全系数求解为基础,建立一种新的边坡系统可靠度的计算方法,采用Monte-Carlo模拟方法生成一组随机参数,利用Excel编程实现安全系数的快速计算,对计算结果进行统计分析,获得边坡系统可靠度。以简单均质边坡为例说明该方法的实现过程,并将计算结果与GEO-SLOPE中基于固定滑面的概率分析结果进行对比,说明该方法能够从理论上更为合理地评估滑动面不确定所导致的边坡系统风险,计算效率也显著高于常规Monte-Carlo法模拟计算系统可靠度的效率。
A fixed slip surface is needed when FOSM、PEM and FORM are used to calculate the reliability index of slopes. This process may lead to underestimate of the system risk of slopes. To solve this problem,a system limit state surface in strength parameter space is defined to illustrate the new system reliability analysis approach. This new approach is to approximate the system limit state surface based on the global minimum safety factor searching process. Then the safety factors of the simulation strength parameters can be calculated by Excel. The system reliability index can be obtained by statistical analysis of the simulated safety factors. A case study is taken to illustrate the approach. The results show that the new approach can evaluate the system risk adequately and efficiently.
A fixed slip surface is needed when FOSM、PEM and FORM are used to calculate the reliability index of slopes. This process may lead to underestimate of the system risk of slopes. To solve this problem,a system limit state surface in strength parameter space is defined to illustrate the new system reliability analysis approach. This new approach is to approximate the system limit state surface based on the global minimum safety factor searching process. Then the safety factors of the simulation strength parameters can be calculated by Excel. The system reliability index can be obtained by statistical analysis of the simulated safety factors. A case study is taken to illustrate the approach. The results show that the new approach can evaluate the system risk adequately and efficiently.
引文
[1]陈祖煜.土质边坡稳定分析——原理·方法·程序[M].北京:中国水利水电出版社,2003:273–283.(CHEN Zuyu.Stability analysis of soil slopes—theory,methods and programs[M].Beijing:China Water Power Press,2003:273–283.(in Chinese))
[2]WHITMAN R V.Evaluating calculated risk in geotechnical engineering[J].Journal of Geotechnical Engineering,2014,110(2):143–188.
[3]KLAPPERICH H,STURM U,SAVIDIS S A.Discussion of evaluating calculated risk in geotechnical engineering[J].Journal of Geotechnical Engineering,1985,111(6):825–826.
[4]WHITMAN R V.Closure of“evaluating calculated risk in geotechnical engineering”[J].Journal of Geotechnical Engineering,2009,111(6):826–827.
[5]LOW B K,TANG W H.Efficient reliability evaluation using spreadsheet[J].Journal of Engineering Mechanics,1997,123(7):749–752.
[6]陈祖煜,陈立宏,王玉杰,等.滑坡和建筑物抗滑稳定分析中的可靠度分析和分项系数设计方法[C]//水利水电工程风险分析及可靠度设计技术进展.北京:中国水利水电出版社,2010:27–39.(CHEN Zuyu,CHEN Lihong,WANG Yujie,et al.Reliability analysis and partial factor design methods for slope stability[C]//Proceedings of the Symposium on Risk Analysis and Reliability Based Design for Water Resources and Hydropower Projects.Beijing:China Water Power Press,2010:27–39.(in Chinese))
[7]ZHANG C Q,ZHOU H,FENG X T,et al.A new interpretation for the polyaxial strength effect of rock[J].International Journal of Rock Mechanics and Mining Sciences,2010,47(3):496–501.
[8]BAI B,YUAN W,LI X.A new double reduction method for slope stability analysis[J].Journal of Central South University,2014,21(3):1 158–1 164.
[9]白冰,袁维,石露,等.一种双折减法与经典强度折减法的关系[J].岩土力学,2015,36(5):1 275–1 281.(BAI Bing,YUAN Wei,SHI Lu,et al.Comparing a new double reduction method to classic strength reduction method for slope stability analysis[J].Rock and Soil Mechanics,2015,36(5):1 275–1 281.(in Chinese))
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[11]WU T H.2008 Peck lecture:The observational method:case history and models[J].Journal of Geotechnical and Geoenvironmental Engineering,2011,137(10):862–873.
[12]KULHAWY F H.Uncertainty,reliability,and foundation engineering:The 5th Peter Lumb Lecture[C]//Foundation Engineering in the Face of Uncertainty@s Honoring Fred H.Kulhawy:[s.n.],2015:209–214.
[13]BAECHER G B,CHRISTIAN J T.Reliability and statistics in geotechnical engineering[M].New York:Wiley,2003:303–469.
[14]WONG F S.Slope reliability and response surface method[J].Journal of Geotechnical Engineering,1985,111(1):32–53.
[15]谭晓慧.多滑面边坡的可靠性分析[J].岩石力学与工程学报,2001,20(6):822–825.(TAN Xiaohui.Reliability analysis of slopes with multi slip surface[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(6):822–825.(in Chinese))
[16]DITLEVSEN O,MADSEN H O.Structural reliability methods[M].New York:Wiley,1996:33–52.
[17]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 Dianqing,ZHOU Chuangbin.System reliability analysis of rock slope considering multiple correlated failure modes[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(3):541–551.(in Chinese))
[18]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):1 349–1 359.
[19]LOW B K,TANG W H.Efficient spreadsheet algorithm for first-order reliability method[J].Journal of Engineering Mechanics,2007,133(12):1 378–1 387.
[20]郑宏,田斌,刘德富,等.关于有限元边坡稳定性分析中安全系数的定义问题[J].岩石力学与工程学报,2005,24(13):2 225–2 230.(ZHENG Hong,TIAN Bin,LIU Defu,et al.On definitions of safety factor of slope stability analysis with finite element method[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(13):2 225–2 230.(in Chinese))
[21]HALDAR A,MAHADEVAN S.Probability,reliability,and statistical methods in engineering design[M].[S.l.]:John Wiley and Sons,Incorporated,2000:250–272.
[22]DUNCAN J M.Factors of safety and reliability in geotechnical engineering[J].Journal of Geotechnical and Geoenvironmental Engineering,2000,126(4):307–316.
[2]WHITMAN R V.Evaluating calculated risk in geotechnical engineering[J].Journal of Geotechnical Engineering,2014,110(2):143–188.
[3]KLAPPERICH H,STURM U,SAVIDIS S A.Discussion of evaluating calculated risk in geotechnical engineering[J].Journal of Geotechnical Engineering,1985,111(6):825–826.
[4]WHITMAN R V.Closure of“evaluating calculated risk in geotechnical engineering”[J].Journal of Geotechnical Engineering,2009,111(6):826–827.
[5]LOW B K,TANG W H.Efficient reliability evaluation using spreadsheet[J].Journal of Engineering Mechanics,1997,123(7):749–752.
[6]陈祖煜,陈立宏,王玉杰,等.滑坡和建筑物抗滑稳定分析中的可靠度分析和分项系数设计方法[C]//水利水电工程风险分析及可靠度设计技术进展.北京:中国水利水电出版社,2010:27–39.(CHEN Zuyu,CHEN Lihong,WANG Yujie,et al.Reliability analysis and partial factor design methods for slope stability[C]//Proceedings of the Symposium on Risk Analysis and Reliability Based Design for Water Resources and Hydropower Projects.Beijing:China Water Power Press,2010:27–39.(in Chinese))
[7]ZHANG C Q,ZHOU H,FENG X T,et al.A new interpretation for the polyaxial strength effect of rock[J].International Journal of Rock Mechanics and Mining Sciences,2010,47(3):496–501.
[8]BAI B,YUAN W,LI X.A new double reduction method for slope stability analysis[J].Journal of Central South University,2014,21(3):1 158–1 164.
[9]白冰,袁维,石露,等.一种双折减法与经典强度折减法的关系[J].岩土力学,2015,36(5):1 275–1 281.(BAI Bing,YUAN Wei,SHI Lu,et al.Comparing a new double reduction method to classic strength reduction method for slope stability analysis[J].Rock and Soil Mechanics,2015,36(5):1 275–1 281.(in Chinese))
[10]CHRISTIAN J T.The thirty-ninth Karl Terzaghi lecture:Geotechnical Engineering reliability:How well do we know what we are doing[R].[S.l]:[s.n.],2004.
[11]WU T H.2008 Peck lecture:The observational method:case history and models[J].Journal of Geotechnical and Geoenvironmental Engineering,2011,137(10):862–873.
[12]KULHAWY F H.Uncertainty,reliability,and foundation engineering:The 5th Peter Lumb Lecture[C]//Foundation Engineering in the Face of Uncertainty@s Honoring Fred H.Kulhawy:[s.n.],2015:209–214.
[13]BAECHER G B,CHRISTIAN J T.Reliability and statistics in geotechnical engineering[M].New York:Wiley,2003:303–469.
[14]WONG F S.Slope reliability and response surface method[J].Journal of Geotechnical Engineering,1985,111(1):32–53.
[15]谭晓慧.多滑面边坡的可靠性分析[J].岩石力学与工程学报,2001,20(6):822–825.(TAN Xiaohui.Reliability analysis of slopes with multi slip surface[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(6):822–825.(in Chinese))
[16]DITLEVSEN O,MADSEN H O.Structural reliability methods[M].New York:Wiley,1996:33–52.
[17]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 Dianqing,ZHOU Chuangbin.System reliability analysis of rock slope considering multiple correlated failure modes[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(3):541–551.(in Chinese))
[18]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):1 349–1 359.
[19]LOW B K,TANG W H.Efficient spreadsheet algorithm for first-order reliability method[J].Journal of Engineering Mechanics,2007,133(12):1 378–1 387.
[20]郑宏,田斌,刘德富,等.关于有限元边坡稳定性分析中安全系数的定义问题[J].岩石力学与工程学报,2005,24(13):2 225–2 230.(ZHENG Hong,TIAN Bin,LIU Defu,et al.On definitions of safety factor of slope stability analysis with finite element method[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(13):2 225–2 230.(in Chinese))
[21]HALDAR A,MAHADEVAN S.Probability,reliability,and statistical methods in engineering design[M].[S.l.]:John Wiley and Sons,Incorporated,2000:250–272.
[22]DUNCAN J M.Factors of safety and reliability in geotechnical engineering[J].Journal of Geotechnical and Geoenvironmental Engineering,2000,126(4):307–316.