边坡工程模糊随机可靠度分析
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摘要
将模糊随机理论应用于边坡可靠性评价当中,为了考虑随机变量的模糊随机性,引入稳定系数的隶属函数对边坡的实际工作状态进行模糊可靠评价。提出模糊随机极限状态方程的二次构造思想,即将模糊随机理论和响应面法相结合,首先利用响应面法进行一次构造,得到可靠度响应面函数,在此基础上借助隶属函数的补函数作为辅助,进行二次构造极限状态方程来计算边坡的模糊随机可靠度。结果表明,该方法计算简便、收敛速度快,克服了对模糊概率密度函数直接积分求解时过程复杂、耗费机时的缺点,具有较高的计算精度和广泛的工程实用性。计算所得到的可靠性指标更加能够真实地反映边坡的稳定状态,为边坡工程可靠性研究提供了一种新的方法。
Fuzzy stochastic theory is applied to the slope reliability evaluation.Considering the fuzzy and stochastic features of random variables,the subordinate function of stability factor is introduced to perform fuzzy reliability analysis for the actual working condition of the slope.The secondary structure of fuzzy random limit state equation is proposed on the basis of combining the fuzzy stochastic theory with the response surface method.The response surface method is used on a structure firstly to obtain the reliability response surface function,based on which the complementary function of subordinate function is used as an auxiliary to carry on the secondary limit state equation to calculate the random fuzzy reliability of the slope.Rather than directly solving the fuzzy probability density function by integral calculus,which is complicated and time-consuming,this method is proved to be simple with fast convergence and high precision of calculation,thereby can be used widely.The slope stability can be reflected more accurately by the calculated reliability indexes.The method can be regarded as a new approach of studying the reliability of slopes.
Fuzzy stochastic theory is applied to the slope reliability evaluation.Considering the fuzzy and stochastic features of random variables,the subordinate function of stability factor is introduced to perform fuzzy reliability analysis for the actual working condition of the slope.The secondary structure of fuzzy random limit state equation is proposed on the basis of combining the fuzzy stochastic theory with the response surface method.The response surface method is used on a structure firstly to obtain the reliability response surface function,based on which the complementary function of subordinate function is used as an auxiliary to carry on the secondary limit state equation to calculate the random fuzzy reliability of the slope.Rather than directly solving the fuzzy probability density function by integral calculus,which is complicated and time-consuming,this method is proved to be simple with fast convergence and high precision of calculation,thereby can be used widely.The slope stability can be reflected more accurately by the calculated reliability indexes.The method can be regarded as a new approach of studying the reliability of slopes.
引文
[1]DODAGOUDAR G R,VENKATACHALAM G.Reliabili-ty Analysis of Slopes Using Fuzzy Sets Theory[J].Com-puters and Geotechnics,2000,27(2):101-115.(inChinese)
[2]李彰明.模糊分析在边坡稳定性评价中的应用[J].岩石力学与工程学报,1997,16(5):491-495.(LIZhang-ming.Application of Fuzzy Analysis in Slope Sta-bility Evaluation[J].Chinese Journal of Rock Mechanicsand Engineering,1997,16(5):491-495.(in Chi-nese))
[3]李文秀.岩土边坡稳定性的模糊测度分析[J].岩土工程学报,1996,18(2):11-16.(LI Wen-xiu.FuzzyMeasure Analysis for the Stability of Rock and Soil Slopes[J].Chinese Journal of Geotechnical Engineering,1996,18(2):11-16.(in Chinese))
[4]谭晓慧.边坡稳定分析的模糊概率法[J].合肥工业大学学报(自然科学版),2001,24(3):443-446.(TAN Xiao-hui.The Stability Analysis of Slope by FuzzyProbability Method[J].Journal of Hefei University ofTechnology,2001,24(3):443-446.(in Chinese))
[5]楼芬,邓建.AHP-FUZZY法在露天矿边坡稳定性分析中的应用[J].采矿技术,2008,8(2):28-30.(LOU Fen,DENG Jian.The Application of FUZZY AHPMethod in the Slope Stability Analysis of Open-Pit Mine[J].Mining Technology,2008,8(2):28-30.(inChinese))
[6]徐卫亚,蒋中明,石安池.基于模糊集理论的边坡稳定性分析[J].岩土工程学报,2003,25(4):410-413.(XU Wei-ya,JIANG Zhong-ming,SHI An-chi.SlopeStability Analysis Using Fuzzy Sets Theory[J].ChineseJournal of Geotechnical Engineering,2003,25,(4):410-413.(in Chinese))
[7]GAYTON N,BOURINET J M,LEMARIE M C.A NewStatistical Approach for Structural Reliability Problem[J].Structure Safety,1990,7(1):57-66.
[8]苏永华,赵明华,蒋德松,等.响应面方法在边坡稳定可靠度分析中的应用[J].岩石力学与工程学报,2006,25(7):1418-1424.(SU Yong-hua,ZHAOMing-hua,JIANG De-song,et al.Application of Re-sponse Surface Method to Reliability Analysis of SlopeStability[J].Chinese Journal of Rock Mechanics andEngineering,2006,25(7):1418-1424.(in Chinese))
[9]RAJASHEKHAR M R,ELLINGWOOD B R.A NewLook at the Response Surface Approach for Reliability A-nalysis[J].Structure Safety,1993,12(3):205-220.
[10]徐辉.基于模糊集理论的边坡稳定模糊随机可靠度分析[D].杭州:浙江大学,2006.(XU Hui.Fuzzy Reli-ability Analysis of Slope Capacity Based on Fuzzy Sets[D].Hangzhou:Zhejiang University,2006.(in Chi-nese))
[11]冯夏庭.智能岩石力学导论[M].北京:科学出版社,2000.(FENG Xia-ting.An Introduction to IntelligentRock Mechanics[M].Beijing:Science Press,2000.(inChinese))
[12]GIASI C I,MASI P,CHERUBINI C.Probabilistic andFuzzy Reliability Analysis of a Sample Slope Near Aliano[J].Engineering Geology,2003,67(3-4):391-402.
[13]李胡生.岩土参数随机-模糊统计中的隶属函数形式[J].同济大学学报,1993,21(3):362-368.(LIHu-sheng.On the Membership Functions in a Random-Fuzzy Statistics Method for Geotechnical Parameters[J].Journal of Tongji University,1993,21(3):362-368.(in Chinese))
[14]祁生文,伍法权,刘春玲,等.地震边坡稳定性的工程地质分析[J].岩石力学与工程学报,2004,23(16):2793-2797.(QI Sheng-wen,WU Fa-quan,LIU Chun-ling,et al.Engineering Geology Analysis on Stability ofSlope under Earthquake[J].Chinese Journal of Geotech-nical Engineering,2004,23(16):2793-2797.(inChinese))
[2]李彰明.模糊分析在边坡稳定性评价中的应用[J].岩石力学与工程学报,1997,16(5):491-495.(LIZhang-ming.Application of Fuzzy Analysis in Slope Sta-bility Evaluation[J].Chinese Journal of Rock Mechanicsand Engineering,1997,16(5):491-495.(in Chi-nese))
[3]李文秀.岩土边坡稳定性的模糊测度分析[J].岩土工程学报,1996,18(2):11-16.(LI Wen-xiu.FuzzyMeasure Analysis for the Stability of Rock and Soil Slopes[J].Chinese Journal of Geotechnical Engineering,1996,18(2):11-16.(in Chinese))
[4]谭晓慧.边坡稳定分析的模糊概率法[J].合肥工业大学学报(自然科学版),2001,24(3):443-446.(TAN Xiao-hui.The Stability Analysis of Slope by FuzzyProbability Method[J].Journal of Hefei University ofTechnology,2001,24(3):443-446.(in Chinese))
[5]楼芬,邓建.AHP-FUZZY法在露天矿边坡稳定性分析中的应用[J].采矿技术,2008,8(2):28-30.(LOU Fen,DENG Jian.The Application of FUZZY AHPMethod in the Slope Stability Analysis of Open-Pit Mine[J].Mining Technology,2008,8(2):28-30.(inChinese))
[6]徐卫亚,蒋中明,石安池.基于模糊集理论的边坡稳定性分析[J].岩土工程学报,2003,25(4):410-413.(XU Wei-ya,JIANG Zhong-ming,SHI An-chi.SlopeStability Analysis Using Fuzzy Sets Theory[J].ChineseJournal of Geotechnical Engineering,2003,25,(4):410-413.(in Chinese))
[7]GAYTON N,BOURINET J M,LEMARIE M C.A NewStatistical Approach for Structural Reliability Problem[J].Structure Safety,1990,7(1):57-66.
[8]苏永华,赵明华,蒋德松,等.响应面方法在边坡稳定可靠度分析中的应用[J].岩石力学与工程学报,2006,25(7):1418-1424.(SU Yong-hua,ZHAOMing-hua,JIANG De-song,et al.Application of Re-sponse Surface Method to Reliability Analysis of SlopeStability[J].Chinese Journal of Rock Mechanics andEngineering,2006,25(7):1418-1424.(in Chinese))
[9]RAJASHEKHAR M R,ELLINGWOOD B R.A NewLook at the Response Surface Approach for Reliability A-nalysis[J].Structure Safety,1993,12(3):205-220.
[10]徐辉.基于模糊集理论的边坡稳定模糊随机可靠度分析[D].杭州:浙江大学,2006.(XU Hui.Fuzzy Reli-ability Analysis of Slope Capacity Based on Fuzzy Sets[D].Hangzhou:Zhejiang University,2006.(in Chi-nese))
[11]冯夏庭.智能岩石力学导论[M].北京:科学出版社,2000.(FENG Xia-ting.An Introduction to IntelligentRock Mechanics[M].Beijing:Science Press,2000.(inChinese))
[12]GIASI C I,MASI P,CHERUBINI C.Probabilistic andFuzzy Reliability Analysis of a Sample Slope Near Aliano[J].Engineering Geology,2003,67(3-4):391-402.
[13]李胡生.岩土参数随机-模糊统计中的隶属函数形式[J].同济大学学报,1993,21(3):362-368.(LIHu-sheng.On the Membership Functions in a Random-Fuzzy Statistics Method for Geotechnical Parameters[J].Journal of Tongji University,1993,21(3):362-368.(in Chinese))
[14]祁生文,伍法权,刘春玲,等.地震边坡稳定性的工程地质分析[J].岩石力学与工程学报,2004,23(16):2793-2797.(QI Sheng-wen,WU Fa-quan,LIU Chun-ling,et al.Engineering Geology Analysis on Stability ofSlope under Earthquake[J].Chinese Journal of Geotech-nical Engineering,2004,23(16):2793-2797.(inChinese))
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