考虑土质边坡多失效模式的区域概率风险分析方法
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摘要
针对现有边坡风险分析仅考虑单一失效模式及风险分析结果难以被工程师理解等问题,提出了考虑边坡多失效模式的区域概率风险分析方法。首先给出了区域概率的概念,建立了以区域概率定量表征边坡稳定性的方法,推导了基于区域概率的边坡系统风险评价公式,探讨了该公式的适用性。在此基础上采用直接蒙特卡罗模拟计算边坡区域失效概率。最后以一不排水黏性土坡为例阐明了所提方法的有效性。结果表明:区域概率风险分析方法为表征边坡的关键失效区提供了一种简单、直接的可视化工具,为工程师制定合理的边坡加固设计方案提供了参考依据。基于区域概率风险分析方法的边坡系统风险评价公式不仅能够有效地回避边坡风险评价中多滑面间安全系数及滑块体积之间相关性计算问题,而且能够准确地量化边坡多破坏模式的系统风险。传统的风险评价方法可能显著低估边坡系统风险,使得边坡设计方案偏危险。边坡失效概率最大的滑面不一定是边坡失效风险最大的滑面,在边坡加固设计中,失效风险较大的滑面也应该予以关注。
Conventional slope system risk assessment commonly concerns a single failure mode in each numerical realization and their reliability analysis results are difficult to be understood by geotechnical engineers with weak mathematical background. To address the difficulties, this study proposes a slope system risk estimation method based on region probability incorporating multiple failure modes in the slope system. First, the concept of region probability is provided. The method for representing slope stability quantitively with region probability is then established. The formula for estimating of slope system risk based on region probability is derived and its applicability is discussed. Monte Carlo simulation(MCS) is then employed to calculate the region failure probability. An undrained cohesive slope cut is used to demonstrate the performance of the proposed approach. The results indicate that the region failure probability provides a simple, straightforward and visual tool for the identification of key dangerous regions of the slope, which in turn can give insights into the design of countermeasures for slope reinforcement and risk mitigation. In addition, the region failure probability-based risk assessment method can properly estimate the slope system risk and effectively avoid sophisticated correlations among the sliding blocks and the factor of the large number of potential slip surfaces. Conventional risk assessment methods may lead to a significant underestimation of slope system risk, which may incur an under-design of slope and is detrimental to the slope system. The slip surface associated with the largest risk may not be the slip surface associated with the largest failure possibility. The slip surface associated with the largest risk deserves the same attention as that associated with the largest failure possibility in the slope design and reinforcement.
Conventional slope system risk assessment commonly concerns a single failure mode in each numerical realization and their reliability analysis results are difficult to be understood by geotechnical engineers with weak mathematical background. To address the difficulties, this study proposes a slope system risk estimation method based on region probability incorporating multiple failure modes in the slope system. First, the concept of region probability is provided. The method for representing slope stability quantitively with region probability is then established. The formula for estimating of slope system risk based on region probability is derived and its applicability is discussed. Monte Carlo simulation(MCS) is then employed to calculate the region failure probability. An undrained cohesive slope cut is used to demonstrate the performance of the proposed approach. The results indicate that the region failure probability provides a simple, straightforward and visual tool for the identification of key dangerous regions of the slope, which in turn can give insights into the design of countermeasures for slope reinforcement and risk mitigation. In addition, the region failure probability-based risk assessment method can properly estimate the slope system risk and effectively avoid sophisticated correlations among the sliding blocks and the factor of the large number of potential slip surfaces. Conventional risk assessment methods may lead to a significant underestimation of slope system risk, which may incur an under-design of slope and is detrimental to the slope system. The slip surface associated with the largest risk may not be the slip surface associated with the largest failure possibility. The slip surface associated with the largest risk deserves the same attention as that associated with the largest failure possibility in the slope design and reinforcement.
引文
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[6]Li D,Xiao T,Cao Z,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.
[7]蒋水华,杨建华,姚池,等.考虑土体参数空间变异性边坡失稳风险定量评估[J].工程力学,2018,35(1):136-147.Jiang Shuihua,Yang Jianhua,Yao Chi,et al.Quantitative risk assessment of slope failure considering spatial variability of soil properties[J].Engineering Mechanics,2018,35(1):136-147.(in Chinese)
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[9]Li L,Chu X.Risk assessment of slope failure by representative slip surfaces and response surface function[J].KSCE Journal of Civil Engineering,2016,20(5):1783-1792.
[10]Zhang J,Huang H W.Risk assessment of slope failure considering multiple slip surfaces[J].Computers and Geotechnics,2016,74:188-195.
[11]Jiang S,Huang J,Yao C,et al.Quantitative risk assessment of slope failure in 2-D spatially variable soils by limit equilibrium method[J].Applied Mathematical Modelling,2017,47:710-725.
[12]Cheng Y M,Lansivaara T,Wei W B.Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods[J].Computers and Geotechnics,2007,34(3):137-150.
[13]Reale C,Xue J,Gavin K.System reliability of slopes using multimodal optimization[J].Géotechnique,2016,66(5):413-423.
[14]Tun Y W,Pedroso D M,Scheuermann A,et al.Probabilistic reliability analysis of multiple slopes with genetic algorithms[J].Computers and Geotechnics,2016,77:68-76.
[15]张鲁渝.边坡稳定分析软件ZSlope的开发[J].岩石力学与工程学报,2004,23(16):2830-2835.Zhang Luyu.Development of software zslope for slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(16):2830-2835.(in Chinese)
[16]闫超,刘松玉,籍晓蕾.一种基于强度折减法的次级滑动面分析方法研究[J].岩土力学,2016,37(4):935-942.Yan Chao,Liu Songyu,Ji Xiaolei.Research on a secondary sliding surface analysis approach based on strength reduction method[J].Rock and Soil Mechanics,2016,37(4):935-942.(in Chinese)
[17]薛海斌,党发宁,尹小涛,等.基于岩土材料软化特性的滑坡多级滑动面分析方法研究[J].岩土力学,2015,36(11):3235-3242.Xue Haibin,Dang Faning,Yin Xiaotao,et al.Research on analytical method of multi-slip surfaces of landslide based on softening characteristics of geomaterial[J].Rock and Soil Mechanics,2015,36(11):3235-3242.(in Chinese)
[18]蒋水华,李典庆,周创兵,等.考虑自相关函数影响的边坡可靠度分析[J].岩土工程学报,2014,36(3):508-518.Jiang Shuihua,Li Dianqing,Zhou Chuangbing,et al.Slope reliability analysis considering effect of autocorrelation functions[J].Chinese Journal of Geotechnical Engineering,2014,36(3):508-518.(in Chinese)
[19]李典庆,蒋水华,周创兵,等.考虑参数空间变异性的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(8):1413-1422.Li Dianqing,Jiang Shuihua,Zhou Chuangbing,et al.Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1413-1422.(in Chinese)
[20]Cho S E.Probabilistic assessment of slope stability that considers the spatial variability of soil properties.Journal of Geotechnical and Geoenvironmental Engineering,2010,136(7):975-984.
[21]Chowdhury R N,Xu D W.Geotechnical system reliability of slopes[J].Reliability Engineering&System Safety,1995,47(3):141-151.
[22]Oka Y,Wu T H.System reliability of slope stability[J].Journal of Geotechnical Engineering,1990,116(8):1185-1189.
[23]Christian J T.Issues of reliability in stability of slopes[J].InGeo-Congress 2013:Stability and Performance of Slopes and Embankments III,2013:2246-2261.
[24]Juang C H,Zhang J,Gong W.Reliability-based assessment of stability of slopes[J].IOP Conference Series:Earth and Environmental Science,2015,26(1):12006.
[25]Phoon K,Kulhawy F H.Characterization of geotechnical variability[J].Canadian Geotechnical Journal,1999,36(4):612-624.
[26]杨智勇,曹子君,李典庆,等.颗粒接触摩擦系数空间变异性对颗粒流双轴数值试验的影响[J].工程力学,2017,34(5):235-246.Yang Zhiyong,Cao Zijun,Li Dianqing,et al.Effect of spatially variable friction coefficient of granular materials on its macro-mechanical behaviors using biaxial compression numerical simulation[J].Engineering Mechanics,2017,34(5):235-246.(in Chinese)
[27]祁小辉,李典庆,周创兵,等.考虑土体空间变异性的边坡最危险滑动面随机分析方法[J].岩土工程学报,2013,35(04):745-753.Qi Xiaohui,Li Dianqing,Zhou Chuangbing,et al.Stochastic analysis method of critical slip surfaces in soil slopes considering spatial variability[J].Chinese Journal of Geotechnical Engineering,2013,35(4):745-753.(in Chinese)
[28]闫澍旺,朱红霞,刘润.天津港土性相关距离的计算研究和统计分析[J].岩土力学,2009,30(7):2179-2185.Yan Shuwang,Zhu Hongxia,Liu Run.Numerical studies and statistic analyses of correlation distances of soil properties in Tianjin Port[J].Rock and Soil Mechanics,2009,30(7):2179-2185.(in Chinese)
[29]田密,李典庆,曹子君,等.基于贝叶斯理论的土性参数空间变异性量化方法[J].岩土力学,2017,38(11):3355-3362.Tian Mi,Li Dianqing,Cao Zijun,et al.Quantification of inherent spatial variability of soil parameters using Bayesian approaches[J].Rock and Soil Mechanics,2017,38(11):3355-3362.(in Chinese)
[30]邓志平,李典庆,曹子君,等.考虑地层变异性和土体参数变异性的边坡可靠度分析[J].岩土工程学报,2017,39(6):986-995.Deng Zhiping,Li Dianqing,Cao Zijun,et al.Slope reliability analysis considering geological uncertainty and spatial variability of soil parameters[J].Chinese Journal of Geotechnical Engineering,2017,39(6):986-995.(in Chinese)
[31]李静萍,程勇刚,李典庆,等.基于多重响应面法的空间变异土坡系统可靠度分析[J].岩土力学,2016,37(1):147-155,165.Li Jingping,Cheng Yonggang,Li Dianqing,et al.System reliability analysis of spatially variable soil slopes using the multiple response surfaces method[J].Rock and Soil Mechanics,2016,37(1):147-155,165.(in Chinese)
[32]王贺,张洁,陈飞扬.强降雨条件下花岗岩残积土边坡的时变可靠度[J].武汉大学学报(工学版),2016,49(5):763-767.Wang He,Zhang Jie,Chen Feiyang.Time-dependent reliability of slopes made of completely decomposed granite under intense rainfall[J].Engineering Journal of Wuhan University,2016,49(5):763-767.(in Chinese)
[33]罗正东,董辉,陈铖,等.基于克里金模型的边坡稳定可靠度分析方法[J].岩土力学,2015,36(增刊1):439-444.Luo Zhengdong,Dong Hui,Chen Cheng,et al.An analytic method for slope stability reliability based on Kriging model[J].Rock and Soil Mechanics,2015,36(Suppl 1):439-444.(in Chinese)
[34]Zhu D,Griffiths D V,Huang J,et al.Probabilistic stability analyses of undrained slopes with linearly increasing mean strength[J].Géotechnique,2017,67(8):733-746.
[35]Ang A H S,Tang W H.Probability concepts in engineering:emphasis on applications in civil and environmental engineering[M].Hoboken,New Jersey:John Wiley&Sons,Inc,2007.
[36]Wenping G,Lei W,Sara K,et al.Robust geotechnical design of earth slopes using fuzzy sets[J].Journal of Geotechnical and Geoenvironmental Engineering,2015,141(1):04014084.
[37]Ali A,Huang J,Lyamin A V,et al.Simplified quantitative risk assessment of rainfall-induced landslides modelled by infinite slopes[J].Engineering Geology,2014,179:102-116.
[38]Jiang S H,Li D Q,Cao Z J,et al.Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation[J].Journal of Geotechnical and Geoenvironmental Engineering,2015,141(2):04014096.
[39]US Army Corps of Engineers.Engineering and design:introduction to probability and reliability methods for use in geotechnical engineering[Z].Engineer Technical Letter 1110-2-547.Washington,DC:Department of the Army,1997.
[2]左自波,张璐璐,程演,等.基于MCMC法的非饱和土渗流参数随机反分析[J].岩土力学,2013,34(8):2393-2400.Zuo Zibo,Zhang Lulu,Cheng Yan,et al.Probabilistic back analysis of unsaturated soil seepage parameters based on Markov chain Monte Carlo method[J].Rock and Soil Mechanics,2013,34(8):2393-2400.(in Chinese)
[3]Huang J,Griffiths D V.Modelling spatial variability in geotechnical engineering[J].Georisk:Assessment and Management of Risk for Engineered Systems and Geohazards,2016,10(1):1.
[4]Lacasse S,Nadim F,Kalsnes B.Living with landslide risk[J].Geotechnical Engineering Journal of the SEAGS&AGSSEA,2010,41(4):1-13.
[5]Huang J,Lyamin A V,Griffiths D V,et al.Quantitative risk assessment of landslide by limit analysis and random fields[J].Computers and Geotechnics,2013,53:60-67.
[6]Li D,Xiao T,Cao Z,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.
[7]蒋水华,杨建华,姚池,等.考虑土体参数空间变异性边坡失稳风险定量评估[J].工程力学,2018,35(1):136-147.Jiang Shuihua,Yang Jianhua,Yao Chi,et al.Quantitative risk assessment of slope failure considering spatial variability of soil properties[J].Engineering Mechanics,2018,35(1):136-147.(in Chinese)
[8]Cheng H Z,Chen J.Risk assessment of slope failure considering the variability in soil properties[J].Computers and Geotechnics,2018,103:61-72.
[9]Li L,Chu X.Risk assessment of slope failure by representative slip surfaces and response surface function[J].KSCE Journal of Civil Engineering,2016,20(5):1783-1792.
[10]Zhang J,Huang H W.Risk assessment of slope failure considering multiple slip surfaces[J].Computers and Geotechnics,2016,74:188-195.
[11]Jiang S,Huang J,Yao C,et al.Quantitative risk assessment of slope failure in 2-D spatially variable soils by limit equilibrium method[J].Applied Mathematical Modelling,2017,47:710-725.
[12]Cheng Y M,Lansivaara T,Wei W B.Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods[J].Computers and Geotechnics,2007,34(3):137-150.
[13]Reale C,Xue J,Gavin K.System reliability of slopes using multimodal optimization[J].Géotechnique,2016,66(5):413-423.
[14]Tun Y W,Pedroso D M,Scheuermann A,et al.Probabilistic reliability analysis of multiple slopes with genetic algorithms[J].Computers and Geotechnics,2016,77:68-76.
[15]张鲁渝.边坡稳定分析软件ZSlope的开发[J].岩石力学与工程学报,2004,23(16):2830-2835.Zhang Luyu.Development of software zslope for slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(16):2830-2835.(in Chinese)
[16]闫超,刘松玉,籍晓蕾.一种基于强度折减法的次级滑动面分析方法研究[J].岩土力学,2016,37(4):935-942.Yan Chao,Liu Songyu,Ji Xiaolei.Research on a secondary sliding surface analysis approach based on strength reduction method[J].Rock and Soil Mechanics,2016,37(4):935-942.(in Chinese)
[17]薛海斌,党发宁,尹小涛,等.基于岩土材料软化特性的滑坡多级滑动面分析方法研究[J].岩土力学,2015,36(11):3235-3242.Xue Haibin,Dang Faning,Yin Xiaotao,et al.Research on analytical method of multi-slip surfaces of landslide based on softening characteristics of geomaterial[J].Rock and Soil Mechanics,2015,36(11):3235-3242.(in Chinese)
[18]蒋水华,李典庆,周创兵,等.考虑自相关函数影响的边坡可靠度分析[J].岩土工程学报,2014,36(3):508-518.Jiang Shuihua,Li Dianqing,Zhou Chuangbing,et al.Slope reliability analysis considering effect of autocorrelation functions[J].Chinese Journal of Geotechnical Engineering,2014,36(3):508-518.(in Chinese)
[19]李典庆,蒋水华,周创兵,等.考虑参数空间变异性的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(8):1413-1422.Li Dianqing,Jiang Shuihua,Zhou Chuangbing,et al.Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1413-1422.(in Chinese)
[20]Cho S E.Probabilistic assessment of slope stability that considers the spatial variability of soil properties.Journal of Geotechnical and Geoenvironmental Engineering,2010,136(7):975-984.
[21]Chowdhury R N,Xu D W.Geotechnical system reliability of slopes[J].Reliability Engineering&System Safety,1995,47(3):141-151.
[22]Oka Y,Wu T H.System reliability of slope stability[J].Journal of Geotechnical Engineering,1990,116(8):1185-1189.
[23]Christian J T.Issues of reliability in stability of slopes[J].InGeo-Congress 2013:Stability and Performance of Slopes and Embankments III,2013:2246-2261.
[24]Juang C H,Zhang J,Gong W.Reliability-based assessment of stability of slopes[J].IOP Conference Series:Earth and Environmental Science,2015,26(1):12006.
[25]Phoon K,Kulhawy F H.Characterization of geotechnical variability[J].Canadian Geotechnical Journal,1999,36(4):612-624.
[26]杨智勇,曹子君,李典庆,等.颗粒接触摩擦系数空间变异性对颗粒流双轴数值试验的影响[J].工程力学,2017,34(5):235-246.Yang Zhiyong,Cao Zijun,Li Dianqing,et al.Effect of spatially variable friction coefficient of granular materials on its macro-mechanical behaviors using biaxial compression numerical simulation[J].Engineering Mechanics,2017,34(5):235-246.(in Chinese)
[27]祁小辉,李典庆,周创兵,等.考虑土体空间变异性的边坡最危险滑动面随机分析方法[J].岩土工程学报,2013,35(04):745-753.Qi Xiaohui,Li Dianqing,Zhou Chuangbing,et al.Stochastic analysis method of critical slip surfaces in soil slopes considering spatial variability[J].Chinese Journal of Geotechnical Engineering,2013,35(4):745-753.(in Chinese)
[28]闫澍旺,朱红霞,刘润.天津港土性相关距离的计算研究和统计分析[J].岩土力学,2009,30(7):2179-2185.Yan Shuwang,Zhu Hongxia,Liu Run.Numerical studies and statistic analyses of correlation distances of soil properties in Tianjin Port[J].Rock and Soil Mechanics,2009,30(7):2179-2185.(in Chinese)
[29]田密,李典庆,曹子君,等.基于贝叶斯理论的土性参数空间变异性量化方法[J].岩土力学,2017,38(11):3355-3362.Tian Mi,Li Dianqing,Cao Zijun,et al.Quantification of inherent spatial variability of soil parameters using Bayesian approaches[J].Rock and Soil Mechanics,2017,38(11):3355-3362.(in Chinese)
[30]邓志平,李典庆,曹子君,等.考虑地层变异性和土体参数变异性的边坡可靠度分析[J].岩土工程学报,2017,39(6):986-995.Deng Zhiping,Li Dianqing,Cao Zijun,et al.Slope reliability analysis considering geological uncertainty and spatial variability of soil parameters[J].Chinese Journal of Geotechnical Engineering,2017,39(6):986-995.(in Chinese)
[31]李静萍,程勇刚,李典庆,等.基于多重响应面法的空间变异土坡系统可靠度分析[J].岩土力学,2016,37(1):147-155,165.Li Jingping,Cheng Yonggang,Li Dianqing,et al.System reliability analysis of spatially variable soil slopes using the multiple response surfaces method[J].Rock and Soil Mechanics,2016,37(1):147-155,165.(in Chinese)
[32]王贺,张洁,陈飞扬.强降雨条件下花岗岩残积土边坡的时变可靠度[J].武汉大学学报(工学版),2016,49(5):763-767.Wang He,Zhang Jie,Chen Feiyang.Time-dependent reliability of slopes made of completely decomposed granite under intense rainfall[J].Engineering Journal of Wuhan University,2016,49(5):763-767.(in Chinese)
[33]罗正东,董辉,陈铖,等.基于克里金模型的边坡稳定可靠度分析方法[J].岩土力学,2015,36(增刊1):439-444.Luo Zhengdong,Dong Hui,Chen Cheng,et al.An analytic method for slope stability reliability based on Kriging model[J].Rock and Soil Mechanics,2015,36(Suppl 1):439-444.(in Chinese)
[34]Zhu D,Griffiths D V,Huang J,et al.Probabilistic stability analyses of undrained slopes with linearly increasing mean strength[J].Géotechnique,2017,67(8):733-746.
[35]Ang A H S,Tang W H.Probability concepts in engineering:emphasis on applications in civil and environmental engineering[M].Hoboken,New Jersey:John Wiley&Sons,Inc,2007.
[36]Wenping G,Lei W,Sara K,et al.Robust geotechnical design of earth slopes using fuzzy sets[J].Journal of Geotechnical and Geoenvironmental Engineering,2015,141(1):04014084.
[37]Ali A,Huang J,Lyamin A V,et al.Simplified quantitative risk assessment of rainfall-induced landslides modelled by infinite slopes[J].Engineering Geology,2014,179:102-116.
[38]Jiang S H,Li D Q,Cao Z J,et al.Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation[J].Journal of Geotechnical and Geoenvironmental Engineering,2015,141(2):04014096.
[39]US Army Corps of Engineers.Engineering and design:introduction to probability and reliability methods for use in geotechnical engineering[Z].Engineer Technical Letter 1110-2-547.Washington,DC:Department of the Army,1997.