土体参数空间变异性对边坡失效模式间相关性及系统可靠度的影响
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摘要
常用的计算失效模式间近似相关系数存在一定的误差,采用Pearson相关系数准确地表征边坡失效模式间相关性。基于近似相关系数和Pearson相关系数,研究了土体参数空间变异性对边坡失效模式间相关性、代表性失效模式数目、边坡系统失效概率上、下限3方面的影响。简要介绍了选取边坡代表性滑动面的风险聚类法以及系统失效概率上、下限的Ditlevsen双模界限公式。以单层和两层边坡为例研究了近似相关系数的适用性。结果表明:常用的近似相关系数不能考虑土体参数空间变异性对边坡失效模式间相关性的影响,而Pearson相关系数能够有效地反映土体参数空间变异性对边坡失效模式间相关性的影响。当土体参数空间变异性较弱时,近似相关系数与Pearson相关系数间差别明显,基于近似相关系数会选取过多的代表性滑动面,不能有效地反映边坡代表性破坏模式。此外,基于近似相关系数计算的边坡系统失效概率上限会超过1,系统失效概率上、下限范围很宽,使得系统失效概率上、下限失去了意义。相比之下,基于Pearson相关系数计算的边坡系统失效概率上、下限范围较窄,能够有效地反映系统失效概率变化情况。
The commonly used approximation for evaluating the correlation coefficients between failure modes has a certain degree of error. This paper uses Pearson correlation coefficient to characterize the correlation between different slope failure mechanisms. Based on the correlation coefficients calculated from two different methods, this paper studies the effect of soil spatial variability on correlation coefficients between failure modes, the number of failure modes of a slope and the bimodal bounds of system failure probability. A brief introduction to risk aggregation method aiming at selecting representative slip surfaces, and Ditlevsen's formulas for calculating bimodal bounds of system failure probability is presented. A single-layered and a two-layered slopes are studied to evaluate applicability of the approximation correlation coefficients. The results show that the commonly used approximation correlation coefficients cannot reflect the effect of soil spatial variability on correlation between failure modes, whereas the Pearson correlation coefficients can. When the spatial variability of soil properties is weak, there is large discrepancy between approximation correlation coefficients and Pearson correlation coefficients. Too many representative slip surfaces are selected and the representative failure modes cannot be reflected effectively based on approximate correlation coefficients. Furthermore, the upper-bound limit of system failure probability calculated by approximation correlation coefficients is probably greater than 1, and the bimodal bounds of system failure probability are too wide, all of these make system failure probability become meaningless. By contrast, the calculated bimodal bounds of system failure probability based on Pearson correlation coefficients are narrower, showing the changes of system failure probability effectively.
The commonly used approximation for evaluating the correlation coefficients between failure modes has a certain degree of error. This paper uses Pearson correlation coefficient to characterize the correlation between different slope failure mechanisms. Based on the correlation coefficients calculated from two different methods, this paper studies the effect of soil spatial variability on correlation coefficients between failure modes, the number of failure modes of a slope and the bimodal bounds of system failure probability. A brief introduction to risk aggregation method aiming at selecting representative slip surfaces, and Ditlevsen's formulas for calculating bimodal bounds of system failure probability is presented. A single-layered and a two-layered slopes are studied to evaluate applicability of the approximation correlation coefficients. The results show that the commonly used approximation correlation coefficients cannot reflect the effect of soil spatial variability on correlation between failure modes, whereas the Pearson correlation coefficients can. When the spatial variability of soil properties is weak, there is large discrepancy between approximation correlation coefficients and Pearson correlation coefficients. Too many representative slip surfaces are selected and the representative failure modes cannot be reflected effectively based on approximate correlation coefficients. Furthermore, the upper-bound limit of system failure probability calculated by approximation correlation coefficients is probably greater than 1, and the bimodal bounds of system failure probability are too wide, all of these make system failure probability become meaningless. By contrast, the calculated bimodal bounds of system failure probability based on Pearson correlation coefficients are narrower, showing the changes of system failure probability effectively.
引文
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[20]LI L,CHU X S.Multiple response surfaces for slope reliability analysis[J].International Journal for Numerical and Analytical Methods in Geomechanics,2015,39(2):175-192.
[21]褚雪松,王旭春,张勇强,等.基于代表性滑动面的边坡系统可靠度分析[J].煤炭学报,2014,39(6):1077-1083.CHU Xue-song,WANG Xu-chun,ZHANG Yong-qiang,et al.Slope system reliability analysis based on representative slip surfaces[J].Journal of China Coal Society,2014,39(6):1077-1083.
[22]LOW B K,ZHANG J,TANG W H.Efficient system reliability analysis illustrated for a retaining wall and a soil slope[J].Computers and Geotechnics,2011,38(2):196-204.
[23]CHO S E.First-order reliability analysis of slope considering multiple failure modes[J].Engineering Geology,2013,154:98-105.
[24]ANG A H S,TANG W H.Probability concepts in engineering planning and design,vol.II,decision,risk,and reliability[M].New York:John Wiley and Sons,1984.
[25]GEO-SLOPE International Ltd.Stability modeling with SLOPE/W 2007 Version:An engineering methodology[M].Calgary:GEO-SLOPE International Ltd.,2010.
[26]DITLEVSEN O.Narrow reliability bounds for structural systems[J].Journal of Structural Mechanics,1979,7(4):453-472.
[27]HUANG J S,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.
[2]PHOON K K,KULHAWY F H.Characterization of geotechnical variability[J].Canadian Geotechnical Journal,1999,36(4):612-624.
[3]吴振君,王水林,葛修润.约束随机场下的边坡可靠度随机有限元分析方法[J].岩土力学,2009,30(10):3086-3092.WU Zhen-jun,WANG Shui-lin,GE Xiu-run.Slope reliability analysis by random FEM under constraint random field[J].Rock and Soil Mechanics,2009,30(10):3086-3092.
[4]薛亚东,方超,葛嘉诚.各向异性随机场下的边坡可靠度分析[J].岩土工程学报,2013,35(增刊2):77-82.XUE Ya-dong,FANG Chao,GE Jia-cheng.Slope reliability in anisotropic random fields[J].Chinese Journal of Geotechnical Engineering,2013,35(Supp.2):77-82.
[5]李典庆,祁小辉,周创兵,等.考虑参数空间变异性的无限长边坡可靠度分析[J].岩土工程学报,2013,35(10):1799-1806.LI Dian-qing,QI Xiao-hui,ZHOU Chuang-bing,et al.Reliability analysis of infinite soil slopes considering spatial variability of soil parameters[J].Chinese Journal of Geotechnical Engineering,2013,35(10):1799-1806.
[6]李亚军,刘斯宏,傅中志,等.多层地基土坡的随机有限元模型不同参数比较分析(英文)[J].岩土工程学报,2014,36(1):162-169.LI Ya-jun,LIU Si-hong,FU Zhong-zhi,et al.Comparative study on the effect of different parameters of random finite element models of an embankment supported by multilayered foundations[J].Chinese Journal of Geotechnical Engineering,2014,36(1):162-169.
[7]HICKS M A,SAMY K.Influence of heterogeneity on undrained clay slope stability[J].Quarterly Journal of Engineering Geology and Hydrogeology,2002,35(1):41-49.
[8]BABU G L S,MUKESH M D.Effect of soil variability on reliability of soil slopes[J].Géotechnique,2004,54(5):335-337.
[9]GRIFFITHS D V,FENTON G A.Probabilistic slope stability analysis by finite elements[J].Journal of Geotechnical and Geoenvironmental Engineering,2004,130(5):507-518.
[10]CHO S E.Effects of spatial variability of soil properties on slope stability[J].Engineering Geology,2007,92(3/4):97-109.
[11]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.
[12]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.
[13]LI D Q,QI X H,PHOON K K,et al.Effect of spatially variable shear strength parameters with linearly increasing mean trend on reliability of infinite slopes[J].Structural Safety,2014,49:45-55.
[14]HONG H P,ROH G.Reliability evaluation of earth slopes[J].Journal of Geotechnical and Geoenvironmental Engineering,2008,134(12):1700-1705.
[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 Xiao-hui.Reliability analysis of a slope with several slide surfaces[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(6):822-825.
[16]CHOWDHURY R N,XU D W.Slope system reliability with general slip surfaces[J].Soils and Foundations,1994,34(3):99-105.
[17]ZHANG J,ZHANG L M,TANG W H.New methods for system reliability analysis of soil slopes[J].Canadian Geotechnical Journal,2011,48(7):1138-1148.
[18]LI L,WANG Y,CAO Z J,et al.Risk de-aggregation and system reliability analysis of slope stability using representative slip surfaces[J].Computers and Geotechnics,2013,53:95-105.
[19]LI L,WANG Y,CAO Z J.Probabilistic slope stability analysis by risk aggregation[J].Engineering Geology,2014,176:57-65.
[20]LI L,CHU X S.Multiple response surfaces for slope reliability analysis[J].International Journal for Numerical and Analytical Methods in Geomechanics,2015,39(2):175-192.
[21]褚雪松,王旭春,张勇强,等.基于代表性滑动面的边坡系统可靠度分析[J].煤炭学报,2014,39(6):1077-1083.CHU Xue-song,WANG Xu-chun,ZHANG Yong-qiang,et al.Slope system reliability analysis based on representative slip surfaces[J].Journal of China Coal Society,2014,39(6):1077-1083.
[22]LOW B K,ZHANG J,TANG W H.Efficient system reliability analysis illustrated for a retaining wall and a soil slope[J].Computers and Geotechnics,2011,38(2):196-204.
[23]CHO S E.First-order reliability analysis of slope considering multiple failure modes[J].Engineering Geology,2013,154:98-105.
[24]ANG A H S,TANG W H.Probability concepts in engineering planning and design,vol.II,decision,risk,and reliability[M].New York:John Wiley and Sons,1984.
[25]GEO-SLOPE International Ltd.Stability modeling with SLOPE/W 2007 Version:An engineering methodology[M].Calgary:GEO-SLOPE International Ltd.,2010.
[26]DITLEVSEN O.Narrow reliability bounds for structural systems[J].Journal of Structural Mechanics,1979,7(4):453-472.
[27]HUANG J S,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.
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