土体性质互相关性的估计以及不确定性的量化分析
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摘要
土体参数如土体黏聚力、内摩擦角之间存在互相关性,这一特性对岩土设计分析具有重要意义。互相关性可以用互相关系数表征。准确的计算这一系数需要较多试验数据,而实际工程中岩土的试验数据较少。这就导致所得互相关系数的不确定性较大。为此,介绍了如何用自助抽样法去量化这一不确定性,并以工程实例说明。
Soil properties such as cohesion(c') and internal friction angle(φ') often exhibit cross-correlation, which has been shown to greatly affect geotechnical design. The cross-correlation between c' and φ' is characterized by a cross-correlation coefficient ρ, reliable estimation of which, however, generally requires extensive data. In practice, the number of measurement data is usually sparse, leading to great statistical uncertainty in the estimated ρ. This paper adopts the bootstrap method, using which the statistical uncertainty in estimated ρ is objectively and explicitly quantified. c' and φ' data from a real site are adopted for illustration.
Soil properties such as cohesion(c') and internal friction angle(φ') often exhibit cross-correlation, which has been shown to greatly affect geotechnical design. The cross-correlation between c' and φ' is characterized by a cross-correlation coefficient ρ, reliable estimation of which, however, generally requires extensive data. In practice, the number of measurement data is usually sparse, leading to great statistical uncertainty in the estimated ρ. This paper adopts the bootstrap method, using which the statistical uncertainty in estimated ρ is objectively and explicitly quantified. c' and φ' data from a real site are adopted for illustration.
引文
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[8] 唐小松,李典庆,周创兵,等.基于Bootstrap方法的岩土体参数联合分布模型识别[J].岩土力学,2015,36(4):913-922.TANG X S,LI D Q,ZHOU C B,et al.Bootstrap method for joint probability distribution identification of correlated geotechnical parameters[J].Rock and Soil Mechanics,2015,36(4):913-922.
[9] 王晓明,曹正波.基于Bootstrap方法确定岩土参数的标准值[J].地震工程学报,2015,37(增刊1):7-11.WANG X M,CAO Z B.Determination of the standard value of geotechnical parameters using a bootstrap method[J].China Earthquake Engineering Journal,2015,37(S1):7-11.
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[12]LUO Z,Atamturktur S,Juang C H.Bootstrapping for characterizing the effect of uncertainty in sample statistics for braced excavations[J].Journal of Geotechnical and Geoenvironmental Engineering,2012,139(1):13-23.
[2] 涂帆,常方强.土性参数的互相关性对加筋土挡墙可靠度的影响[J].岩石力学与工程学报,2005,24(15):2654-2658.TU F,CHANG F Q.Effect of cross-correlations among soil parameters on reliability of reinforced retaining walls[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(15):2654-2658.
[3] 赵炼恒,左仕,陈静瑜,等.考虑参数互相关性的滑坡抗剪强度参数可靠度反演分析[J].华南理工大学学报(自然科学版),2016,44(6):121-128.ZHAO L H,ZUO S,CHEN J Y,et al.Reliability back analysis of shear strength parameters of landslide considering mutual-correlation between parameters[J].Journal of South China University of Technology(Natural Science),2016,44(6):121-128.
[4] 雷兴刚,周小平.岩土介质强度参数相关性的敏感度分析[J].云南农业大学学报,1999,14(2):171-175.LEI X G,ZHOU X P.Analyses of susceptibility in the strength parameters interrelationship of rock and soil media[J].Journal Yunnan Agricultural University,1999,14(2):171-175.
[5] 兰雁,赵寿刚,沈细中,等.土体强度指标的互相关性对堤防稳定性的影响[J].人民黄河,2007,29(3):12-13,20.LAN Y,ZHAO S G,SHEN X Z,et al.Influence of mutual relativity of intensity index of soil mass to stability of embankments[J].Yellow River,2007,29(3):12-13,20.
[6] 骆飞,罗强,蒋良潍,等.小样本岩土参数的Bootstrap估计及边坡稳定分析[J].岩石力学与工程学报,2017,36(2):370-379.LUO F,LUO Q,JIANG L W,et al.Bootstrap estimation for geotechnical parameters of small samples and slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(2):370-379.
[7] 谢桂华.岩土参数随机性分析与边坡稳定可靠度研究[D].长沙:中南大学,2009.XIE G H.Stochastic analysis of geotechnical parameters and study on stable reliability of slope[D].Changsha:Central South University,2009.
[8] 唐小松,李典庆,周创兵,等.基于Bootstrap方法的岩土体参数联合分布模型识别[J].岩土力学,2015,36(4):913-922.TANG X S,LI D Q,ZHOU C B,et al.Bootstrap method for joint probability distribution identification of correlated geotechnical parameters[J].Rock and Soil Mechanics,2015,36(4):913-922.
[9] 王晓明,曹正波.基于Bootstrap方法确定岩土参数的标准值[J].地震工程学报,2015,37(增刊1):7-11.WANG X M,CAO Z B.Determination of the standard value of geotechnical parameters using a bootstrap method[J].China Earthquake Engineering Journal,2015,37(S1):7-11.
[10]Efron B,Tibshirani R J.An Introduction to the Bootstrap:Monographs on Statistics and Applied Probability[M].New York,London:Chapman and Hall/CRC,1993.
[11]Chernick M R.Bootstrap Methods:A Guide for Practitioners and Researchers[M].2nd ed.Hoboken:Wiley-Interscience,2008.
[12]LUO Z,Atamturktur S,Juang C H.Bootstrapping for characterizing the effect of uncertainty in sample statistics for braced excavations[J].Journal of Geotechnical and Geoenvironmental Engineering,2012,139(1):13-23.