间接测量数据条件下岩土参数空间变异性定量分析方法对比研究
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摘要
准确估计随机场参数和相关函数是定量描述岩土参数空间变异性的关键。基于间接测量的静力触探试验数据,系统对比了传统统计方法与贝叶斯方法确定砂土有效内摩擦角随机场参数和相关函数的有效性,指出了两种方法存在差异的原因,并探讨了静力触探试验样本数量对两种方法计算精度的影响。研究结果表明:传统统计方法未考虑砂土有效内摩擦角与锥尖阻力间经验回归方程的不确定性,识别相关函数的正确率较低,并且传统统计方法会高估砂土有效内摩擦角的标准差,低估其波动范围。而贝叶斯方法由于合理地考虑了经验回归方程的不确定性,可以准确地确定砂土有效内摩擦角的随机场参数和相关函数。根据间接测量数据量化岩土参数空间变异性时,应考虑回归模型不确定性的影响。此外,随着静力触探试验样本数量增加,贝叶斯方法识别砂土有效内摩擦角相关函数的正确率逐渐提高,随机场参数估计结果的不确定性逐渐降低。为了提高岩土参数空间变异性定量表征结果的准确性,应广泛收集岩土工程勘察资料。
Accurate determination of random field parameters and correlation function is the key for probabilistic characterization of inherent spatial variability(ISV) of soil properties. Based on indirect cone penetration test(CPT) data, the conventional statistical methods and Bayesian approaches are compared for their validity of estimating random field parameters and correlation function of sand effective friction angle, φ'. The reason for the difference between these two methods is presented. Effects of sampling size of indirect CPT data on the accuracy of these two methods are also investigated. The results indicate that the conventional statistical methods don't consider the model uncertainty associated with the transformation model between φ' and CPT data, leading to a low rate of correct identification of true correlation function of φ', overestimating standard deviation and underestimating scale of fluctuation. However, the Bayesian approaches can take the model uncertainty into proper consideration and reasonably determine the random field parameters and correlation function of φ'. Model uncertainty should be carefully considered when indirect test data is used to characterize ISV of soil properties. In addition, the rate of correct identification of true correlation function of φ' estimated from Bayesian approaches improves and the uncertainties of random field parameters of φ' gradually decrease with increasing sampling size of indirect CPT data. It is suggested that large numbers of site observation data should be collected for improving the accuracy of probabilistically characterizing ISV of soil properties.
Accurate determination of random field parameters and correlation function is the key for probabilistic characterization of inherent spatial variability(ISV) of soil properties. Based on indirect cone penetration test(CPT) data, the conventional statistical methods and Bayesian approaches are compared for their validity of estimating random field parameters and correlation function of sand effective friction angle, φ'. The reason for the difference between these two methods is presented. Effects of sampling size of indirect CPT data on the accuracy of these two methods are also investigated. The results indicate that the conventional statistical methods don't consider the model uncertainty associated with the transformation model between φ' and CPT data, leading to a low rate of correct identification of true correlation function of φ', overestimating standard deviation and underestimating scale of fluctuation. However, the Bayesian approaches can take the model uncertainty into proper consideration and reasonably determine the random field parameters and correlation function of φ'. Model uncertainty should be carefully considered when indirect test data is used to characterize ISV of soil properties. In addition, the rate of correct identification of true correlation function of φ' estimated from Bayesian approaches improves and the uncertainties of random field parameters of φ' gradually decrease with increasing sampling size of indirect CPT data. It is suggested that large numbers of site observation data should be collected for improving the accuracy of probabilistically characterizing ISV of soil properties.
引文
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[3]陈晓平,孙慕群,吴起星.软基上复杂土坡稳定可靠度研究[J].岩石力学与工程学报,2004,23(6):925-929.CHEN Xiao-ping,SUN Mu-qun,WU Qi-xing.Reliability study of complex slope stability on soft soil[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(6):925-929.
[4]CHO S E.Probabilistic stability analysis of rainfall-induced landslides considering spatial variability of permeability[J].Engineering Geology,2014,171(8):11-20.
[5]SALGADO R,KIM D.Reliability analysis of load and resistance factor design of slopes[J].Journal of Geotechnical and Geoenvironmental Engineering,2014,140(1):57-73.
[6]蒋水华,李典庆,周创兵,等.考虑参数空间变异性的非饱和土坡可靠度分析[J].岩土力学,2014,35(9):2569-2578.JIANG Shui-hua,LI Dian-qing,ZHOU Chuang-bing,et al.Reliability analysis of unsaturated slope considering spatial variability[J].Rock and Soil Mechanics,2014,35(9):2569-2578.
[7]KASAMA K,WHITTLE A J.Effect of spatial variability on the slope stability using random field numerical limit analyses[J].Georisk,2016,10(1):42-54.
[8]PHOON K K,QUEK S T,AN P.Identification of statistically homogeneous soil layers using modified Bartlett statistics[J].Journal of Geotechnical and Geoenvironmental Engineering,2003,129(7):649-659.
[9]FENTON G A.Estimation for stochastic soil models[J].Journal of Geotechnical and Geoenvironmental Engineering,1999,125(6):470-485.
[10]UZIELLI M,VANNUCCHI G,PHOON K K.Random field characterisation of stress-nomalised cone penetration testing parameters[J].Géotechnique,2005,55(1):3-20.
[11]STUEDLEIN A W,KRAMER S L,ARDUINO P,et al.Geotechnical characterization and random field modeling of desiccated clay[J].Journal of Geotechnical and Geoenvironmental Engineering,2012,138(11):1301-1313.
[12]LLORET-CABOT M,FENTON G A,HICKS M A.On the estimation of scale of fluctuation in geostatistics[J].Georisk Assessment and Management of Risk for Engineered Systems and Geohazards,2014,8(2):129-140.
[13]张继周,缪林昌,林飞,等.苏中腹地湖相沉积土层相关距离的统计分析[J].工程地质学报,2014,22(2):348-354.ZHANG Ji-zhou,LIAO Lin-chang,LIN Fei,et al.Statistical analyses of correlation distances of lacustrine sedimentary soil in central region of Jiangsu province[J].Journal of Engineering Geology,2014,22(2):348-354.
[14]林军,蔡国军,邹海峰,等.基于随机场理论的江苏海相黏土空间变异性评价[J].岩土工程学报,2015,37(7):1278-1287.LIN Jun,CAI Guo-jun,ZOU Hai-feng,et al.Assessment of spatial variability of Jiangsu marine clay based on random field theory[J].Chinese Journal of Geotechnical Engineering,2015,37(7):1278-1287.
[15]李小勇,谢康和.土性参数相关距离的计算研究和统计分析[J].岩土力学,2000,21(4):350-353.LI Xiao-yong,XIE Kang-he.Numerical studies and statiatie analyses on coerrlation distances of soil character parameters[J].Rock and Soil Mechanics,2000,21(4):350-353.
[16]WANG Y,AU S K,CAO Z J.Bayesian approach for probabilistic characterization of sand friction angles[J].Engineering Geology,2010,114(3-4):354-363.
[17]CAO Z J,Wang Y.Bayesian approach for probabilistic site characterization using cone penetration tests[J].Journal of Geotechnical and Geoenvironmental Engineering,2013,139(2):267-276.
[18]CAO Z J,WANG Y.Bayesian model comparison and selection of spatial correlation functions for soil parameters[J].Structural Safety,2014,49:10-17.
[19]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[J].岩土力学,2017,38(11):3355-3362.TIAN Mi,LI Dian-qing,CAO Zi-jun,et al.Quantificationof spatial variability of soil parameters using Bayesian approaches[J].Rock and Soil Mechanics,2017,38(11):3355-3362.
[20]MAYNE P W,CHRISTOPHER B R,DEJONG J.Subsurface investigations-geotechnical site characterization,No.FHWA NHI-01-031,Federal Highway Administration,U.S[S].Washington D.C:Department of Transportation,2002.
[21]BAECHER G B,CHRISTIAN J T.Reliability and statistics in geotechnical engineering[M].New York:John Wiley&Sons,2003.
[22]ANG A H-S,TANG W H.Probability concepts in engineering:Emphasis on applications to civil and environmental engineering[M].New York:John Wiley&Sons,2007.
[23]SIVIA D S,SKILLING J.Data analysis:A Bayesian tutorial[M].New York:Oxford University Press,2006.
[24]PHOON K K,KULHAWY F H.Characterization of geotechnical variability[J].Canadian Geotechnical Journal,1999,36(4):612-624.