基于静力触探的土层自动划分方法与不确定性表征
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摘要
提出了一种基于I_c数据自动划分土层的贝叶斯方法,所提方法不仅能够在考虑I_c的空间变异性的条件下自动划分土层,识别最可能的土层界面,而且能够定量地表征土层界面的不确定性,为制定下一步勘探方案和岩土工程设计提供参考依据。本文采用基于子集模拟的贝叶斯更新方法(CBUS)求解贝叶斯方程,产生土层厚度的后验分布样本,并计算每个可能的土层数目对应的模型证据,确定最可能土层数和最可能的土层界面深度,计算界面深度的标准差作为土层界面不确定性的量化指标。最后,通过上海市轨道交通10号线伊犁站基坑开挖现场的I_c数据和模拟I_c数据说明了所提方法的有效性和正确性。结果表明:所提方法划分的土层合理地反映了不同土层I_c的统计特性。相邻土层I_c的统计特性差异越大,界面深度的标准差越小,识别出的土层界面越可靠,反之亦然。
A Bayesian framework is developed to probabilistically identify the underground stratigraphy based on I_c data. The proposed Bayesian framework identifies the most probable soil layer boundaries with the consideration of spatial variability of I_c and quantifies the uncertainties in the underground stratigraphy, which provides valuable information for making future site investigation plans and geotechnical designs. A subset simulation-based Bayesian updating algorithm(CBUS) is used to generate posterior samples of soil layer thicknesses and to calculate the model evidence for determining the most probable number of soil layers and the most probable soil layer boundaries, and the standard deviations of boundaries are calculated to quantify the uncertainty in soil layer boundaries. Finally, the proposed approach is illustrated and verified using the real I_c data obtained from a deep excavation site at Yili station of Shanghai No. 10 subway line and simulated I_c data from a virtual site. The results show that the underground stratigraphy identified by the proposed approach is based on the statistical similarity of I_cdata. With the increase of statistical difference in I_c data within two adjacent soil layers, the standard deviation of the soil layer boundary between them decreases, and the soil layer boundary identified by the proposed approach is more reliable, and vice versa.
A Bayesian framework is developed to probabilistically identify the underground stratigraphy based on I_c data. The proposed Bayesian framework identifies the most probable soil layer boundaries with the consideration of spatial variability of I_c and quantifies the uncertainties in the underground stratigraphy, which provides valuable information for making future site investigation plans and geotechnical designs. A subset simulation-based Bayesian updating algorithm(CBUS) is used to generate posterior samples of soil layer thicknesses and to calculate the model evidence for determining the most probable number of soil layers and the most probable soil layer boundaries, and the standard deviations of boundaries are calculated to quantify the uncertainty in soil layer boundaries. Finally, the proposed approach is illustrated and verified using the real I_c data obtained from a deep excavation site at Yili station of Shanghai No. 10 subway line and simulated I_c data from a virtual site. The results show that the underground stratigraphy identified by the proposed approach is based on the statistical similarity of I_cdata. With the increase of statistical difference in I_c data within two adjacent soil layers, the standard deviation of the soil layer boundary between them decreases, and the soil layer boundary identified by the proposed approach is more reliable, and vice versa.
引文
[1]GB 50021—2001岩土工程勘察规范[S].2009.(GB 50021—2001 Code for investigation of geotechnical engineering[S].2009.(in Chinese))
[2]李广信.我国的岩土工程规范标准纵横谈[J].工程勘察,2004(1):11–15.(LI Guang-xin.Discussion on the code and standard of geotechnical engineering in China[J].Geotechnical Investigation&Surveying,2004(1):11–15.(in Chinese))
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[4]ROBERTSON P K,CAMPANELLA R G.Interpretation of cone penetration tests Part I:sand[J].Canadian Geotechnical Journal,1983,20(4):718–733.
[5]ROBERTSON P K,CAMPANELLA R G.Interpretation of cone penetration tests Part II:clay[J].Canadian Geotechnical Journal,1983,20(4):734–745.
[6]ROBERTSON P K.Soil classification using the cone penetration test[J].Canadian Geotechnical Journal,1990,27(1):151–158.
[7]JEFFERIES M G,DAVIES M P.Use of CPTu to estimate equivalent SPT N60[J].Geotechnical Testing Journal,1993,16(4):458–468.
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[13]KU C S,JUANG C H,OU C Y.Reliability of CPT Ic as an index for mechanical behavior classification of soils[J].Géotechnique,2010,60(11):861–875.
[14]WANG Y,HUANG K,CAO Z J.Probabilistic identification of underground soil stratification using cone penetration tests[J].Canadian Geotechnical Journal,2013,50(7):766–776.
[15]CAO Z J,HUANG K,WANG Y.Bayesian inverse analysis for geotechnical site characterization using cone penetration test[J].International Journal of Reliability and Safety,2014,8(2/3/4):97–116.
[16]ZHANG Z J,TUMAY M T.Statistical to fuzzy approach toward CPT soil classification[J].Journal of Geotechnical and Geoenvironmental Engineering,1999,125(3):179–186.
[17]HEGAZY Y A,MAYNE P W.Objective site characterization using clustering of piezocone data[J].Journal of Geotechnical and Geoenvironmental Engineering,2002,128(12):986–996.
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[20]LI J,CASSIDY M J,HUANG J,et al.Probabilistic identification of soil stratification[J].Géotechnique,2015,66(1):16–26.
[21]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.
[22]WANG Y,HUANG K,CAO Z J.Bayesian identification of soil strata in London clay[J].Géotechnique,2014,64(3):239–246.
[23]CAO Z J,WANG Y.Bayesian model comparison and selection of spatial correlation functions for soil parameters[J].Structural Safety,2014,49:10–17.
[24]CAO Z J,WANG Y,LI D Q.Quantification of prior knowledge in geotechnical site characterization[J].Engineering Geology,2016,203:107–116.
[25]TIAN M,LI D Q,CAO Z J,et al.Bayesian identification of random field model using indirect test data[J].Engineering Geology,2016,210:197–211.
[26]UZIELLI M,VANNUCCHI G.Investigation of correlation structures and weak stationarity using the CPT soil behavior classification index[C]//International Conference on Structural Safety and Reliability·Icossar,2005.
[27]AU S K,BECK J L.Estimation of small failure probabilities in high dimensions by subset simulation[J].Probabilistic Engineering Mechanics,2001,16(4):263–277.
[28]AU S K,BECK J L.Subset simulation and its application to seismic risk based on dynamic analysis[J].Journal of Engineering Mechanics,2003,129(8):901–917.
[29]STRAUB D,PAPAIOANNOU I.Bayesian updating with structural reliability methods[J].Journal of Geotechnical and Geoenvironmental Engineering,2015,141(3):04014134.
[30]STRAUB D.Reliability updating with equality information[J].Probabilistic Engineering Mechanics,2011,26(2):254–258.
[31]GARBUNO-INIGO A,DIAZDELAO F A,AU S K,et al.Bayesian updating and model class selection with Subset Simulation[J].Computer Methods in Applied Mechanics and Engineering,2017,317.
[32]曹子君.子集模拟在边坡可靠性分析中的应用[D].成都:西南交通大学,2009.(CAO Zi-jun.Application of subset simulation on reliability analysis of slope stability[D].Chengdu:Southwest Jiaotong University,2009.(in Chinese))
[33]AU S K,CAO Z J,WANG Y.Implementing advanced Monte Carlo simulation under spreadsheet environment[J].Structural Safety,2010,32(5):281–292.
[34]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,2011,48(1):162–172.
[35]李典庆,肖特,曹子君,等.基于极限平衡法和有限元法的边坡协同式可靠度分析[J].岩土工程学报,2016,38(6):1004–1013.(LI Dian-qing,XIAO Te,CAO Zi-Jun,et al.Auxiliary slope reliability analysis using limit equilibrium method and finite element method[J].Chinese Journal of Geotechnical Engineering,2016,38(6):1004–1013.(in Chinese))
[36]李典庆,肖特,曹子君,等.基于高效随机有限元法的边坡风险评估[J].岩土力学,2016,37(7):1994–2003.(LI Dian-qing,XIAO Te,CAO Zi-Jun,et al.Slope risk assessment using efficient random finite element method[J].Rock and Soil Mechanics,2016,37(7):1994–2003.(in Chinese))
[37]LI D Q,XIAO T,CAO Z J,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.
[38]LI H S,AU S K.Design optimization using subset simulation algorithm[J].Structural Safety,2010,32(6):384–392.
[39]LI H S.Subset simulation for unconstrained global optimization[J].Applied Mathematical Modelling,2011,35(10):5108–5120.
[40]Mathworks,Inc.MATLAB–the language of technical computing,http://cn.mathworks.com,2016.
[2]李广信.我国的岩土工程规范标准纵横谈[J].工程勘察,2004(1):11–15.(LI Guang-xin.Discussion on the code and standard of geotechnical engineering in China[J].Geotechnical Investigation&Surveying,2004(1):11–15.(in Chinese))
[3]DOUGLAS B J,OLSEN R S.Soil classification using electric cone penetrometer[C]//Proceedings of Conference on Cone Penetration Testing and Experience,St.Louis,1981:209–227.
[4]ROBERTSON P K,CAMPANELLA R G.Interpretation of cone penetration tests Part I:sand[J].Canadian Geotechnical Journal,1983,20(4):718–733.
[5]ROBERTSON P K,CAMPANELLA R G.Interpretation of cone penetration tests Part II:clay[J].Canadian Geotechnical Journal,1983,20(4):734–745.
[6]ROBERTSON P K.Soil classification using the cone penetration test[J].Canadian Geotechnical Journal,1990,27(1):151–158.
[7]JEFFERIES M G,DAVIES M P.Use of CPTu to estimate equivalent SPT N60[J].Geotechnical Testing Journal,1993,16(4):458–468.
[8]张诚厚,施健,戴济群.孔压静力触探试验的应用[J].岩土工程学报,1997,19(1):52–59.(ZHANG Cheng-hou,SHI Jian,DAI Ji-qun.The application of piezocone tests in China[J].Chinese Journal of Geotechnical Engineering,1997,19(1):52–59.(in Chinese))
[9]ROBERTSON P K.Interpretation of cone penetration tests–a unified approach[J].Canadian Geotechnical Journal,2009,46(11):121–123.
[10]刘松玉,蔡国军,童立元.现代多功能CPTU技术理论与工程应用[M].北京:科学出版社,2013.(LIU Song-yu,CAI Guo-jun,TONG Li-yuan.Technology theory and engineering application of modern multifunctional CPTU[M].Beijing:Science Press,2013.(in Chinese))
[11]ROBERTSON P K,WRIDE C E.Evaluating cyclic liquefaction potential using the cone penetration test[J].Canadian Geotechnical Journal,1998,35(2):351–359.
[12]刘松玉,蔡国军,邹海峰.基于CPTU的中国实用土分类方法研究[J].岩土工程学报,2013,35(10):1765–1776.(LIU Song-yu,CAI Guo-jun,ZOU Hai-feng.Practical soil classification methods in China based on piezocone penetration tests[J].Chinese Journal of Geotechnical Engineering,2013,35(10):1765–1776.(in Chinese))
[13]KU C S,JUANG C H,OU C Y.Reliability of CPT Ic as an index for mechanical behavior classification of soils[J].Géotechnique,2010,60(11):861–875.
[14]WANG Y,HUANG K,CAO Z J.Probabilistic identification of underground soil stratification using cone penetration tests[J].Canadian Geotechnical Journal,2013,50(7):766–776.
[15]CAO Z J,HUANG K,WANG Y.Bayesian inverse analysis for geotechnical site characterization using cone penetration test[J].International Journal of Reliability and Safety,2014,8(2/3/4):97–116.
[16]ZHANG Z J,TUMAY M T.Statistical to fuzzy approach toward CPT soil classification[J].Journal of Geotechnical and Geoenvironmental Engineering,1999,125(3):179–186.
[17]HEGAZY Y A,MAYNE P W.Objective site characterization using clustering of piezocone data[J].Journal of Geotechnical and Geoenvironmental Engineering,2002,128(12):986–996.
[18]蔡国军,刘松玉,童立元,等.基于聚类分析理论的CPTU土分类方法研究[J].岩土工程学报,2009,31(3):416–424.(CAI Guo-jun,LIU Song-yu,TONG Li-yuan,et al.Soil classification using CPTU data based upon cluster analysis theory[J].Chinese Journal of Geotechnical Engineering,2009,31(3):416–424.(in Chinese))
[19]CHING J Y,WANG J S,JUANG C H,et al.Cone penetration test(CPT)-based stratigraphic profiling using the wavelet transform modulus maxima method[J].Canadian Geotechnical Journal,2015,52(12):1993–2007.
[20]LI J,CASSIDY M J,HUANG J,et al.Probabilistic identification of soil stratification[J].Géotechnique,2015,66(1):16–26.
[21]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.
[22]WANG Y,HUANG K,CAO Z J.Bayesian identification of soil strata in London clay[J].Géotechnique,2014,64(3):239–246.
[23]CAO Z J,WANG Y.Bayesian model comparison and selection of spatial correlation functions for soil parameters[J].Structural Safety,2014,49:10–17.
[24]CAO Z J,WANG Y,LI D Q.Quantification of prior knowledge in geotechnical site characterization[J].Engineering Geology,2016,203:107–116.
[25]TIAN M,LI D Q,CAO Z J,et al.Bayesian identification of random field model using indirect test data[J].Engineering Geology,2016,210:197–211.
[26]UZIELLI M,VANNUCCHI G.Investigation of correlation structures and weak stationarity using the CPT soil behavior classification index[C]//International Conference on Structural Safety and Reliability·Icossar,2005.
[27]AU S K,BECK J L.Estimation of small failure probabilities in high dimensions by subset simulation[J].Probabilistic Engineering Mechanics,2001,16(4):263–277.
[28]AU S K,BECK J L.Subset simulation and its application to seismic risk based on dynamic analysis[J].Journal of Engineering Mechanics,2003,129(8):901–917.
[29]STRAUB D,PAPAIOANNOU I.Bayesian updating with structural reliability methods[J].Journal of Geotechnical and Geoenvironmental Engineering,2015,141(3):04014134.
[30]STRAUB D.Reliability updating with equality information[J].Probabilistic Engineering Mechanics,2011,26(2):254–258.
[31]GARBUNO-INIGO A,DIAZDELAO F A,AU S K,et al.Bayesian updating and model class selection with Subset Simulation[J].Computer Methods in Applied Mechanics and Engineering,2017,317.
[32]曹子君.子集模拟在边坡可靠性分析中的应用[D].成都:西南交通大学,2009.(CAO Zi-jun.Application of subset simulation on reliability analysis of slope stability[D].Chengdu:Southwest Jiaotong University,2009.(in Chinese))
[33]AU S K,CAO Z J,WANG Y.Implementing advanced Monte Carlo simulation under spreadsheet environment[J].Structural Safety,2010,32(5):281–292.
[34]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,2011,48(1):162–172.
[35]李典庆,肖特,曹子君,等.基于极限平衡法和有限元法的边坡协同式可靠度分析[J].岩土工程学报,2016,38(6):1004–1013.(LI Dian-qing,XIAO Te,CAO Zi-Jun,et al.Auxiliary slope reliability analysis using limit equilibrium method and finite element method[J].Chinese Journal of Geotechnical Engineering,2016,38(6):1004–1013.(in Chinese))
[36]李典庆,肖特,曹子君,等.基于高效随机有限元法的边坡风险评估[J].岩土力学,2016,37(7):1994–2003.(LI Dian-qing,XIAO Te,CAO Zi-Jun,et al.Slope risk assessment using efficient random finite element method[J].Rock and Soil Mechanics,2016,37(7):1994–2003.(in Chinese))
[37]LI D Q,XIAO T,CAO Z J,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.
[38]LI H S,AU S K.Design optimization using subset simulation algorithm[J].Structural Safety,2010,32(6):384–392.
[39]LI H S.Subset simulation for unconstrained global optimization[J].Applied Mathematical Modelling,2011,35(10):5108–5120.
[40]Mathworks,Inc.MATLAB–the language of technical computing,http://cn.mathworks.com,2016.