考虑统计不确定性的基坑变形可靠度高效蒙特卡洛分析方法
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摘要
受技术经济条件限制,基坑工程勘察中获取的勘探数据十分有限,无法准确估计岩土体参数的统计特征,不可避免地存在统计不确定性.Bootstrap方法为合理地考虑统计不确定性对基坑工程安全性和可靠性的影响提供了一条有效途径.然而,采用Bootstrap方法考虑统计不确定性通常需要重复执行可靠度分析,计算量大,计算效率低,使其在实际工程应用中受到很大的局限.基于概率密度加权法和Bootstrap方法提出了考虑统计不确定性的基坑变形高效可靠度分析方法,避免了不同岩土体参数概率分布条件下重复计算基坑变形响应,提高了计算效率.以台北TNEC(Taipei National Enterprise Center)基坑工程变形可靠度分析为例,说明了所提方法的有效性.结果表明:所提方法能够合理地考虑统计不确定性对基坑变形可靠度的影响,结合Bootstrap方法与概率密度加权分析法能够在考虑统计不确定性的条件下高效地计算基坑变形可靠度,克服了Bootstrap方法在工程应用中的局限性.
Test data obtained from geotechnical site investigation are very often limited in excavation engineering. Hence, the statistics of geotechnical parameters cannot be estimated accurately, and they are unavoidably associated with uncertainties, which are referred to as "statistical uncertainty". Bootstrap method provides a rational way to quantify the statistical uncertainty. However, its applications require to implement reliability analyses using different probability distributions, which is computationally prohibitive, particularly when the computational model is time-consuming. This paper proposes a Monte Carlo simulation(MCS)-based method for efficient reliability analysis of excavation engineering with consideration of statistical uncertainty based on Bootstrap method and probability density reweighting method(PDRM). The proposed approach avoids repeatedly performing MCS and calculating performance functions for different probability distributions, and allows incorporating statistical uncertainty into reliability analysis of excavation-induced deformation in an efficient and rational way. For illustration, the proposed approach is applied to the reliability analysis of excavation-induced deformation at Taipei National Enterprise Center(TNEC). It is found that the proposed approach accounts, efficiently and rationally, for statistical uncertainty in reliability analysis of excavation-induced deformation. Combining PDRM with Bootstrap method significantly improves the computational efficiency and removes the limitation of Bootstrap method for engineering application.
Test data obtained from geotechnical site investigation are very often limited in excavation engineering. Hence, the statistics of geotechnical parameters cannot be estimated accurately, and they are unavoidably associated with uncertainties, which are referred to as "statistical uncertainty". Bootstrap method provides a rational way to quantify the statistical uncertainty. However, its applications require to implement reliability analyses using different probability distributions, which is computationally prohibitive, particularly when the computational model is time-consuming. This paper proposes a Monte Carlo simulation(MCS)-based method for efficient reliability analysis of excavation engineering with consideration of statistical uncertainty based on Bootstrap method and probability density reweighting method(PDRM). The proposed approach avoids repeatedly performing MCS and calculating performance functions for different probability distributions, and allows incorporating statistical uncertainty into reliability analysis of excavation-induced deformation in an efficient and rational way. For illustration, the proposed approach is applied to the reliability analysis of excavation-induced deformation at Taipei National Enterprise Center(TNEC). It is found that the proposed approach accounts, efficiently and rationally, for statistical uncertainty in reliability analysis of excavation-induced deformation. Combining PDRM with Bootstrap method significantly improves the computational efficiency and removes the limitation of Bootstrap method for engineering application.
引文
[1] Phoon K K, Kulhawy F H. Characterization of geotechnical variability[J]. Canadian Geotechnical Journal, 1999, 36(4):612-624.
[2] Ang H S, Tang W H. Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering[M]. 2nd ed. New York: John Wiley and Sons, 2007:1-25.
[3] ISO2394:2015 General Principles on Reliability of Structures[S].
[4] GB 50199-2013 水利水电工程结构可靠性设计统一标准[S]. 北京:中国计划出版社,2013:15-18. GB 50199-2013 Uniform Standards for Reliability Design of Hydraulic Engineering Structures[S]. Beijing: China Planning Press, 2013:15-18.
[5] Ching J, Phoon K K, Wu S H. Impact of statistical uncertainty on geotechnical reliability estimation[J]. Journal of Engineering Mechanics, 2016, 142(6):04016027.
[6] 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, 2013, 139(1):13-23.
[7] 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 Xiaosong, Li Dianqing, Zhou Chuangbing, et al. Bootstrap method for joint probability distribution identification of correlated geotechnical parameters[J].Rock and Soil Mechanics, 2015, 36(4): 913-922.
[8] 唐小松, 李典庆, 曹子君,等. 有限数据条件下边坡可靠度分析的Bootstrap方法[J]. 岩土力学, 2016, 37(3):893-901. Tang Xiaosong, Li Dianqing, Cao Zijun, et al. A Bootstrap method for analyzing slope reliability based on limited shear-strength parameter data[J]. Rock and Soil Mechanics, 2016, 37(3):893-901.
[9] 谢桂华, 张家生, 刘荣桂. 沉降计算经验系数的Bootstrap 法置信区间估计[J]. 中南大学学报(自然科学版), 2011, 42(9): 2843-2847. Xie Guihua, Zhang Jiasheng, Liu Ronggui. Estimation of confidence interval of empirical coefficients in calculating foundation settlement by Bootstrap method[J]. Journal of Central South University (Science and Technology), 2011, 42(9): 2843-2847.
[10] Efron B, Tibshirani R J. An Introduction to the Bootstrap[M]. London: Chapman and Hall, 1993:45-82.
[11] Li D Q, Tang X S, Phoon K K. Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability[J]. Reliability Engineering & System Safety, 2015, 140:99-106.
[12] Efron B. Bootstrap methods: Another look at the jackknife[J]. The Annals of Statistics, 1979, 7(1): 1-26.
[13] 张浮平, 曹子君, 唐小松,等. 基于蒙特卡洛模拟的高效边坡可靠度修正方法[J]. 工程力学, 2016, 33(7):55-64. Zhang Fuping, Cao Zijun, Tang Xiaosong, et al. Efficient slope reliability updating method based on Monte Carlo simulation[J]. Engineering Mechanics, 2016, 33(7):55-64.
[14] Li D Q, Zhang F P, Cao Z J, et al. Efficient reliability updating of slope stability by reweighting failure samples generated by Monte Carlo simulation[J]. Computers & Geotechnics, 2015, 69:588-600.
[15] 张湾, 李典庆, 曹子君. 基坑开挖参数反分析贝叶斯方法比较研究[J]. 武汉大学学报(工学版), 2016, 49(6):806-811. Zhang Wan, Li Dianqing, Cao Zijun. Comparative study of Bayesian methods for back analysis of deep excavation[J]. Engineering Journal of Wuhan University, 2016, 49(6):806-811.
[16] Kung G T C, Juang C H, Hsiao E C L, et al. Simplified model for wall deflection and ground-surface settlement caused by braced excavation in clays [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2007, 133: 731-747.
[17] Hsiao E C L, Schuster M, Juang C H, et al. Reliability analysis of excavation-induced ground settlement for building serviceability evaluation[J]. Journal of Geotechnical and Geoenvironmental Engineering,2008,134(10): 1448-1458.
[18] Kung T C. Surface settlement induced by excavation with consideration of small strain behavior of Taipei silty clay[D]. Taipei: National Taiwan Univ. of Science and Technology, 2003.
[19] SZ-08-2000上海市地铁基坑工程施工规程[S]. 上海:上海市市政工程管理局,2000:1-3. SZ-08-2000 Specification for Excavation in Shanghai Metro Construction[S]. Shanghai: Shanghai Municipal Administration of Engineering, 2000:1-3.
[2] Ang H S, Tang W H. Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering[M]. 2nd ed. New York: John Wiley and Sons, 2007:1-25.
[3] ISO2394:2015 General Principles on Reliability of Structures[S].
[4] GB 50199-2013 水利水电工程结构可靠性设计统一标准[S]. 北京:中国计划出版社,2013:15-18. GB 50199-2013 Uniform Standards for Reliability Design of Hydraulic Engineering Structures[S]. Beijing: China Planning Press, 2013:15-18.
[5] Ching J, Phoon K K, Wu S H. Impact of statistical uncertainty on geotechnical reliability estimation[J]. Journal of Engineering Mechanics, 2016, 142(6):04016027.
[6] 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, 2013, 139(1):13-23.
[7] 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 Xiaosong, Li Dianqing, Zhou Chuangbing, et al. Bootstrap method for joint probability distribution identification of correlated geotechnical parameters[J].Rock and Soil Mechanics, 2015, 36(4): 913-922.
[8] 唐小松, 李典庆, 曹子君,等. 有限数据条件下边坡可靠度分析的Bootstrap方法[J]. 岩土力学, 2016, 37(3):893-901. Tang Xiaosong, Li Dianqing, Cao Zijun, et al. A Bootstrap method for analyzing slope reliability based on limited shear-strength parameter data[J]. Rock and Soil Mechanics, 2016, 37(3):893-901.
[9] 谢桂华, 张家生, 刘荣桂. 沉降计算经验系数的Bootstrap 法置信区间估计[J]. 中南大学学报(自然科学版), 2011, 42(9): 2843-2847. Xie Guihua, Zhang Jiasheng, Liu Ronggui. Estimation of confidence interval of empirical coefficients in calculating foundation settlement by Bootstrap method[J]. Journal of Central South University (Science and Technology), 2011, 42(9): 2843-2847.
[10] Efron B, Tibshirani R J. An Introduction to the Bootstrap[M]. London: Chapman and Hall, 1993:45-82.
[11] Li D Q, Tang X S, Phoon K K. Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability[J]. Reliability Engineering & System Safety, 2015, 140:99-106.
[12] Efron B. Bootstrap methods: Another look at the jackknife[J]. The Annals of Statistics, 1979, 7(1): 1-26.
[13] 张浮平, 曹子君, 唐小松,等. 基于蒙特卡洛模拟的高效边坡可靠度修正方法[J]. 工程力学, 2016, 33(7):55-64. Zhang Fuping, Cao Zijun, Tang Xiaosong, et al. Efficient slope reliability updating method based on Monte Carlo simulation[J]. Engineering Mechanics, 2016, 33(7):55-64.
[14] Li D Q, Zhang F P, Cao Z J, et al. Efficient reliability updating of slope stability by reweighting failure samples generated by Monte Carlo simulation[J]. Computers & Geotechnics, 2015, 69:588-600.
[15] 张湾, 李典庆, 曹子君. 基坑开挖参数反分析贝叶斯方法比较研究[J]. 武汉大学学报(工学版), 2016, 49(6):806-811. Zhang Wan, Li Dianqing, Cao Zijun. Comparative study of Bayesian methods for back analysis of deep excavation[J]. Engineering Journal of Wuhan University, 2016, 49(6):806-811.
[16] Kung G T C, Juang C H, Hsiao E C L, et al. Simplified model for wall deflection and ground-surface settlement caused by braced excavation in clays [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2007, 133: 731-747.
[17] Hsiao E C L, Schuster M, Juang C H, et al. Reliability analysis of excavation-induced ground settlement for building serviceability evaluation[J]. Journal of Geotechnical and Geoenvironmental Engineering,2008,134(10): 1448-1458.
[18] Kung T C. Surface settlement induced by excavation with consideration of small strain behavior of Taipei silty clay[D]. Taipei: National Taiwan Univ. of Science and Technology, 2003.
[19] SZ-08-2000上海市地铁基坑工程施工规程[S]. 上海:上海市市政工程管理局,2000:1-3. SZ-08-2000 Specification for Excavation in Shanghai Metro Construction[S]. Shanghai: Shanghai Municipal Administration of Engineering, 2000:1-3.