基于贝叶斯理论的土体抗剪强度参数最优二维分布模型识别方法
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摘要
提出了基于贝叶斯理论的土体抗剪强度参数最优二维分布模型的识别方法。首先,介绍了基于Copula函数的土体抗剪强度参数二维分布模型的表征方法。其次,采用蒙特卡洛模拟方法验证了贝叶斯理论识别最优二维分布模型的有效性,对比了贝叶斯独立识别、贝叶斯非独立识别、AIC一步识别,AIC两步识别4种识别方法的识别能力,分析了影响贝叶斯理论识别精度的主要因素。最后,搜集了29组实际工程土体抗剪强度参数试验数据,研究了贝叶斯独立识别和非独立识别在实际工程土体抗剪强度参数最优二维分布模型识别中的应用。结果表明,贝叶斯理论能够结合先验信息有效地识别表征土体抗剪强度参数最优二维分布模型;贝叶斯理论与AIC准则相较在小样本条件下的识别能力和识别精度方面优势明显;土体抗剪强度参数的样本数目、参数间相关性、备选二维分布模型集合以及先验信息都显著影响贝叶斯理论的识别精度。
This paper proposes a Bayesian bivariate distribution identification method for shear strength parameters of soils and rocks. First, the characterization of bivariate distribution for shear strength parameters using Copulas is presented. Then, Monte Carlo simulations are conducted to validate the Bayesian bivariate distribution identification method. Moreover, the identification accuracy in the four methods is compared, and the main factors affecting the accuracy in the Bayesian bivariate distribution identification are identified. Finally, a total of twenty-nine sets of shear strength data are compiled to demonstrate the application of Bayesian theory bivariate distribution identification. The results indicate that with limited project-specific data and prior information, the Bayesian bivariate distribution identification method can successfully identify the best-fit bivariate distribution from a set of alternative bivariate distributions for shear strength parameters. In comparison with AIC, the Bayesian bivariate distribution identification method produces more accurate results for identifying the best-fit bivariate distribution. The sample size, correlation, the type of the true bivariate distribution and prior information of shear strength parameters has a significant impact on the accuracy of the Bayesian bivariate distribution selection method.
This paper proposes a Bayesian bivariate distribution identification method for shear strength parameters of soils and rocks. First, the characterization of bivariate distribution for shear strength parameters using Copulas is presented. Then, Monte Carlo simulations are conducted to validate the Bayesian bivariate distribution identification method. Moreover, the identification accuracy in the four methods is compared, and the main factors affecting the accuracy in the Bayesian bivariate distribution identification are identified. Finally, a total of twenty-nine sets of shear strength data are compiled to demonstrate the application of Bayesian theory bivariate distribution identification. The results indicate that with limited project-specific data and prior information, the Bayesian bivariate distribution identification method can successfully identify the best-fit bivariate distribution from a set of alternative bivariate distributions for shear strength parameters. In comparison with AIC, the Bayesian bivariate distribution identification method produces more accurate results for identifying the best-fit bivariate distribution. The sample size, correlation, the type of the true bivariate distribution and prior information of shear strength parameters has a significant impact on the accuracy of the Bayesian bivariate distribution selection method.
引文
[1] TANG X S, LI D Q, RONG G, et al. Impact of copula selection on geotechnical reliability under incomplete probability information[J]. Computers and Geotechnics, 2013,49:264-278.
[2] CHERUBINI C. Reliability evaluation of shallow foundation bearing capacity on soils[J]. Canadian Geotechnical Journal, 2000,37(1):264-269.
[3] LOW B K. Reliability-based design applied to retaining walls[J]. Geotechnique, 2005,55(1):63-75.
[4] NELSEN R B. An introduction to Copulas[M]. New York: Springer, 2006.
[5] 唐小松, 李典庆, 周创兵, 等. 基于 Copula 函数的基桩荷载-位移双曲线概率分析[J]. 土体力学, 2012,33(1):171-178.
[6] 唐小松, 李典庆, 周创兵, 等. 基于 Copula 函数的抗剪强度参数间相关性模拟及边坡可靠度分析[J]. 土体工程学报, 2012,34(12):2 284-2 291.
[7] 杨超, 黄达, 张永兴. 基于Copula 理论岩体质量Q 值及波速与变形模量多变量相关性研究[J]. 岩石力学与工程学报, 2014,33(3):507-513.
[8] LI D Q, ZHANG L, TANG X S, et al. Bivariate distribution of shear strength parameters using copulas and its impact on geotechnical system reliability[J]. Computers and Geotechnics, 2015,68:184-195.
[9] HUFFMAN J C, STRAHLER A W, STUEDLEIN A W. Reliability-based serviceability limit state design for immediate settlement of spread footings on clay[J]. Soils and Foundations, 2015,55(4):798-812.
[10] MOTAMEDI M, LIANG R Y. Probabilistic landslide hazard assessment using copula modeling technique[J]. Landslides, 2014,11(4):565-573.
[11] WU X Z. Development of fragility functions for slope instability analysis[J]. Landslides, 2014,12(1):165-175.
[12] Li DQ, Tang XS. Modeling and simulation of bivariate distribution of shear strength parameters using copulas[M]// London: CRC Press;Risk and Reliability in Geotechnical Engineering, 2014:77-128.
[13] Ang AH-S, Tang WH. Probability concepts in engineering: emphasis on applications to civil and environmental engineering[M]. 2nd ed. New York: John Wiley and Sons; 2007.
[14] Li DQ, Tang XS, Zhou CB, Phoon KK. Characterization of uncertainty in probabilistic model using bootstrap method and its application to reliability of piles[J]. Apply Math Model, 2015,39(17):5 310-5 326.
[15] Cao Z J, Wang Y. Bayesian model comparison and characterization of undrained shear strength[J]. Geotech Geoenviron Eng, 2014,140(6):04014018.
[16] Wang Y, Au S K, Cao Z J. Bayesian approach for probabilistic characterization of sand friction angles[J]. Eng Geol, 2010,114(3-4):354-63.
[17] Wang Y, Aladejare AE. Bayesian characterization of correlation between uniaxial compressive strength and Young's modulus of rock[J]. Int J Rock Mech Min Sci, 2016,85:9-10.
[18] Li DQ, Zhang L, Tang XS, Zhou W, Li JH, Zhou CB, et al. Bivariate distribution of shear strength parameters using copulas and its impact on geotechnical system reliability[J]. Comput Geotech, 2015;68:184-195.
[19] 唐小松, 李典庆, 周创兵, 等. 基于 Bootstrap 方法的土体体参数联合分布模型识别[J]. 土体力学, 2015,36(4): 913-922.
[20] AKAIKE H. A new look at the statistical model identification[J]. IEEE Transactions on Automatic Control, 1974,19(6):716-723.
[21] WANG Y, AU S K, CAO Z J. Bayesian approach for probabilistic characterization of sand friction angles[J]. Engineering Geology, 2010,114(3):354-363.
[22] WANG Y, CAO Z J. Probabilistic characterization of Young’s modulus of soil using equivalent samples[J]. Engineering Geology, 2013,159:106-118.
[23] 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.
[24] CAO Z J, WANG Y. Bayesian model comparison and characterization of undrained shear strength[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2014,140(6):04014018.
[25] CAO Z J, WANG Y. Bayesian model comparison and selection of spatial correlation functions for soil parameters[J]. Structural Safety, 2014,49:10-17.
[2] CHERUBINI C. Reliability evaluation of shallow foundation bearing capacity on soils[J]. Canadian Geotechnical Journal, 2000,37(1):264-269.
[3] LOW B K. Reliability-based design applied to retaining walls[J]. Geotechnique, 2005,55(1):63-75.
[4] NELSEN R B. An introduction to Copulas[M]. New York: Springer, 2006.
[5] 唐小松, 李典庆, 周创兵, 等. 基于 Copula 函数的基桩荷载-位移双曲线概率分析[J]. 土体力学, 2012,33(1):171-178.
[6] 唐小松, 李典庆, 周创兵, 等. 基于 Copula 函数的抗剪强度参数间相关性模拟及边坡可靠度分析[J]. 土体工程学报, 2012,34(12):2 284-2 291.
[7] 杨超, 黄达, 张永兴. 基于Copula 理论岩体质量Q 值及波速与变形模量多变量相关性研究[J]. 岩石力学与工程学报, 2014,33(3):507-513.
[8] LI D Q, ZHANG L, TANG X S, et al. Bivariate distribution of shear strength parameters using copulas and its impact on geotechnical system reliability[J]. Computers and Geotechnics, 2015,68:184-195.
[9] HUFFMAN J C, STRAHLER A W, STUEDLEIN A W. Reliability-based serviceability limit state design for immediate settlement of spread footings on clay[J]. Soils and Foundations, 2015,55(4):798-812.
[10] MOTAMEDI M, LIANG R Y. Probabilistic landslide hazard assessment using copula modeling technique[J]. Landslides, 2014,11(4):565-573.
[11] WU X Z. Development of fragility functions for slope instability analysis[J]. Landslides, 2014,12(1):165-175.
[12] Li DQ, Tang XS. Modeling and simulation of bivariate distribution of shear strength parameters using copulas[M]// London: CRC Press;Risk and Reliability in Geotechnical Engineering, 2014:77-128.
[13] Ang AH-S, Tang WH. Probability concepts in engineering: emphasis on applications to civil and environmental engineering[M]. 2nd ed. New York: John Wiley and Sons; 2007.
[14] Li DQ, Tang XS, Zhou CB, Phoon KK. Characterization of uncertainty in probabilistic model using bootstrap method and its application to reliability of piles[J]. Apply Math Model, 2015,39(17):5 310-5 326.
[15] Cao Z J, Wang Y. Bayesian model comparison and characterization of undrained shear strength[J]. Geotech Geoenviron Eng, 2014,140(6):04014018.
[16] Wang Y, Au S K, Cao Z J. Bayesian approach for probabilistic characterization of sand friction angles[J]. Eng Geol, 2010,114(3-4):354-63.
[17] Wang Y, Aladejare AE. Bayesian characterization of correlation between uniaxial compressive strength and Young's modulus of rock[J]. Int J Rock Mech Min Sci, 2016,85:9-10.
[18] Li DQ, Zhang L, Tang XS, Zhou W, Li JH, Zhou CB, et al. Bivariate distribution of shear strength parameters using copulas and its impact on geotechnical system reliability[J]. Comput Geotech, 2015;68:184-195.
[19] 唐小松, 李典庆, 周创兵, 等. 基于 Bootstrap 方法的土体体参数联合分布模型识别[J]. 土体力学, 2015,36(4): 913-922.
[20] AKAIKE H. A new look at the statistical model identification[J]. IEEE Transactions on Automatic Control, 1974,19(6):716-723.
[21] WANG Y, AU S K, CAO Z J. Bayesian approach for probabilistic characterization of sand friction angles[J]. Engineering Geology, 2010,114(3):354-363.
[22] WANG Y, CAO Z J. Probabilistic characterization of Young’s modulus of soil using equivalent samples[J]. Engineering Geology, 2013,159:106-118.
[23] 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.
[24] CAO Z J, WANG Y. Bayesian model comparison and characterization of undrained shear strength[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2014,140(6):04014018.
[25] CAO Z J, WANG Y. Bayesian model comparison and selection of spatial correlation functions for soil parameters[J]. Structural Safety, 2014,49:10-17.