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Volume 42 Issue 5
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KONG Xian-jing, SONG Lai-fu, XU Bin, ZOU De-gao. Correlation and distribution model for nonlinear strength parameters of rockfill based on Copula function[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(5): 797-807. DOI: 10.11779/CJGE202005001
Citation: KONG Xian-jing, SONG Lai-fu, XU Bin, ZOU De-gao. Correlation and distribution model for nonlinear strength parameters of rockfill based on Copula function[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(5): 797-807. DOI: 10.11779/CJGE202005001
shu

Correlation and distribution model for nonlinear strength parameters of rockfill based on Copula function

  • 1.

    School of Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China

  • 2.

    The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China

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  • Received Date: August 16, 2019
  • Available Online: December 07, 2022
    Graphical Abstract
    • Abstract
  • The uncertainty and correlation of nonlinear strength parameters of rockfill are the key factors affecting the stability reliability analysis results of rockfill dam slopes. However, the conventional normal distribution model cannot accurately characterize the correlation and non-normal distribution characteristics of nonlinear strength parameters. In this study, the nonlinear strength parameters of rockfill for 1257 groups of 124 rockfill dam projects around the world are summarized. Based on the Copula function, the construction method of joint distribution model for nonlinear strength parameters of rockfill is proposed. The correlation coefficient, optimal marginal distribution function and optimal Copula function for nonlinear strength parameters of rockfill are determined by the least square method and BIC criterion respectively. The results show that there is a significant positive correlation between the nonlinear strength parameters. The joint distribution functions constructed by different Copula functions are significantly different despite the same marginal distribution and correlation coefficient of the nonlinear strength parameters. For the conditional cumulative distribution function, with the decrease of the nonlinear strength parameters, the greater difference is in the conditional cumulative distribution function of the nonlinear strength parameter constructed based on different Copula functions. Compared with the two-dimensional normal distribution model, the nonlinear strength parameter joint distribution model based on the Copula function is flexible and applicable in a wide range, which can more accurately represent the distribution of the original data and provide a simple and effective distribution model for the static and dynamic stability reliability analysis of rockfill dam slopes.
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    • References (33)
  • [1]
    PENMAN A D M. Shear characteristics of a saturated silt, measured in triaxial compression[J]. Géotechnique, 1953, 3(8): 312-328. doi: 10.1680/geot.1953.3.8.312
    [2]
    BISHOP A W, WEBB D L, LEWIN P I. Undisturbed samples of London clay from the Ashford common shaft: strength-effective stress relationships[J]. Géotechnique, 1965, 15(1): 1-31. doi: 10.1680/geot.1965.15.1.1
    [3]
    PONCE V M, BELL J M. Shear strength of sand at extremely low pressures[J]. Journal of the Soil Mechanics and Foundations Division, 1971, 97(4): 625-638. doi: 10.1061/JSFEAQ.0001578
    [4]
    MAKSIMOVIC M. Nonlinear failure envelope for soils[J]. Journal of Geotechnical Engineering, 1989, 115(4): 581-586. doi: 10.1061/(ASCE)0733-9410(1989)115:4(581)
    [5]
    BAKER R. Nonlinear Mohr envelopes based on triaxial data[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2004, 130(5): 498-506. doi: 10.1061/(ASCE)1090-0241(2004)130:5(498)
    [6]
    BARTON Nick, Bjorn KJERNSLI. Shear strength of rockfill[J]. J Geotech Engng Div, ASCE, 1981(GT7): 873-891.
    [7]
    INDRARATNA B, WIJEWAEDENA L S S, BALASUBRAMANIAM A S. Large-scale triaxial testing of greywacke rockfill[J]. Géotechnique, 1993, 43(1): 37-51. doi: 10.1680/geot.1993.43.1.37
    [8]
    吕擎峰, 殷宗泽. 非线性强度参数对高土石坝坝坡稳定性的影响[J]. 岩石力学与工程学报, 2004, 23(16): 2708-2711. doi: 10.3321/j.issn:1000-6915.2004.16.010

    LÜ Qing-feng, YIN Zong-ze. Effect of strength nonlinearity on slope stability of high rockfill dam[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(16): 2708-2711. (in Chinese) doi: 10.3321/j.issn:1000-6915.2004.16.010
    [9]
    陈祖煜, 陈立宏, 孙平. 非线性强度指标边坡稳定安全系数取值标准的研究[J]. 水力发电, 2004, 30(2): 17-20. https://www.cnki.com.cn/Article/CJFDTOTAL-SLFD200402007.htm

    CHEN Zu-yu, CHEN Li-hong, SUN Ping. An investigation on the allowable factors of safety in slope stability analysis using nonlinear strength parameters[J]. Hydroelectric Power, 2004, 30(2): 17-20. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SLFD200402007.htm
    [10]
    陈立宏, 陈祖煜. 堆石非线性强度特性对高土石坝稳定性的影响[J]. 岩土力学, 2007, 28(9): 1807-1810. doi: 10.3969/j.issn.1000-7598.2007.09.008

    CHEN Li-hong, CHEN Zu-yu. Effect of nonlinear strength of rockfill on slope stability of high earth-rock dam[J]. Rock and Soil Mechanics, 2007, 28(9): 1807-1810. (in Chinese) doi: 10.3969/j.issn.1000-7598.2007.09.008
    [11]
    范明桥, 盛金保. 土强度指标φ,c的互相关性[J]. 岩土工程学报, 1997, 19(4): 100-104. doi: 10.3321/j.issn:1000-4548.1997.04.017

    FAN Ming-qiao, SHENG Jin-bao. Correlation of soil strength index φ and c[J]. Chinese Journal of Geotechnical Engineering, 1997, 19(4): 100-104. (in Chinese) doi: 10.3321/j.issn:1000-4548.1997.04.017
    [12]
    LI D Q, CHEN Y F, LU W B, et al. Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables[J]. Computers and Geotechnics, 2011, 38(1): 58-68. doi: 10.1016/j.compgeo.2010.10.006
    [13]
    LOW B K. Reliability analysis of rock slopes involving correlated nonnormals[J]. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(6): 922-935. doi: 10.1016/j.ijrmms.2007.02.008
    [14]
    吴震宇, 陈建康, 许唯临, 等. 高堆石坝非线性强度指标坝坡稳定可靠度分析方法研究及工程应用[J]. 岩土力学与工程学报, 2009, 28(1): 130-137. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200901020.htm

    WU Zhen-yu, CHEN Jian-kang, XU Wei-lin, et al. Research on methodology of reliability analysis of high rockfill dam slope stability using nonlinear strength indexes and its engineering application[J]. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(1): 130-137. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200901020.htm
    [15]
    四川大学水利水电学院. 双江口水电站土质心墙堆石坝坝坡稳定分析及可靠度研究报告[R]. 成都: 四川大学水利水电学院.

    College of Water Resources and Hydroelectric Engineering, Sichuan University. Report on slope stability analysis and reliability research of the Shuangjiangkou rockfill dam[R]. Chengdu: College of Water Resources and Hydroelectric Engineering, Sichuan University, 2008. (in Chinese)
    [16]
    WU Z Y, CHEN J K, LI Y L, et al. An algorithm in generalized coordinate system and its application to reliability analysis of seismic slope stability of high rockfill dams[J]. Engineering Geology, 2015, 188: 88-96. doi: 10.1016/j.enggeo.2015.01.019
    [17]
    SKLAR A. Fonctions de repartition an dimensions et leurs marges[J]. Publications de l Institut de Statistique de l Universite de Paris, 1959, 8: 229-231.
    [18]
    张尧庭. 连接函数(Copula)技术与金融风险分析[J]. 统计研究, 2002, 19(4): 48-51. doi: 10.3969/j.issn.1002-4565.2002.04.011

    ZHANG Yao-ting. Link function (Copula) technology with financial risk analysis[J]. Statistical Research, 2002, 19(4): 48-51. (in Chinese) doi: 10.3969/j.issn.1002-4565.2002.04.011
    [19]
    KOLE E, KOEDIJK K, VERBEEK M. Selecting copulas for risk management[J]. Journal of Banking and Finance, 2007, 31(8): 2405-2423. doi: 10.1016/j.jbankfin.2006.09.010
    [20]
    ZHANG L, SINGH V P. Bivariate flood frequency analysis using the Copula method[J]. Journal of Hydrologic Engineering, 2006, 11(2): 150-164. doi: 10.1061/(ASCE)1084-0699(2006)11:2(150)
    [21]
    ZHANG Q, CHEN Y D, CHEN X, et al. Copula-based analysis of hydrological extremes and implications of hydrological behaviors in the Pearl River basin, China[J]. Journal of Hydrologic Engineering, 2011, 16(7): 598-607. doi: 10.1061/(ASCE)HE.1943-5584.0000350
    [22]
    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]. 岩土工程学报, 2012, 34(12): 2284-2291. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201212023.htm

    TANG Xiao-song, LI Dian-qing, ZHOU Chuang-bing, et al. Modeling dependence between shear strength parameters using Copulas and its effect on slope reliability[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(12): 2284-2291. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201212023.htm
    [23]
    唐小松, 李典庆, 周创兵, 等. 不完备概率信息条件下边坡可靠度分析方法[J]. 岩土工程学报, 2013, 35(6): 1027-1034. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201306007.htm

    TANG Xiao-song, LI Dian-qing, ZHOU Chuang-bing, et al. Reliability analysis of slopes with incomplete probability information[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(6): 1027-1034. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201306007.htm
    [24]
    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]. 岩土力学, 2012, 33(1): 171-178. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201201027.htm

    TANG Xiao-song, LI Dian-qing, ZHOU Chuang-bing, et al. Probabilistic analysis of load- displacement hyperbolic curves of single pile using Copula[J]. Rock and Soil Mechanics, 2012, 33(1): 171-178. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201201027.htm
    [25]
    UZIELLI M, MAYNE P W. Load-displacement uncertainty of vertically loaded shallow footings on sands and effects on probabilistic settlement[J]. Georisk, 2012, 6(1): 50-69.
    [26]
    LI D Q, TANG X S, PHOON K K, et al. Bivariate simulation using Copula and its application to probabilistic pile settlement analysis[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(6): 597-617.
    [27]
    张蕾, 唐小松, 李典庆. 基于Copula函数的土体抗剪强度参数二维分布模型[J]. 土木工程与管理学报, 2013, 30(2): 11-17, 36. https://www.cnki.com.cn/Article/CJFDTOTAL-WHCJ201302002.htm

    ZHANG Lei, TANG Xiao-song, LI Dian-qing, et al. Bivariate distribution model of soil shear strength parameter using Copula[J]. Journal of Civil Engineering and Management, 2013, 30(2): 11-17, 36. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-WHCJ201302002.htm
    [28]
    邢婕, 唐小松, 李典庆, 等. 水利水电工程岩基抗剪强度参数二维分布模型构造的Copula方法[J]. 岩土力学, 2016, 37(3): 783-792. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201603023.htm

    XING Jie, TANG Xiao-song, LI Dian-qing, et al. Bivariate distribution of shear strength parameters for rock mass using Copulas method[J]. Rock and Soil Mechanics, 2016, 37(3): 783-792. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201603023.htm
    [29]
    A KAIKE H. A new look at the statistical model identification[J]. IEEE Transactions on Automatic Control, 1974, 19(6): 716-723.
    [30]
    SCHWARZ G. Estimating the dimension of a model[J]. The Annals of Statistics, 1978, 6(2): 461-464.
    [31]
    DUNCAN J M, BYRNE P M, WONG K S. Strength stress-strain and bulk modulus parameters for finite element-analysis of stress and movements in soil masses[R]. Berkeley: Berkeley University of California, 1978.
    [32]
    NELSEN R B. An introduction to Copulas[M]. New York: Springer, 2006.
    [33]
    李典庆, 唐小松, 周创兵. 基于Copula理论的岩土体参数不确定性表征与可靠度分析[M]. 北京: 科学出版社, 2014.

    LI Dian-qing, TANG Xiao-song, ZHOU Chuang-bing. Uncertain Characterization and Reliability Analysis of Rock and Soil Mass Parameters Based on Copula Theory[M]. Beijing: Science Press, 2014. (in Chinese)
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