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

doi:10.16285/j.rsm.2016.03.022

›› 2016, Vol. 37 ›› Issue (3): 783-792.doi: 10.16285/j.rsm.2016.03.022

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

邢婕^{1, 2}，唐小松^{1, 2}，李典庆^{1, 2}，赵宇飞³

1. 武汉大学水资源与水电工程科学国家重点实验室，湖北武汉 430072；2. 武汉大学水工岩石力学教育部重点实验室，湖北武汉 430072； 3. 中国水利水电科学研究院岩土工程研究所，北京 100044

收稿日期:2014-06-29 出版日期:2016-03-11 发布日期:2018-06-09
通讯作者: 李典庆，男，1975年生，教授，博士生导师，主要从事岩土工程可靠度分析与风险控制方面的研究。E-mail: dianqing@whu.edu.cn E-mail:xingjie0416@whu.edu.cn
作者简介:邢婕，女，1990年生，硕士研究生，主要从事岩土工程可靠度和风险分析方面的研究。
基金资助:
国家自然科学基金项目（No.51225903，No.51329901，No.51509188）；湖北省自然科学基金创新群体项目（No.2014CFA001）。

Bivariate distribution of shear strength parameters for rock mass using Copulas method

XING Jie^{1, 2}, TANG Xiao-song^{1, 2}, LI Dian-qing^{1, 2}, ZHAO Yu-fei³

1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, Hubei 430072, China; 2. Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, Wuhan University, Wuhan, Hubei 430072, China; 3. Department of Geotechnical Engineering, China Institute of Water Resources and Hydropower Research, Beijing 100044, China

Received:2014-06-29 Online:2016-03-11 Published:2018-06-09
Supported by:
This work was supported by the National Natural Science Foundation of China (51225903, 51329901, 51509188) and the Natural Science Foundation of Hubei Province of China (2014CFA001).

摘要/Abstract

摘要： 基于国内103个水利水电工程1 174组岩基抗剪强度试验数据，采用Copula函数研究岩基抗剪强度参数联合分布模型，探讨水利水电工程中岩基抗剪强度参数联合分布模型构建方法。利用最小二乘法求出岩基抗剪强度参数试验数据的相关统计参数，基于AIC准则识别出岩基抗剪强度参数边缘分布。选择4种Copula函数构造岩基抗剪强度参数二维分布模型，探讨了基于Copula函数的岩基抗剪强度参数二维分布模型的优越性。结果表明：水利水电工程岩基抗剪强度参数存在明显的统计负相关性。Copula方法能够构造具有任意边缘分布和任意相关结构的岩基抗剪强度参数联合分布模型，它为构造抗剪强度参数联合分布模型提供了一种简便的工具。已知岩基抗剪强度参数的边缘分布函数和相关系数不能唯一确定岩基抗剪强度参数的联合概率分布模型，在抗剪强度参数边缘分布函数和相关系数完全相同的前提下，不同Copula函数建立的抗剪强度参数联合概率分布模型差异显著。与常用的抗剪强度参数二维正态分布模型相比，基于Copula函数的抗剪强度参数二维分布模型具有较强的灵活性，它能更好地拟合原始观测数据。水利水电工程中惯用小值平均法确定标准值，当摩擦系数取较小值时，不同Copula函数构造的黏聚力的条件累积分布函数差异显著，这将对抗剪强度参数标准值的选取以及相应的设计方案具有明显的影响。

Abstract: Based on 1 174 sets of testing data of shear strength parameters from 103 hydropower projects in China, a Copula-based function is adopted to investigate the joint distribution model of shear strength parameters for rock foundation. The construction method of the joint distribution model is explored. Firstly, the statistics of shear strength parameters have been achieved using the least square method. Then, based on the Akaike Information Criterion (AIC), the best-fit marginal distributions of shear strength parameters is identified. Finally, four Copula functions are chosen to build the bivariate distribution of shear strength parameters. The advantages of using Copulas to model the bivariate distribution of shear strength parameters are discussed. The results indicate that there exists a strong negative correlation among the shear strength parameters of rocks in hydropower projects. The proposed Copula-based approach can incorporate various marginal distributions and Copulas into a multivariate distribution, which provides a flexible way of modeling the bivariate distribution of shear strength parameters. With the known marginal distributions and correlation coefficient of shear strength parameters, the bivariate distribution of shear strength parameters cannot be determined uniquely. The bivariate distributions using various Copulas differ considerably under the premise that the edge distribution function and the correlation coefficient are exactly the same. Compared with the commonly used bivariate normal distribution of shear strength parameters, the proposed Copula-based approach provides a more general way of modeling the bivariate distribution and thus its modeled results are more accurate. Design values of shear strength parameters in hydropower projects are commonly determined by using the small value average method in China. The conditional cumulative distribution functions of cohesion associated with various Copulas differ considerably when friction coefficient takes a smaller value. Such differences directly lead to a significant effect on the determination of design values of shear strength parameters and the associated design schemes of hydraulic structures.

Key words: shear strength parameters, correlation, bivariate distribution, joint probability distribution function, Copula

中图分类号:

TU 459+.2

邢婕，唐小松，李典庆，赵宇飞，. 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]. , 2016, 37(3): 783-792.

XING Jie , TANG Xiao-song , LI Dian-qing , ZHAO Yu-fei，. Bivariate distribution of shear strength parameters for rock mass using Copulas method[J]. , 2016, 37(3): 783-792.

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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

Bivariate distribution of shear strength parameters for rock mass using Copulas method

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