基于Copula理论的岩体抗剪强度参数估值

Abstract
Figure/Table
References
Related Citation (15)

Download: PDF (5292 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract The correlation between rock mass quality indices and shear strength parameters are investigated by means of analyzing the specimens tested in-situ of gently weathered marble rock mass in Jinping I hydropower station. Taking the advantage of Copula theory that the marginal distribution and dependence structure can be studied separately；the marginal distributions of variables under small sample conditions are established. The optimal fitting Copula functions of Q-f and Q-c are selected on basis of researching on the dependence structure between rock mass quality Q and shear strength parameters f and c. For similar rock mass，the guaranteed rates of estimated f and c by other methods can be obtained；and the estimate of f and c can be calculated with a certain guaranteed rates with known Q system by solving the conditional probability of the optimal fitting Copula functions. Then the guaranteed rates of estimated f and c by the predominant slope method and least-squares method are calculated；the estimation of f and c with a certain guaranteed rates are compared to the estimation by Hoek-Brown criterion. The results show that，Q has a positive correlation with f，while Q has a negative correlation with c，the symmetric structured Copula functions Nelsen NO 1 and Nelsen NO 2 are the optimal fitting Copula functions of Q-f and Q-c. The estimation of f and c by the predominant slope method and least-squares methods are skewed because the correlation between rock mass quality and shear strength parameters are ignored；and the rock mass shear strength derived from this paper?s method with guaranteed rates 0.8 is more coincident with practical situation than by Hoek-Brown criterion. This paper's method takes full use of the limited in-situ information，the shear strength parameters with a guaranteed rate can be estimated，it can be used for rock mass shear strength parameter estimation.

Key words： rock mechanics shear strength of rock mass rock mass quality indices in-situ tests Copula theory

Received: 25 December 2012

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors

Cite this article:

URL:

https://rockmech.whrsm.ac.cn/EN/Y2013/V32/I12/2463

[1]	CAI M，KAISER P K，UNO H，et al. Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system[J]. International Journal of Rock Mechanics and Mining Sciences，2004，41(1)：3-19.
[2]	JUSTO J L，JUSTO E，AZANON J M，et al. The use of rock mass classification systems to estimate the modulus and strength of jointed rock[J]. Rock Mechanics and Rock Engineering，2010，43(3)：287-304.
[3]	宋彦辉，巨广宏. 基于原位试验和规范的岩体抗剪强度与Hoek- Brown准则估值比较[J]. 岩石力学与工程学报，2012，31(5)：1 000-1 006.(SONG Yanhui，JU Guanghong. Determination of rock mass shear strength based on in-situ tests and codes and comparison with estimation by Hoek-Brown criterion[J]. Chinese Journal of Rook Mechanics and Engineering，2012，31(5)：1 000-1 006.(in Chinese)) " target="_blank">
[4]	胡盛明，胡修文. 基于量化的GSI系统和Hoek-Brown准则的岩体力学参数的估计[J]. 岩土力学，2011，32(3)：861-866.(HU Shengming，HU Xiuwen. Estimation of rock mass parameters based on quantitative GSI system and Hoek-Brown criterion[J]. Rock and Soil Mechanics，2011，32(3)：861-866.(in Chinese)) " target="_blank">
[5]	BARTON N. Some new Q-value correlations to assist in site characterization and tunnel design[J]. International Journal of Rock Mechanics and Mining Sciences，2002，39(2)：185-216.
[6]	YANG X L，YIN J H. Slope equivalent Mohr-Coulomb strength parameters for rock masses satisfying the Hoek-Brown criterion[J]. Rock Mechanics and Rock Engineering，2010，43(4)：505-511.
[7]	HOEK E，WOOD D，SHAH S. A modified Hoek-Brown criterion for jointed rock masses[C]// Proceedings of Rock Characterization， Symposium of International Society of Rock Mechanics. [S. l.]：[s. n.]，1992：209-213. " target="_blank">
[8]	张永杰，曹文贵，赵明华，等. 基于地质强度指标与区间理论的岩体抗剪强度确定方法[J]. 岩土力学，2011，32(8)：2 447-2 452. (ZHANG Yongjie，CAO Wengui，ZHAO Minghua，et al. Method for determining rock mass shear strength based on interval theory and geological strength index[J]. Rock and Soil Mechanics，2011，32(8)：2 447-2 452.(in Chinese)) " target="_blank">
[9]	武雄，贾志欣，陈祖煜，等. 工程岩体抗剪强度确定综合方法——GMEM 研究[J]. 岩石力学与工程学报，2005，24(2)：246-251.(WU Xiong，JIA Zhixin，CHEN Zuyu，et al. Research on a synthetical method GMEM on ascertaining shear strength for engineering rock mass[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(2)：246-251.(in Chinese))
[10]	宫凤强，李夕兵，邓建. 小样本岩土参数概率分布的正态信息扩散法推断[J]. 岩石力学与工程学报，2006，25(12)：2 559-2 564. (GONG Fengqiang，LI Xibing，DENG Jian. Probability distribution of small samples of geotechnical parameters using normal information spread method[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(12)：2 559-2 564.(in Chinese)) " target="_blank">
[11]	SKLAR A. Fonctions de répartition àn dimensions et leurs magres[J]. Publications de l?Institut de Statistique de l?Université de Paris，1959，(8)：229-231. " target="_blank">
[12]	韦艳华，张世英. Copula理论及其在金融分析上的运用[M]. 北京：清华大学出版社，2008：9-11.(WEI Yanhua，ZHANG Shiying. Copula theory and its applications in financial analysis[M].Beijing：Tsinghua University Press，2008：9-11.(in Chinese)) " target="_blank">
[13]	宋松柏，蔡焕杰，金菊良，等. Copula函数及其在水文中的运用[M]. 北京：科学出版社，2012：93-94.(SONG Songbai，CAI Huanjie， JIN Juliang，et al. Copula theory and its applications in hydrology[M]. Beijing：Science Press，2004：93-94.(in Chinese)) " target="_blank">
[14]	SHIAU J T. Fitting drought duration and severity with two-dimensional Copulas[J]. Water Resources Management，2006，20(5)：795-815.
[15]	SONG S B，SINGH V P. Frequency analysis of droughts using the Plackett Copula and parameter estimation by genetic algorithm[J]. Stochastic Environmental Research and Risk Assessment，2010，24(5)，783-805. " target="_blank">
[16]	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.(TANG Xiaosong，LI Dianqing，ZHOU Chuangbing，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)) " target="_blank">
[17]	黄润秋，许模，陈剑平，等. 岩体结构精细描述及其工程应用[M].科学出版社，2004：180-187.(HUANG Runqiu，XU Mo，CHEN Jianping，et al. The fine description of rocks structure and its engineering application[M]. BeiJing：Science Press，2004：180-187.(in Chinese)) " target="_blank">
[18]	胡卸文，钟沛林，任志刚. 岩体块度指数及其工程意义[J]. 水利学报，2002，33(3)：80-83.(HU Xiewen，ZHONG Peilin，REN Zhigang. Rock-mass block index and its engineering practice significance[J]. Journal of Hydraulic Engineering，2002，33(3)：80-83.(in Chinese)) " target="_blank">
[19]	樊妮，赫孝良，赵谦. 基于Bayesian思想的最优Copula函数选择[J]. 工程数学学报，2012，29(4)：516-522.(FAN Ni，HE Xiaoliang，ZHAO Qian. Optimal Copula function selection based on Bayesian methodology[J]. Chinese Journal of Engineering Mathematics，2012，29(4)：516-522.(in Chinese)) " target="_blank">
[20]	唐家银. 基于Copula对随即元间相依性的研究及其运用[硕士学位论文][D]. 成都：西南交通大学，2005.(TANG Jiayin. The study and applicability involving dependence between random varieties based on Copulas. [M. S. Thesis][D]. Chengdu：Southwest Jiaotong University，2005.(in Chinese)) " target="_blank">
[21]	NELSEN R B. An instruction to Copulas[M]. New York：Springer，2006：116-118. " target="_blank">
[22]	张雨. Archimedean Copula 函数在干旱分析中的运用[硕士学位论文][D]. 杨凌：西北农林科技大学，2010.(ZHANG Yu. Application of Archimedean Copulas functions in drought analysis[M. S. Thesis][D]. Yangling：Northwest A and F University，2010.(in Chinese)) " target="_blank">
[23]	中华人民共和国国家标准编写组. GB50487—2008水利水电工程地质勘察规范[S]. 北京：中国计划出版社，2009.(The National Standards Compilation Group of People?s Republic of China. GB50487—2008 Code for geological investigation of water resources and hydropower engineering[S]. Beijing：China Planning Press，2009.(in Chinese)) " target="_blank">
[24]	HOEK E，DIEDERICHS M S. Empirical estimation of rock mass modulus[J]. International Journal of Rock Mechanics and Mining Sciences，2006，43(2)：203-215. " target="_blank">