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Mathematical Problems in Engineering
Volume 2014, Article ID 693062, 11 pages
Research Article

A Copula-Based Method for Estimating Shear Strength Parameters of Rock Mass

1School of Civil Engineering, Chongqing University, Chongqing 400045, China
2State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400045, China
3Key Laboratory of New Technology for Construction of Cities in Mountain Area, Ministry of Education, Chongqing 400045, China
4School of Civil, Environmental and Mining Resource Engineering, The University of Western Australia, Crawley, WA 6009, Australia

Received 14 June 2014; Revised 30 September 2014; Accepted 14 October 2014; Published 4 November 2014

Academic Editor: Xi Frank Xu

Copyright © 2014 Da Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The shear strength parameters (i.e., the internal friction coefficient and cohesion ) are very important in rock engineering, especially for the stability analysis and reinforcement design of slopes and underground caverns. In this paper, a probabilistic method, Copula-based method, is proposed for estimating the shear strength parameters of rock mass. The optimal Copula functions between rock mass quality and , and for the marbles are established based on the correlation analyses of the results of 12 sets of in situ tests in the exploration adits of Jinping I-Stage Hydropower Station. Although the Copula functions are derived from the in situ tests for the marbles, they can be extended to be applied to other types of rock mass with similar geological and mechanical properties. For another 9 sets of in situ tests as an extensional application, by comparison with the results from Hoek-Brown criterion, the estimated values of and from the Copula-based method achieve better accuracy. Therefore, the proposed Copula-based method is an effective tool in estimating rock strength parameters.