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| ESTIMATION OF SHEAR STRENGTH PARAMETERS OF ROCK MASS BASED ON COPULA THEORY |
| YANG Chao1，HUANG Da1，2， ZHANG Yongxing 1，2，WU Junhong1 |
| (1. College of Civil Engineering，Chongqing University，Chongqing 400045，China；2. Key Laboratory of New Technology for Construction of China in Mountainous Area，Chongqing University，Chongqing 400045，China) |
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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.
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Received: 25 December 2012
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2013, Vol. 32 
