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)
摘要以锦屏I级水电站坝址微新大理岩岩体原位大剪试验结果为例，分析岩体质量指标与抗剪强度参数间的相关性。利用Copula理论可将边缘分布和相关结构分开研究的优点，建立小样本条件下各变量的边缘分布函数，并在分析岩体质量指标Q与抗剪强度参数f，c间相关结构特点的基础上构造拟合Q-f，Q-c间关系的最优Copula函数。对于相同岩性的同类岩体，在已知Q条件下求条件概率便可得到抗剪强度参数估值的保证率，或可计算一定保证率下的抗剪参数估值。最后运用该函数分析常用的优定斜率法、最小二乘法的保证率，并与Hoek-Brown准则估值进行比较。研究结果表明，岩体质量指标与抗剪断内摩擦因素f呈较高的正相关关系，与抗剪断黏结力c则呈较高的负相关关系，而具有对称结构的Nelsen NO 1和Nelsen NO 2则分别是拟合Q-f、Q-c间关系的最优Copula函数。常用的最优斜率法与最小二乘法由于忽略岩体质量指标与抗剪强度参数的相关性，因此造成较大的偏差，而具有保证率为0.8的抗剪强度估值与Hoek-Brown经验准则相比更接近实际值。该方法注重充分地利用现场有限的数据信息，可以得到具有一定保证率的抗剪强度参数估值，为岩体抗剪强度参数估值提供一种新的途径。
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.
杨 超1，黄 达1，2， 张永兴1，2，吴俊宏1. 基于Copula理论的岩体抗剪强度参数估值[J]. 岩石力学与工程学报, 2013, 32(12): 2463-2470.
YANG Chao1，HUANG Da1，2， ZHANG Yongxing 1，2，WU Junhong1. ESTIMATION OF SHEAR STRENGTH PARAMETERS OF ROCK MASS BASED ON COPULA THEORY. , 2013, 32(12): 2463-2470.
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2013, Vol. 32 
