基于Copula理论岩体质量Q值及波速与变形模量多变量相关性研究

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摘要以锦屏I级水电站坝址大理岩岩体原位变形试验和勘察结果为例，在分析岩体变形模量、纵波波速以及岩体质量指标Q值间的两两相关关系的基础上，利用Copula函数能够描述多变量相关性的优点，构造了拟合，和Q值间关系的最优Copula函数，并在岩体变形模量估值中进行运用。研究结果表明，三维Clayton Copula函数是拟合岩体波速，Q值和变形模量间相关关系最优Copula函数。利用构造的 - -Q间关系的最优Copula函数求条件概率，可在已知岩体和Q值条件下计算其他方法对变形模量估值的保证率，或者计算具有一定保证率的岩体变形模量估值，得到具有最优拟合的变形模量估值。该方法建立多因素间的相关关系，使现场试验和勘察的数据得到充分利用，为建立岩体变形模量与岩体参数间相关关系及估值提供一种新的途径。

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关键词 ：岩石力学, 变形模量, 岩体参数, Copula理论, 相关性

Abstract：There are strong correlations between deformation modulus of rock mass and physico-mechanical parameters or rock mass quality indices. These correlations were usually used for the estimation of deformation modulus. However，most of these correlations are established between a single parameter and deformation modulus；the other related parameters obtained from the in-situ tests or engineering geology survey are underused. Based on the correlation investigation between deformation modulus and wave velocity( )，deformation modulus and Q system，wave velocity and Q system of marble rock mass in Jinping I hydropower station，taking the advantage of Copula functions that can describe the correlations of multivariate，the optimal fitting Copula function of - -Q is selected. Then it has been applied to the estimation of deformation modulus. The result shows that Clayton Copula is the optimal fitting Copula function of Em- -Q. The guaranteed rates of estimated by other methods can be obtained；and the estimation of can be calculated with a certain guaranteed rates；the optimal fitting estimation of can be obtained with known and Q system by solving the conditional probability of the optimal fitting Copula functions. The multivariable correlation of rock mass quality，wave velocity and deformation modulus is established by this paper?s method. It takes full use of the information from the in-situ tests or engineering geology survey. It provides a new approach for establishing the correlations between deformation modulus and parameters of rock masses and estimation for deformation modulus.

Key words： rock mechanics deformation modulus rock mass parameters Copula theory correlation

收稿日期: 2013-04-25

引用本文:

杨超1，黄达1，2，张永兴1，2. 基于Copula理论岩体质量Q值及波速与变形模量多变量相关性研究[J]. 岩石力学与工程学报, 2014, 33(3): 507-513.
YANG Chao1，HUANG Da1，2，ZHANG Yongxing1，2. MULTIVARIABLE CORRELATION OF ROCK MASS QUALITY INDEX Q SYSTEM VALUE，WAVE VELOCITY AND DEFORMATION MODULUS BASED ON COPULA THEORY. , 2014, 33(3): 507-513.

链接本文:

http://www.rockmech.org/CN/Y2014/V33/I3/507

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