Correlated and uncorrelated linear regression statistical methods for probabilistic characteristics of shear strength

Calculating the mean value and the standard deviation is the key step to determine the characteristic value of the shear strength parameters. The calculation of the standard deviation is much more difficult than that of the mean value due to the limited sets of strength tests. The traditional linear regression method can not obtain the valid standard deviation of shear strength index. A modified linear regression method capable to calculate the standard deviation of shear strength index is proposed based on the probability theory and the Taylor expansion method. Different assumptions dependent or independent of cohesion and friction coefficient are employed. Considering that the main variation of the shear strength of soil is determined by means of the friction coefficient under the large confining pressure, the problem of sample number can be solved by using all the test results under large pressure together based on the hypothesis that the cohesion and the friction coefficient are uncorrelated. The modified regression method and moment method are adopted to calculate the standard deviation and the correlation coefficient of shear strength indexes of core clay of Xiaolangdi Embankment Dam. The results show that different methods can provide good prediction of the uncertainty of shear strength whether the cohesion and the friction coefficient are correlated or not in assumption. The standard deviations obtained from the moment methods should be used with the coefficient of correlation. When the correlation between the cohesion and the friction coefficient is ignored, the uncorrelated regression methods should be adopted.