The stress and deformation sensitivity analysis of high earth-rock dams requires knowledge of the statistical mean and standard deviation of deformation parameters of dam materials. However, these parameters are typically determined through grouped tests and sorting. Given the small sample size in each group and the consequently large parameter errors, the inaccuracy of the resulting statistical parameters is evident. The least squares method fits all test points of each group in the same coordinate system for regression calculation, which not only helps to better address the issue of a small sample size, but also eliminates the errors caused by the grouping of test parameters. However, it is found that when the least squares method is applied to the elastic modulus and bulk modulus parameters of the Duncan–Chang E-B model, the residual errors have heteroscedasticity and correlation, which violates the use condition of the least squares method. In order to eliminate the heteroscedasticity and correlation of the fitting residuals of the elastic modulus and bulk modulus parameters of the Duncan–Chang E-B model, this paper decomposes the covariance matrix of the regression residuals to obtain its square root matrix, multiplies the explanatory variables, dependent variables and residual vectors of the regression equation by the square root matrix of the covariance, respectively, and performs variable substitution. The new regression equation has the homogeneity of variance and the irrelevance of the residual. The mean and variance of the model parameters are obtained directly by calculating all the experimental data. The variance of the new parameters is smaller than that of the classical least squares method. The results demonstrate that this generalized least squares method improves the estimation accuracy of elastic modulus and bulk modulus parameters of the Duncan–Chang E-B model.
Chi et al. (Tue,) studied this question.