A Method for Determining the Soil Shear Strength by Eliminating the Heteroscedasticity and Correlation of the Regression Residual

Due to cost and variability of geotechnical test results, the number of samples for geotechnical material parameters in one engineering project is limited, resulting in a certain degree of errors in the calculation of probability distribution, mean, and variance of mechanical parameters of the geotechnical materials. To improve the reliability of geotechnical engineering design, reducing the variance of shear strength is one of the methods. Currently, the least squares method is widely used to regress the shear strength of soil; however, the regression residuals often exhibit heteroscedasticity and correlation, which undermine the validity of the variance estimates of soil shear strength parameters. This study aims to address this issue by applying the generalized least squares method to eliminate the heteroscedasticity and correlation of regression residuals. The results of triaxial consolidated drained (CD) tests on the coarse-grained soil; triaxial unconsolidated undrained(UU), CD, and consolidated undrained (CU) tests on gravelly clay; and triaxial CD tests on sand were analyzed to estimate the mean and variance of their shear strength. The results show that while the mean values of shear strength parameters remain largely unchanged, the generalized least squares method reduces the standard deviation of cohesion by an average of 30.575% and that of the internal friction angle by 14.21%. This reduction in variability enhances the precision of parameter estimation, which is critical for reliability-based design in geotechnical engineering, as it leads to more consistent safety assessments and optimized structural designs. The reliability analysis of an infinitely long slope stability shows that the reliability index of the soil slope calculated by the traditional method is either large or small. The generalized least squares method, which eliminates the heteroscedasticity and correlation of the regression residuals, should be adopted to regress the shear strength of soil.