Work

Parameter Variance of the Duncan Formula for Nonlinear Shear Strength of Coarse-Grained Soil

Year: 2025

Type: article

Abstract: Currently, the shear strength of coarse-grained soil is commonly determined using the Duncan formula, which establishes a relationship between the shear strength and confining pressure. Specifically, the parameters of the Duncan formula are estimated based on available test data using least squares regression, which mitigates the limitations associated with small sample sizes and significant errors in the classic grouping method. However, hypothesis testing in mathematical statistics reveals that the residual variances from the classic least squares estimation exhibit heteroscedasticity and autocorrelation, violating the fundamental assumptions required for least squares regression. Consequently, parameter estimates obtained through classic least squares regression have large variances, leading to unreliable statistical inferences. To address this issue, we propose a generalized least squares method that corrects for heteroscedasticity and autocorrelation of the residuals. Triaxial test data for five different coarse-grained soil materials are analyzed using the proposed method. The results show that the mean values of the estimated parameters of the Duncan formula are close to those obtained using the classic method, while their variances are significantly reduced, demonstrating the effectiveness of the proposed approach.

Source: Applied Sciences

DOI: 10.3390/app151810225

Authors: Heng Chi, Hengdong Wang, Yufeng Jia, Degao Zou

Institutions: Dalian University of Technology, Shanghai Municipal Engineering Design Institute (Group) Co., Ltd (China)

Language: English

Topic: Geotechnical Engineering and Analysis

Subfield: Safety, Risk, Reliability and Quality

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: National Natural Science Foundation of China