Material-category-specific nonlinear estimation of Duncan E-B model parameters for coarse-grained dam materials

Abstract

Reliable preliminary estimation of Duncan E-B model parameters for coarse-grained dam materials remains difficult because these parameters are commonly obtained from large-scale triaxial tests, whereas conventional empirical values do not adequately represent material-category and state differences. This study develops a material-category-specific, physically interpretable nonlinear estimation framework based on 617 large-scale consolidated drained triaxial-test records, including 440 blasted-rockfill records and 177 natural-gravel records. Product-form equations were established for the initial tangent modulus E i , bulk modulus B t , and internal friction angle φ by jointly considering void ratio e , coefficient of uniformity C u , parent-rock uniaxial compressive strength σ r , median particle size d 50 , and confining pressure σ 3 . RANSAC was used only to diagnose atypical observations, whereas all records in each material category were retained for final coefficient identification and performance evaluation. For blasted rockfill and natural gravel, respectively, the five-variable E i models yielded RMSE values of 43.37 and 42.04 MPa, MAE values of 31.21 and 31.84 MPa, MAPE values of 18.45% and 17.45%, and R² values of 0.687 and 0.766. The corresponding B t models yielded RMSE values of 16.79 and 16.17 MPa and R² values of 0.697 and 0.658, while the φ models yielded RMSE values of 1.51° and 1.36° and R² values of 0.785 and 0.640. Model robustness and engineering applicability were examined through a grouped holdout assessment, comparisons with multiple linear regression, ridge regression, and random forest regression, and validation using five independent engineering cases. In the grouped comparison, the proposed equations yielded the lowest RMSE, MAE, and MAPE and the highest R² for all six material and target combinations. Order-independent permutation analysis showed that void ratio was the dominant material-state variable for E i and B t , whereas confining pressure was the dominant predictor of φ . Because R f showed no stable monotonic relation with the input variables, category medians of 0.683 and 0.766 were adopted, giving rounded preliminary recommendations of 0.68 and 0.77. The proposed equations retain the conventional Duncan E-B parameter structure and provide transparent preliminary estimates within the ranges covered by the modelling database.