Indirect estimation of resilient modulus (M_r) of subgrade soil: Gene expression programming vs multi expression programming

Accurate prediction of resilient modulus (M_R) in compacted subgrade soil is crucial for planning secure and environmentally friendly flexible pavement systems. This research assembled a dataset of 2813 data points from twelve compacted soils. The dry density, confining stress, deviator stress, number of freeze-thaw cycles, and moisture content were among the important variables considered for determining the M_R. Subsequently, this study employs ensemble machine learning methodologies, specifically gene expression programming (GEP) and multi-expression programming (MEP), to investigate the subject further. The precision and anticipatory proficiency of both the GEP and MEP models are assessed through statistical evaluations, encompassing crucial metrics (R, RMSE, MAE, RSE, RRMSE, and ρ). The GEP and MEP models align well with validation criteria, underscoring their robustness in predicting novel data and showcasing their broad applicability. The GEP model consistently outperformed the MEP model, with higher coefficient of regression (R²) values in both training (0.992 vs. 0.983) and testing (0.981 vs. 0.972) phases, demonstrating its superior predictive accuracy and robustness. In summary, the GEP model consistently outperforms the MEP model in accuracy and prediction, making it the preferred choice for subgrade soil M_R prediction. Sensitivity analysis was done, which ranked the parameters by their influence: dry density (26.6 %), confining stress (22.7 %), weighted plasticity index (15.3 %), moisture content (13.5 %), deviator stress (12.5 %), and freeze and thaw cycles (9.4 %). This research aims to enhance the utilization of GEP and MEP in civil engineering for more accurate and efficient M_R prediction, ultimately reducing time and costs.