Gene expression programming-based multivariate model for earth infrastructure: predicting ultimate bearing capacity of rock socketed shafts in layered soil-rock strata

The evaluation of ultimate bearing capacity (Q_u) of rock socketed shafts (RSSs) is crucial for the design of foundation systems. This study proposes a new data-driven multivariate formulation using gene expression programming (GEP) to assess Q_u of RSSs in layered soil-rock strata. A dataset of 151 points from the literature was used to develop the prediction model. Six influencing features were considered: the material constant for rock (m_i), unconfined compression strength (σ_c), geological strength index (GSI), length of socket in soil (L_ss), length of socket in rock (L_sr), and diameter of the socket base (d). The model predicts the ultimate bearing capacity factor (N_u). The proposed GEP-based formulation showed high accuracy. For the training data, the correlation coefficient (R) was 0.90, with root mean square error (RMSE), mean absolute error (MAE), relative root mean square error (RRMSE), relative standard error (RSE), and performance index (ρ) values of 1.40, 0.98, 0.37, 0.18, and 0.2, respectively. For the testing data, R was 0.86, with RMSE, MAE, RRMSE, RSE, and ρ values of 1.37, 0.93, 0.49, 0.26, and 0.26, respectively. The model’s efficiency was validated through comparison with existing correlations, sensitivity analysis, and rock socketed shaft test results. The proposed GEP-based model showed significantly improved performance over the ensemble learning (EL) model from the previous study, with a 44.23% higher R value, a 22% lower RMSE, and a 26% lower MAE. Additionally, a computer application was developed to facilitate quick estimation of N_u, enhancing the model’s practical applicability in earth systems and infrastructure.