What question did this study set out to answer?

The aim is to improve the prediction of end-bearing capacity in rock-socketed shafts using optimized models.

February 10, 2026Open Access

Improving end-bearing capacity prediction of rock-socketed shafts using Gaussian-augmented optimized extreme gradient boosting models

Key Points

The aim is to improve the prediction of end-bearing capacity in rock-socketed shafts using optimized models.
Compiling a database of 151 rock-socketed shafts from literature.
Employing algorithms like arithmetic, brainstorm, and whale optimization to enhance XGBoost models.
Conducting multicollinearity and sensitivity analyses on features affecting predictions.
XGBoost estimated end-bearing capacity with RMSE of 0.9205 and MAE of 0.7024; performance (R) was 0.9295.
XGBoost_AOA model performance improved to 0.9894 using the optimized dataset.
Multicollinearity analysis showed problematic relationships between rock mass rating and geological strength index.

Abstract

This research employs conventional and optimized extreme gradient boosting (XGBoost) models to predict the end-bearing capacity (\ (\: N\: \) ) of rock-socketed shafts. The arithmetic optimization (AOA), brainstorm optimization (BOA), and whale optimization (WOA) algorithms were used to optimize the XGBoost model. To conduct this research, a database of the \ (\: N\: \) of 151 rock-socketed shafts was compiled from the literature. The database (mentioned by OData) was preprocessed, and the \ (\: N\: \) of the 136 rock-socketed shafts was obtained. The Gaussian-noise technique was employed to create a synthetic database based on the \ (\: N\: \) of 136 rock-socketed shafts. A database of the \ (\: N\: \) of 500 rock-socketed shafts was generated and preprocessed. The \ (\: N\: \) of 460 rock-socketed shafts (136 original + 324 synthetic after preprocessing datasets) developed a second database (mentioned by OSData). The XGBoost, XGBoostAOA, XGBoostBOA, and XGBoostWOA models were trained and tested using both databases. The performance analysis revealed that the XGBoost model estimated the \ (\: N\: \) with a root mean square error (RMSE) of 0. 9205, mean absolute error of (MAE) of 0. 7024, and a performance (R) of 0. 9295 using the OData. Later, the performance of the XGBoostAOA model was enhanced to 0. 9894 using the OSData. It was also observed that OSData improved generalizability and reduced overfitting in the XGBoostAOA model. Moreover, the multicollinearity analysis revealed that the rock mass rating (RMR) and geological strength index (GSI) exhibit problematic multicollinearity. In addition, the sensitivity analysis demonstrated that the RMR and GSI features have contributions of 20. 301% and 20. 369%, respectively, in estimating \ (\: N\: \). For the first time, this research mapped a relationship between feature multicollinearity and sensitivity to analyze the overfitting of the soft computing models. Moreover, SHapley Additive exPlanations (SHAP) analysis identified compressive strength and rock mass rating as dominant predictors (0. 65–1. 36), while the geological strength index showed minimal influence (< 0. 10). Finally, this research provides a Graphical User Interface application to help the geotechnical engineers and designers estimate the \ (\: N\: \).

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