Pareto-optimized stacked ensemble machine learning framework for predicting bearing capacity of driven piles from static load test data

Since traditional empirical methods frequently fail to capture complex soil-pile interactions, accurately evaluating the bearing capacity of driven piles remains a critical yet difficult task in geotechnical engineering. In this regard, this study proposes a novel machine learning framework for predicting the pile bearing capacity (PBC) of driven piles using a stacking guided by a multi-objective Pareto optimization approach. Using a comprehensive dataset that includes 472 records from the literature, the framework combines random forest (RF), K-nearest neighbor (KNN), and extreme gradient boosting (XGBoost) to increase predictive accuracy and generalizability. The dataset consists of a range of geological, geometric, and loading conditions, in addition to explanatory input features from the standard penetration test (SPT) dataset, such as pile diameter, soil depth, different soil layers, and the SPT-N values. Model interpretability is achieved through Shapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP), revealing key influencers such as pile diameter and SPT-N values along the shaft and tip. The stacking model improved predictive accuracy over the respective base-level models, using a Pareto-optimized stacking model, achieving a coefficient of determination of 0.9471. It also had reduced mean squared error (MSE) and mean absolute error (MAE) on the testing dataset as compared to the base-level models. Sensitivity and parametric analyses of the PBC confirmed that the model calculations were significant and demonstrated that pile diameter and soil layer thicknesses influence PBC. Finally, this approach provides geotechnical engineers with an accurate and interpretable tool to predict PBC, supporting safer and more cost-effective pile foundation designs in complex soil conditions.