Machine Learning–Based Prediction of Seismic Bearing Capacity for Strip Foundations Adjacent to c–φ Soil Slopes

The seismic bearing capacity of strip foundations located near slopes is a critical design issue in geotechnical engineering, particularly for cohesive–frictional (c–φ) soils where complex failure mechanisms may develop under earthquake loading. While numerical approaches provide reliable predictions, their computational cost limits their applicability for extensive parametric analyses. In this study, a hybrid numerical–machine learning framework is proposed to efficiently predict the normalized seismic bearing capacity coefficient (Qu/γB) of strip footings adjacent to slopes. A comprehensive database of 1620 cases is generated using finite difference simulations performed with FLAC2D v7 under pseudo-static seismic conditions. The influence of six dimensionless parameters, including slope geometry (H/B, β), footing position (b/B), soil strength (c/γB, φ), and seismic loading intensity (kₕ), is systematically investigated. Four machine learning algorithms, namely Extreme Gradient Boosting (XGBoost), Deep Neural Network (DNN), Random Forest (RF), and k-Nearest Neighbors (KNN), are trained and evaluated using multiple statistical indicators. The results show that XGBoost provides the highest predictive accuracy, achieving R2 = 0.98 and a mean absolute error of 0.0085. It should be emphasized that this performance reflects the model’s ability to reproduce FLAC2D numerical outputs under idealized assumptions, rather than a demonstrated predictive validity for actual, in-situ soil and foundation behavior. Feature importance and SHAP analyses reveal that the internal friction angle (φ) and seismic coefficient (kₕ) are the dominant parameters controlling seismic bearing capacity, while geometric factors such as H/B and b/B exhibit a secondary influence. The proposed framework enables rapid and accurate interpolation of seismic bearing capacity within the sampled parameter space. Compared to existing studies, the originality of this work lies in the development of a finite difference-based dataset for c–φ soils, combined with interpretable machine learning techniques. It should be noted that the trained model constitutes a surrogate of the FLAC2D numerical framework under idealized assumptions (homogeneous isotropic soil, rigid footing, perfect soil-footing contact, zero dilatancy, pseudo-static seismic loading), and is not intended as a general predictive tool for real, heterogeneous field conditions. The proposed approach provides a computationally efficient tool for preliminary parametric studies and screening-level assessments under pseudo-static loading conditions of shallow foundations near slopes under pseudo-static seismic loading conditions. Its direct application to site-specific seismic design or risk assessment, where ground-motion characteristics and vertical seismic components must be explicitly considered, is not recommended without further validation against dynamic analyses and experimental data.