Machine Learning-Based Prediction of Shallow Foundation Bearing Capacity Incorporating Slope Inclination as a Predictive Feature

Abstract

Accurate prediction of the ultimate bearing capacity of shallow foundations is important for safe geotechnical design, particularly under varying slope and soil conditions where conventional analytical methods may be limited by simplifying assumptions. This study developed and evaluated machine learning models for predicting the ultimate bearing capacity of shallow foundations using slope inclination, footing width, foundation depth, and soil friction angle as input variables. A dataset of 399 samples obtained from a previously validated finite element method (FEM)-based investigation was used to train and test Multiple Linear Regression (MLR), Support Vector Regression (SVR), and Extreme Gradient Boosting (XGBoost) models. Model performance was evaluated using the coefficient of determination (R²), Root Mean Square Error (RMSE), and 10-fold cross-validation. Unlike previous studies that primarily considered conventional foundation and soil parameters, this study incorporates slope inclination within a unified machine learning framework and compares statistical, kernel-based, and ensemble learning approaches under the same evaluation conditions. XGBoost achieved the highest predictive performance, with a testing R² of 0.9938 and an RMSE of 31.669, followed by SVR with an R² of 0.9534 and an RMSE of 86.900. MLR showed comparatively lower performance, with an R² of 0.8396 and an RMSE of 161.158. The 10-fold cross-validation results further indicated stable XGBoost performance, with a mean R² of 0.991 and a standard deviation of 0.003. These results indicate that XGBoost provides high predictive performance for the evaluated dataset and may support bearing capacity estimation for shallow foundation design.