Low-Data Modeling of Shallow Foundations on Cohesive Slopes: A Comparison between Hybrid FEM–RSM and ML Models

Abstract

In geotechnical engineering, accurately predicting the seismic bearing capacity of shallow foundations on cohesive slopes requires proper consideration of nonlinear effects and parameter interactions. However, most studies in the literature address these complex effects inadequately, either with numerical methods that demand a large number of analyses or with machine learning (ML) models that require large and heterogeneous data sets. In this study, it is aimed to propose an approach that allows for a robust analysis of the system and at the same time provides accurate forecasting for situations where working with small and homogeneous data sets is mandatory. Within the scope of the study, seismic bearing capacity analyses were performed using Plaxis 2D for 273 cases where eight independent variables took different values according to the Face Centered Composite Design (FCCD), and a database was created. Multiple Linear (MLR), Multiple Nonlinear (MNLR) Regression Models were established, and ML models, such as Support Vector Regression (SVR), Random Forest (RF), and Extreme Gradient Boosting (XGBoost), were trained. The models were compared with both in-sample and out-of-sample estimation performance, and parametric sensitivity analyses were evaluated by methods such as ANOVA and SHAP. The results show that the MNLR model with natural logarithmic transformation is the most successful method in terms of both accuracy (R² ≈ 0.98) and reflecting parameter interactions, while the SVR algorithm demonstrates the best generalization ability among ML models under low-data conditions. The results also confirm that the ML models effectively capture the parameter effects.

Keywords

• Seismic bearing capacity
• response surface methodology
• finite element method
• soft computing methods

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