Modeling of settlement of shallow-founded rocking structures using explainable physics-guided machine learning

Rocking foundation is an unorthodox seismic design philosophy of structures that enhances the performance of structures by absorbing and dissipating seismic energy into soil. This paper examines the application of physics-guided machine learning (PGML) technique to model the settlement of shallow-founded rocking structures during earthquake loading. An approximate physics-based model (PBM) is derived for rocking-induced total settlement as a function of critical contact area ratio and cumulative rotation of the foundation. The output of the PBM is fed as an additional input feature to machine learning (ML) algorithms to develop PGML models. The performances of PGML models are compared with the performances of purely data-driven ML models, the PBM outputs, and results obtained from an empirical relationship. To shed light on the explainability of ML and PGML models, Shapley Additive Explanations (SHAP values) are used to decipher and interpret the model predictions and their dependency on input features. It is found that PGML models, especially physics-guided gradient boosting and random forest regression, improve the prediction accuracy when compared to their purely data-driven ML counterparts by combining the knowledge extracted from experimental data with the mechanics of the problem considered. SHAP analysis reveals that the PGML model predictions and their dependency on input features are consistent with the existing domain knowledge, and that the inclusion of physics in PGML models help improve the prediction accuracy, especially in cases where other input features fail to capture the combined complex interaction among the variables involved.