Seismic Stability of Unsupported Rectangular Excavations in Cohesive-Frictional Soils: FELA Simulations and Comparative Analysis Using MARS, GP, and GMDH Models

In this study, three sophisticated nonlinear regression algorithms—multivariate adaptive regression splines (MARS), genetic programming (GP), and the group method of data handling (GMDH)—are utilized to develop an explicit equation for predicting the seismic stability number (N) for unsupported rectangular excavations in frictional cohesive soil. The study aims to advance geotechnical engineering by providing models that improve the accuracy and reliability of seismic stability assessments in underground structures. The dataset consists of 400 finite element limit analysis (FELA) solutions obtained from lower bound (LB) and upper bound (UB) simulations. These solutions serve as the foundation for constructing data-driven models using the MARS, GP, and GMDH techniques. The predictive performance of these models is evaluated using multiple performance metrics, including regression error characteristic curves and Taylor charts, ensuring a comprehensive assessment of accuracy and reliability. Additionally, a sensitivity analysis is conducted to identify the most influential parameters affecting seismic stability. Among the developed models, the GP-based approach exhibited the highest predictive performance, achieving R² values of 0.9866 for training and 0.9880 for testing. The model demonstrated low RMSE and MAE values, indicating superior accuracy. Sensitivity analysis results highlight that the internal friction angle (ϕ) and the excavated depth ratio (H/B) are the most critical parameters, with impact values of \({R}_{ij}\) = 0.91 and 0.88, respectively. These findings reinforce the potential of advanced nonlinear regression models, particularly GP, in accurately forecasting the seismic stability number (N) for unsupported excavations. The results contribute to practical geotechnical applications, supporting the design of earthquake-resistant excavations.