Mean limiting pressure factors determination in contiguous pile walls using RAFELA and nonlinear regression models in spatially random soil

• Random adaptive finite element limit analysis (RAFELA) predicts pressure factors. • MARS and GMDH models developed for CPWs using nonlinear regression techniques. • MARS achieves the highest accuracy with R² of 0.983 for training and 0.969 for testing. • Soil variability, adhesion factor, and uniformity most influence the pressure factor. • User-friendly ML models bridge theory and practice for geotechnical applications. This study employs random adaptive finite element limit analysis (RAFELA) combined with advanced machine learning (ML) techniques to predict the mean limiting pressure factor in contiguous pile walls (CPWs). Two nonlinear regression models, multivariate adaptive regression splines (MARS) and the group method of data handling (GMDH), are developed to forecast the mean limiting pressure factor. The models were evaluated using several statistical performance parameters, scatter plots, residual error curves, and eight statistical performance metrics to ensure predictive accuracy and reliability. Based on the statistical analysis and comparison, the proposed MARS model is the most accurate model, with R 2 = 0.983 for training and R 2 = 0.969 for the testing phase, followed by GMDH (R 2 = 0.971 for training and R 2 = 0.944 for testing). Comprehensive measures (COM) reveal that the MARS model, with the lowest COM value of 1.006, outperforms the GMDH model (COM = 4.943), demonstrating superior accuracy in predicting the limiting pressure factor ( μ N r a n ). Feature importance analysis reveals that the output μ N r a n is most influenced by soil variability ( C o V c = 0.749), followed by the adhesion factor ( α = 0.735) and soil uniformity ( Θ c = 0.681), whereas the S/D ratio has the lowest impact (0.378). Moreover, the proposed ML models provide user-friendly empirical equations to calculate the mean limiting pressure factor, requiring minimal computational expertise, thus bridging the gap between theoretical stochastic studies and practical field applications. This research enhances geotechnical design efficiency with robust ML solutions, supporting safer and more sustainable excavation practices under complex subsurface conditions.