Reliability-Based Design for Strip-Footing Subjected to Inclined Loading Using Hybrid LSSVM ML Models

The bearing capacity of strip footings is significantly influenced by uncertainties related to the footing, soil conditions, and load inclination. Given the inherent unpredictability in footing design, the reliability-based design of geotechnical structures has garnered considerable interest in the research community. This paper presents a state-of-the-art probabilistic design for footings under inclined loading using the first-order reliability method (FORM) combined with a hybrid least squares support vector machine (LSSVM) learning approach. A comprehensive dataset comprising 920 samples from the literature, with the reduction factor (RF) as the output parameter, was utilized to simulate hybrid LSSVM models based on particle swarm optimization (PSO) and Harris hawks optimization (HHO). The input variables for predicting the bearing capacity include the load eccentricity-to-width ratio, embedment ratio, load inclination-to-friction angle, and load arrangement. The performance metrics indicate that among the three proposed machine learning models, the LSSVM-PSO model achieves the best predictive performance, with an R² of 0.991 and an RMSE of 0.051 during training and an R² of 0.962 and an RMSE of 0.109 during testing. The model’s performance was further evaluated via rank analysis, reliability analysis, regression plots, and uncertainty analysis. The reliability index (β) and corresponding probability of failure (POF) computed using FORM were compared with the actual values for both phases. The study concluded that the LSSVM-PSO is the most reliable method for reliability-based design, demonstrating superior performance and reliability. This hybrid approach offers a robust framework for addressing uncertainties in geotechnical engineering, enhancing the reliability and accuracy of footing design under inclined loading conditions.