Machine learning-driven reliability assessment of liquefaction probability based on state parameter analysis

The state parameter ( ψ ) utilising the concept of critical state soil mechanics integrates the effect of relative density and effective stress and offers notable advantages for liquefaction assessment. This study presents a ψ -based liquefaction analysis using the first-order reliability method (FORM) and second-order reliability method (SORM) to evaluate the liquefaction probability of failure ( P L ) considering the parametric uncertainty. Four machine learning (ML) models, which include long short-term memory (LSTM), bidirectional LSTM (BiLSTM), gated recurrent unit (GRU), and Bayesian nonparametric general regression (BNGR), were developed to predict P L . The reliability analysis confirmed the robustness of the results, with P L values consistent with those obtained by established methodologies. A mapping function relating the safety factor (SF) to the P L was developed using the cone penetration test (CPT) database. Performance evaluation using 15 statistical indices, alongside sensitivity and uncertainty analysis, demonstrates the relative significance of input parameters and prediction reliability. The GRU model outperformed other ML models in terms of overall performance. The BiLSTM model achieved the highest R 2 values of 0.976 in training, and the GRU model (0.961) in testing, with comparable root mean square error (RMSE) values of 0.046 and 0.065, respectively. Additionally, the BNGR model showed promising results in accuracy and model complexity with the lowest Akaike information criterion (AIC) value of 11.62. Williams plots were used to illustrate the models’ applicability domain, while sensitivity analysis underscores the significance of input parameters, with ψ emerging as the most influential parameter. This research provides a comprehensive framework for enhancing the accuracy and reliability of liquefaction evaluation in engineering and infrastructure design.