Reliability-based state parameter liquefaction probability prediction using soft computing techniques

The state parameter (ѱ) accounts for both relative density and effective stress, which influence the cyclic stress or liquefaction characteristic of the soil significantly. This study presents a ѱ-based probabilistic liquefaction evaluation method using six soft computing (SC) techniques. The liquefaction probability of failure (P_L) is calculated using the first-order second moment (FOSM) method based on the cone penetration test (CPT) database. Then, six SC techniques, such as Gaussian process regression (GPR), relevance vector machine (RVM), functional network (FN), genetic programming (GP), minimax probability machine regression (MPMR) and multivariate adaptive regression splines (MARS), are used to predict P_L. The performance of these models is examined using nine statistical indices. Additionally, plots such as regression plots, Taylor diagrams, error matrix and rank analysis are shown to assess the SC model's performance. Finally, sensitivity analysis is performed using the cosine amplitude method (CAM) to assess the influence of input parameters on output. The current study demonstrates that SC models based on state parameter predict P_L effectively. RVM and MPMR models closely follow the GPR model in terms of performance, which is superior to the other models. Notably, two equations are generated using GP and MARS models to predict P_L. The results of the sensitivity analysis reveal the magnitude of earthquake (M_w) as the most sensitive parameter. The outcomes of this research will offer risk evaluations for geotechnical engineering designs and expand the use of state parameter-based SC models in liquefaction analysis.