Probabilistic Response Analysis of Laterally Loaded Piles Under Parametric Uncertainty Using Monte Carlo Simulation and Hybrid Metaheuristic Algorithms

In the present study, the probabilistic response behavior of a laterally loaded free-head long vertical pile was investigated using an analytical closed-form solution developed within the Winkler beam-on-elastic-foundation framework. Two structural property parameters, undrained shear strength and elastic modulus were lognormally modelled as random variables and four distinct levels of uncertainty. By systematically varying the soil, Monte Carlo Simulations technique was used (1000 samples/case). It is observed that reliability decreases as the soil variability increases. With increase in coefficient of variations from 10% to 25%, maximum deflection-based probability of failure increased from 0% to 2.90% and reliability decreased from 3.09 to 1.90. To further boost prediction ability, Extreme Gradient Boosting (XGB) combined with three metaheuristics: Marine Predators Algorithm (XGB-MPA), Genetic Algorithm (XGB-GA), and the Artificial Gorilla Troops Optimizer (XGB-GTO) was developed. The model evaluation shows that the hierarchy of model performance was as follows: XGB-MPA > XGB-GA > XGB-GTO, in which XGB-MPA having the highest trailing score of 29.8, which also signifies the lowest prediction errors and the best generalization capability. Lastly, SHAP analysis showed soil stiffness is the primary predictor (+ 0.08), with higher values consistently reducing lateral deflection.