Machine learning approaches for bridge pier clear-water scour and reliability: a comparative study

Local scour at bridge piers remains a leading cause of structural failure, yet design practice continues to rely on deterministic equations that return a single equilibrium depth and no measure of the confidence attached to it. This study couples machine-learning prediction with probabilistic reliability analysis for clear-water scour at cylindrical piers. Two models, a support vector regression optimised by the dung beetle algorithm (DBO-SVR) and a gradient boosting machine (GBM), were trained on 153 fully documented laboratory records to predict the relative equilibrium scour depth, using five dimensionless predictors. DBO-SVR generalised well, with coefficients of determination of 0.7937 in training and 0.7791 in testing, whereas GBM reproduced its training partition almost exactly and retained little of that accuracy out of sample, falling from 0.9995 to 0.6245; over twenty-five independent random splits the mean test values were 0.744 and 0.645 respectively. Exact Shapley attribution identified the flow intensity ratio as the dominant predictor, accounting for 64 per cent of the explained test variance in DBO-SVR and 87 per cent in GBM and confirming the physical consistency of both models. The predictive distributions were propagated through a Monte Carlo simulation of 200,000 samples in which residuals were resampled from their empirical distribution rather than assumed Normal. Under a capacity-based limit state, in which the normalised embedment capacity is treated as a lognormal variable of mean 1.60 and coefficient of variation 0.20, the reliability index reaches only 1.43 for DBO-SVR and 1.30 for GBM, far below the target levels of the AASHTO, ISO, JCSS and FHWA standards, and the ordering is preserved across every capacity dispersion between 0.10 and 0.35. Resampling the residuals from a fitted Normal rather than from their empirical distribution shifted the reliability index by up to 0.24 at the thresholds the simulation can resolve, in a direction that was not uniform across models and thresholds. A time-dependent analysis based on the Melville and Chiew formulation indicates that the AASHTO Extreme Event target is breached at a normalised time of 0.0092 for DBO-SVR and 0.0061 for GBM, roughly forty and twenty-six minutes into a 72-hour flood, and that the least demanding of the four levels is breached within six hours. The study is restricted to clear-water conditions and to laboratory-scale data; the models are offered as decision-support tools that require recalibration against prototype measurements before field application, and neither should be deployed at its conditional mean, since both under-predict scour demand in a fraction of extreme configurations.