Empirical correlations are extensively employed in geotechnical engineering for their practical simplicity, yet their deterministic nature and neglect of inherent uncertainties often constrain their predictive reliability. This study proposes a joint hierarchical Bayesian model (HBM) that reconstructs three widely used correlations between undrained shear strength (su) and piezocone cone penetration test (CPTU) parameters: (qt−σv)/σv′, (qt−u2)/σv′, and (u2−u0)/σv′. By integrating global and site-specific datasets, the HBM improves generalization while maintaining site-level accuracy, particularly in scenarios with limited data. Compared with conventional local and global Bayesian models (LBM and GBM), the HBM demonstrates better model performance and reduced uncertainty. To combine predictions from different empirical models, an adaptive strategy based on the adaptive moment estimation (ADAM) algorithm is proposed to learn optimal model weights. This data-driven method provides adaptive weighting of model outputs as an alternative to traditional Bayesian model averaging (BMA). Validation results show that the ADAM-based approach reduces root-mean-square error (RMSE) by 7%–10%, mean absolute error (MAE) by 6%–10%, and continuous ranked probability score (CRPS) by 2%–5% compared with BMA. Overall, the integration of HBM with adaptive weighting offers a robust and effective framework for enhancing empirical predictions in geotechnical engineering.
Xiong et al. (Mon,) studied this question.