Hydraulic Engineering Assessment of Empirical Equations for Predicting Peak Discharge in Small Earthen Pond Failures

This study evaluates, through a comparative statistical analysis, the predictive performance of empirical equations for estimating peak discharge during earthen pond failures, using a curated dataset of 78 reliable historical failure cases covering the documented period of available records, selected from an initial international database of 1893 cases. The analysis focuses on reservoirs with storage volumes below 6 hm3, a range that remains insufficiently addressed by existing breach-outflow models despite its importance for hydraulic, mining, and agricultural infrastructures. The procedure established a key comparative evaluation between equations to define the fit volume intervals. The results indicate that predictive uncertainty and error dispersion increase significantly as reservoir volume decreases, with a critical high-variability interval identified between 3.5 and 6 hm3 for both overtopping and piping failure mechanisms. A key finding is that predictive performance is strongly dependent on stored volume segmentation, as no single empirical formulation dominates the entire volume range; instead, 10 of 63 different equations achieve optimal accuracy within 5 specific storage intervals considering the RMSE, MAD and MAE error values. These findings emphasize the necessity of volume-dependent equation selection, based on comparative performance evaluation, and the development of specialized predictive models for small earthen reservoirs to ensure reliable risk assessment.