PSI - Issue 84

Pietro Giaretta et al. / Procedia Structural Integrity 84 (2026) 449–456

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These results indicate that the CSU formula, although widely used for predicting local scour at piers, systematically overestimates the scour depth at the 48-hour timescale observed in the present experiments. While this overestimation is conservative and therefore acceptable from a safety perspective, it may be attributed to two factors: the influence of the coefficient 4she , which is not applied in the previous formulation of the CSU equation, and the experimental duration, which in this study is limited to 48 hours

Fig. 4. (a) comparison between the scour depth obtained from the present study experiments and from the CSU equation in its original formulation and (b) from the present study experiments accounting for the temporal evolution (about 80% of equilibrium scour) and from the CSU equation by applying the coefficient 4 she When the Sheppard coefficient is calculated and included, the scour depth predicted by the CSU equation decreases by approximately 10% for the pier alone, while it results substantially unchanged when calculated for the pier foundation systems. The second factor relates to the time limitation inherent in laboratory experiments. For circular wide piers (i.e., piers with diameters much larger than the flow depth), after 48 hours the scour depth reaches roughly 80% of its asymptotic value (Giaretta, 2025). By analogy, elongated piers may also be considered wide due to their increased effective width with skew angle and the presence of the foundation. Therefore, it is reasonable to assume that the scour depth measured in the present study corresponds to approximately 80% of the equilibrium value. Accordingly, in Fig. 5 the scour depth predicted by the CSU equation is adjusted through the application of 4she , while the scour depths measured in the present study are divided by 0.8 to approximate their asymptotic values. Excluding the particular configuration in which no scour occurs, the results for all other pier-foundation systems are bounded by the 45° line and the +10% error, revealing a limited and appropriate overdesign. For the pier without a foundation, the CSU formula consistently underestimates scour depth, with errors falling around the –20%. An underestimation of this magnitude is unacceptable, as it may compromise the reliability of the predicted maximum scour depth. 4. Conclusions This study investigates the behaviour of local scour around elongated bridge piers supported by foundations, with particular attention to the effects of skew angle and foundation geometry. The analysis is based on controlled laboratory experiments developed under clear-water conditions. Initially, scour development is examined for an elongated pier at three skew angles and for a circular pier, all without foundations. Subsequently, elongated piers supported by rectangular foundations are analysed, considering two foundation sizes with the top aligned with the riverbed level, as well as a case in which the larger foundation protrudes 2 cm above the initial bed level. For all pier foundation configurations, three skew angles are investigated. Comparisons between circular and elongated piers without foundations show that, at short experimental durations (4 hours), the circular pier causes greater scour depth than the elongated pier aligned with the flow and the 15° skewed