PSI - Issue 84

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

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30°, the scour depth is slightly lower than that observed for the isolated pier. Maintaining the top of the foundation at the riverbed level, with the larger one (130 mm × 280 mm), no scour occurs when the pier is parallel to the flow, and in this configuration, the foundation completely protects the bed. This full protection is possible only when the foundation is perfectly aligned with the flow and the bed remains perfectly flat under clear-water conditions, without bedforms of contraction erosion that could temporarily expose the foundation and initiate local erosion. Once the pier is skewed to 15° or 30°, local scour develops again, and scour depths become larger than those at the pier alone, meaning the foundation is no longer beneficial and can even worsen conditions. When this larger foundation is raised 2 cm above the initial riverbed, scour occurs even for the parallel pier, and the resulting scour depth exceeds that of the isolated pier. This implies that if the foundation becomes exposed due to contraction or general scour, the system is highly vulnerable. At 15°, this configuration leads to the greatest scour ratio observed. At 30°, by contrast, the maximum scour depth is similar across all experiments, suggesting that at this skew angle the maximum scour depth in the experimented setup is governed primarily by the skew angle itself rather than the presence, size, or exposure of the foundation.

Fig. 3. Ratio between the scour depth at the pier-foundation system (ds) and that at the pier alone (ds,pier), as a function of the skew-angle and foundation geometry

The CSU formula (HEC-18) is among the most widely used approaches for predicting scour depth at skewed piers of complex geometry, including circular or elongated piers supported by foundations. This study compares the experimental results with the CSU prediction to evaluate its performance. It is important to note that the coefficient proposed by Sheppard 4 she , which considers the coarseness of the riverbed material respect to the pier width, is not applied in the original formulation considered here. Additionally, the scour depths obtained in the present study correspond to a duration of 48 hours. The influence of both aspects is examined later. Figure 4 presents the comparison between the dimensional scour depths measured in the experiments and those predicted by the CSU equation. The 45° line represents perfect agreement, while the dashed lines indicate ±10% and ±20% error bands. Overall, the CSU formula tends to overestimate the scour depth for most configurations tested in the present study, as evidenced by the majority of data points lying above the 45° line. This deviation becomes more pronounced as the pier geometry becomes more complex. For the elongated pier without a foundation, the predicted scour depths fall within the ±10% bounds, indicating a limited overestimation and a slight underestimation. When the small foundation is added (not exposed), the discrepancy generally increases falling along the +20% error line, with scour depths from the experiments clearly lower than those predicted by the CSU formulation. A more substantial divergence is observed for cases involving the large foundation. For the unexposed configuration, nearly all points lie well above the +20% envelope, showing that the CSU formula accounts for the increased scour induced by the larger near-bed obstruction in a stronger way than observed experimentally. A particular condition arises when the pier-foundation system is parallel to the flow direction. The difference is significant since in the present study no scour takes place, while the CSU formula estimation provide scour formation. When the large foundation is exposed, the overprediction generally follows the previous case behaviour, overestimating the scour above the +20% line in most of the cases.