Local scour at a single pier by the Colorado State University equation: ys/y1 = 2.0 K1K2K3(a/y1)0.65Fr0.43. Local pier scour only — contraction scour and long-term degradation are separate components of the total.
Take y1 and V1 directly upstream of the pier from the design-flood hydraulic model (typically Q100 for design, Q500 for the check flood).
When θ > 5° the nose-shape factor drops out (K1 = 1.0) and the skew factor K2 takes over, with L/a capped at 12.
| K1 nose shape | – |
| K2 attack angle | – |
| K3 bed condition | – |
| Physical limit (2.4a Fr≤0.8 / 3.0a) | – |
Scour is the single most common cause of bridge failure in floods, which is why the check flood exists: run Q100 for design and Q500 for stability, and remember the CSU number here is only the local component — total design scour adds contraction scour and long-term degradation from the same hydraulic study. The equation is deliberately conservative in cohesive soils and weak rock; in the Gulf, where wadis flow twice a decade over cemented material, an HEC-18 number taken at face value can bury a pile cap needlessly deep — that is what the rock-scour and cohesive procedures of HEC-18 chapters 6–7 are for. Two things that quietly dominate the answer: attack angle (a 20° skew on a long wall pier can double ys through K2 alone — align piers with the flood flow, not the low-flow channel) and debris rafts, which effectively widen a. Countermeasures, riprap sizing and monitoring live in HEC-23.