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.
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.
The Federal Highway Administration's Evaluating Scour at Bridges (HEC-18) gives the standard method for local scour at bridge piers in the United States and is used as a reference well beyond it. Local pier scour is estimated with the Colorado State University (CSU) equation:
| Symbol | Meaning | Typical values |
|---|---|---|
| ys | local scour depth below the ambient bed | result, m |
| y1, V1 | flow depth and mean velocity directly upstream of the pier | from the hydraulic model for the design flood |
| a | pier width normal to the flow (projected width if skewed) | m |
| K1 | pier nose shape | square 1.1 · round / circular 1.0 · sharp 0.9 · pile group 1.0 |
| K2 | angle of attack θ, pier length L | (cos θ + (L/a) sin θ)0.65; 1.0 when θ ≤ 5° |
| K3 | bed condition | clear-water / plane bed 1.1 · small–medium dunes 1.1–1.2 · large dunes 1.3 |
Two limits close the calculation: for wide piers HEC-18 caps ys at 2.4 a when Fr1 ≤ 0.8 and at 3.0 a when Fr1 > 0.8, and the equation applies to non-cohesive beds — cohesive soils and erodible rock use the separate procedures of HEC-18 chapters 6 and 7.
Round-nose pier, a = 1.5 m, aligned with the flow, plane bed; design flood y1 = 3.0 m, V1 = 2.5 m/s. Fr1 = 2.5 / √(9.81 × 3.0) = 0.46. Then ys = 2.0 × 1.0 × 1.0 × 1.1 × 3.0 × (0.5)0.65 × 0.460.43 = 2.0 × 1.1 × 3.0 × 0.637 × 0.717 ≈ 3.0 m, below the wide-pier cap of 2.4 a = 3.6 m. Add contraction scour and long-term degradation from the same hydraulic study to obtain the total scour, then set the pile cap or footing below it (HEC-18 puts the top of the footing below the total scour line and checks the piles for the exposed length).
Foundations are designed for the 100-year flood or the overtopping flood if that produces the worse scour, and checked for stability under the 500-year flood with reduced factors of safety. Countermeasures — riprap sizing, collars, monitoring — are covered in HEC-23, and the hydraulic inputs (y1, V1) should come from a one- or two-dimensional model of the crossing, not from a normal-depth estimate, when the bridge constricts the floodplain.
HEC-18 (FHWA Hydraulic Engineering Circular 18) uses the Colorado State University equation: ys / y1 = 2.0 K1 K2 K3 (a / y1)^0.65 Fr1^0.43, where ys is the local scour depth, y1 the approach flow depth, a the pier width, Fr1 the approach Froude number and K1, K2, K3 the corrections for pier nose shape, angle of attack and bed condition.
Is HEC-18 local scour the total scour depth?No. Total scour at a pier is the sum of long-term degradation, contraction scour and local pier scour. This calculator gives the local component only; the other two come from the hydraulic study of the crossing.
Which flood do I use for scour design?HEC-18 designs the foundation for the 100-year flood (or the overtopping flood if smaller) and checks stability under the 500-year check flood, with reduced safety factors for the check flood.
Why does the angle of attack matter so much?K2 = (cos θ + (L/a) sin θ)^0.65 grows with the pier length-to-width ratio. A 20° skew on a long wall pier can roughly double the local scour, which is why piers are aligned with the flood flow rather than the low-flow channel.
The CSU equation above gives only the local scour at the pier. The foundation is designed for the total scour, which HEC-18 builds from three parts measured from the same reference bed:
Where the bridge narrows the flow (approach embankments, a narrower channel, piers taking up width), the bed lowers across the opening. First decide whether the approach flow moves the bed material: compare the mean approach velocity V with the critical velocity for the median grain size,
Live-bed (V > Vc, sediment arriving from upstream), modified Laursen equation:
with k1 = 0.59, 0.64 or 0.69 as the ratio of shear velocity to fall velocity of the bed material rises past 0.5 and 2 (mostly bed load, some suspended load, mostly suspended load).
Clear-water (V < Vc, no supply from upstream, typical of set-back overbank areas):
Here y1, y2 are flow depths upstream and in the contracted section, y0 the existing depth there, Q the discharges and W the bottom widths (net of pier widths in the bridge opening). Take the hydraulic values from a one- or two-dimensional model of the crossing for the design flood.
HEC-18 5th edition (FHWA-HIF-12-003, April 2012) superseded the 2001 edition. It added alternative pier scour procedures, including the Florida DOT method that accounts for sediment size and very wide piers, a new approach for coarse bed material, new sections on scour in cohesive soils and erodible rock, contraction scour in cohesive materials, revised pressure-flow (deck overtopping) guidance, and a chapter on geotechnical considerations. The old term "general scour" was dropped.
Protection of existing scour-critical bridges (riprap, partially grouted riprap, guide banks, monitoring) is designed with HEC-23. Sources: FHWA, Evaluating Scour at Bridges, 5th edition (HEC-18) and the Michigan Tech bridge scour workshop notes. See also open caisson foundations for deep-scour rivers and the failure library for scour collapses.