Predicting Local Scour at Bridge Piers

When water flows around a bridge pier, vortices form that can remove sediment from the riverbed. This erosion, known as local scour, creates a depression that can undermine the pier foundation if it becomes too deep. Designers evaluate scour during bridge planning to ensure foundations extend below the expected erosion depth. The widely used HEC‑18 guideline from the U.S. Federal Highway Administration provides an empirical equation for estimating local scour depth at piers in sandy beds. This calculator implements a simplified version of that equation.

The HEC‑18 pier scour equation for clear-water conditions is expressed as $$y_s=2.0K{1}_{}K{2}_{}K{3}_{}a{Fr}^{0.43}{\frac{a}{y_1}}^{}0.65$$ where $y_s$ is the predicted scour depth below the bed, a is the effective pier width, $Fr$ is the Froude number of the approaching flow, and y₁ is the undisturbed flow depth. The correction factors K₁, K₂, and K₃ account for pier shape, flow angle of attack, and bed conditions respectively. For most design situations, the bed armoring factor K₄ is taken as 1.0 and omitted in this simplified form.

The Froude number represents the ratio of inertial to gravitational forces in the flow and is defined by $Fr=\frac{V}{\sqrt{g{y}_1}}$, where V is the mean approach velocity and g is gravitational acceleration, taken as 9.81 m/s². Flows with higher Froude numbers generate stronger vortices and therefore deeper scour holes. The ratio $\frac{a}{y_1}$ captures the relative size of the pier to the flow depth; larger piers relative to depth cause more severe contraction and flow acceleration, increasing scour potential.

Each correction factor reflects physical characteristics observed in experiments. The shape factor K₁ adjusts for the form of the pier nose. Sharp-nosed piers produce smaller separation zones and thus lower scour depths, leading to values around 1.0. Square or cylindrical piers generate larger vortices and may use K₁ between 1.1 and 1.5. The angle factor K₂ accounts for flow attacking the pier at an oblique angle; as the angle increases, effective width increases and scour deepens. The bed condition factor K₃ reflects the influence of bed forms or debris. Clear beds without significant scour-inducing obstructions may use 1.0, while beds with debris or ice can warrant higher values around 1.1 to 1.3.

The table below provides typical factor values for quick reference.

Parameter	Condition	Factor
K1	Sharp nose	1.0
K1	Round nose	1.1
K1	Square nose	1.5
K2	0° attack	1.0
K2	15° attack	1.1
K3	Clean bed	1.0
K3	Debris or ice	1.1–1.3

To demonstrate the calculation, consider a round pier 1.5 m wide in 3 m of water with an approach velocity of 2 m/s. Assuming a sharp nose (K₁ = 1.1), flow aligned with the pier (K₂ = 1.0), and minor debris (K₃ = 1.1), the Froude number is $Fr=\frac{2}{\sqrt{9.81\times 3}}=0.37$. Substituting into the HEC‑18 equation yields $y_s=2.0\times 1.1\times 1.0\times 1.1\times 1.5\times 0.37{}^{0.43}\times \left(\frac{1.5}{3}\right){}^{0.65}=1.34\backslash ,m$. The total depth from the water surface to the bottom of the scour hole would then be 3 m + 1.34 m = 4.34 m.

Understanding scour mechanics helps bridge engineers design foundations that resist erosion. If the predicted scour exceeds the depth of the footing, countermeasures such as riprap aprons, guide banks, or pier modifications may be necessary. Monitoring scour during floods with sonar devices or visual inspections can validate design assumptions and identify when maintenance is needed.

It is important to note that the HEC‑18 equation is empirical and based on laboratory studies under controlled conditions. Real rivers may exhibit complex sediment transport, armoring, or cohesive soils that deviate from the sandy-bed assumption. In cohesive soils, scour develops more slowly and may require different empirical relationships. Designers often apply a factor of safety or perform sensitivity analyses to account for these uncertainties.

Additionally, local scour combines with general contraction scour and long-term channel degradation. The total scour depth at a pier is the sum of these components. This calculator addresses only the local scour component, providing a starting point for evaluating foundation depth. Comprehensive bridge design should consider all scour mechanisms in accordance with hydraulic engineering circulars and local guidelines.

By experimenting with the input factors, users can see how changes in flow conditions or pier geometry influence scour depth. For instance, doubling the approach velocity significantly increases the Froude number and thus the scour depth, underscoring the nonlinear nature of the equation. Similarly, reducing pier width or orienting the bridge so that flow strikes the pier head-on can mitigate scour.

In summary, predicting scour depth is essential for the safe design of bridge foundations. The HEC‑18 method offers a practical balance between theoretical complexity and empirical observation. This calculator encapsulates that method in an accessible form, helping engineers, students, and inspectors evaluate scour risk and appreciate the hydraulic forces acting on bridge piers.