What this calculator does
A culvert usually does not fail by crushing or by overtopping. It fails when the bed under it is washed away. The water accelerates into the barrel to get through, and that acceleration is what digs the hole — most often at the inlet, and sometimes at the outlet and around the abutments. This tool sizes the hole, because that is the depth the bed protection has to cover.
How to use it
- Enter the design discharge and the barrel width and height — capacity itself is what the culvert capacity calculator is for.
- Enter the headwater depth above the inlet invert. The opening is limited to whichever is smaller, the headwater or the barrel height, because a part-full barrel does not scour at full height.
- Enter the bed grain size, its specific gravity and the critical scour parameter for that material. No bed database is held here.
- Read the local hole depth and the ratio to the barrel width — the ratio is what tells you whether the protection is workable at all.
Governing formula
u* = C_d · v · √g → τ_c = θ_c · ρ_w · (s−1) · g · D50 → y_s = 0.325 · (y_t · D50 / τ_c) Where:
-
C_d= Inlet discharge coefficient -
v= Barrel velocity [m/s] -
θ_c= Critical scour parameter -
s= Sediment specific gravity -
D50= Median grain size [m] -
y_t= Opening height at the inlet [m]
Derived Equations:
τ_local = ρ_w · u*² τ* = u*² / ((s−1)gD50) Worked example — 1.5 m × 1.2 m barrel carrying 3 m³/s over sand
The figures below were produced by running this page's own engine with the example inputs (Design discharge (m³/s), Barrel width (m), Barrel height (m), Headwater depth above invert (m), Median grain size (D50) (m), Sediment specific gravity (–), Critical scour parameter (–), Inlet discharge coefficient (–), Manning's n (–)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Local scour depth at the inlet | 0 m |
|---|---|
| Bed is mobile at this flow | — |
| Depth as a multiple of barrel width | 0 – |
| Live-bed alternative (NOT added) | 0 m |
| Local bed shear at the inlet | 31784 Pa |
| Critical shear for the material | 4.86 Pa |
| Applied ÷ critical shear | 6545 – |
| Barrel velocity | 2 m/s |
| What this means | Scour reaches about 0.00 m below the invert (0.00 × barrel width), against a critical shear 6545.45 × the applied shear. The inlet is the location to protect; bed protection extending at least that far upstream and downstream of the inlet is the usual response. A live-bed movement of roughly 0.00 m is also possible downstream if the material can be replenished along the reach — this is an alternative behaviour, not an addition to the 0.00 m hole. |
- The headwater of 1.0 m limits the opening, so the flow area is 1.5 m² and the velocity is 2 m/s.
- The inlet shear velocity is 0.9 × 2 × √9.81 ≈ 5.64 m/s, giving about 31,800 Pa of local shear — far above the critical shear of 0.06 · 1000 · 1.65 · 9.81 · 0.005 ≈ 4.9 Pa.
- So the bed is mobile and the local hole comes to roughly 0.33 m below the invert, which is why inlet protection is not optional at this flow.
Assumptions & limitations
Engineering calculation. Local scour at the culvert inlet from the HEC-18 inlet shear relation, with the live-bed alternative reported separately rather than added to it.
- The scour coefficient, the critical scour parameter and the grain size are USER inputs. This tool holds no scour-coefficient table, no bed-material database and reads nothing from any code.
- This predicts LOCAL scour at the culvert. Contraction scour at the structure, bend scour in the approach, and general bed degradation over the reach are NOT included and are usually larger.
- The live-bed figure is an ALTERNATIVE to the local hole, not an addition to it. Summing the two would produce a depth neither mechanism actually produces.
- Debris, failure of the inlet protection during construction, and post-flood conditions when the bed has already been disturbed are not modelled.
- No code check is applied. Whether the predicted depth is acceptable at this site is a design decision that depends on consequences, not only on this number.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- US FHWA HEC-18 — Evaluating Scour at Culverts, as the framework behind the local scour relation.
- HDS-5 — culvert design.