Culvert Element

The Culvert element analyzes the hydraulic capacity of culvert crossings using the FHWA HDS-5 (Hydraulic Design of Highway Culverts) methodology. It evaluates both inlet control and outlet control conditions and reports the governing headwater elevation, capacity, and road overtopping flow.

When to Use

• Evaluating existing or proposed culvert crossings
• Sizing culverts for roadway crossings
• Determining headwater elevation and adequacy for design storms
• Analyzing road overtopping conditions

Barrel Shapes

Two barrel shapes are supported:

• Circular: Defined by diameter (D). Area = π/4 × D². Hydraulic radius R = D/4 (flowing full).
• Box (Rectangular): Defined by width (W) and height (H). Area = W × H. Hydraulic radius R = (W×H) / (2×(W+H)).

Entrance Types

HydraLink includes 15 entrance configurations. Each entrance type has inlet control polynomial coefficients calibrated to FHWA HY-8 v7.7 output and an entrance loss coefficient K_e (HDS-5 Table C.2) for outlet control.

Circular Culverts

Entrance Type	Ke	Description
Concrete - Square Edge w/ Headwall	0.50	Standard headwall with square-edged entrance
Concrete - Groove End w/ Headwall	0.20	Grooved (bell) end set in a headwall
Concrete - Groove End Projecting	0.20	Grooved (bell) end projecting from fill
Concrete - Beveled Edge (1:1)	0.20	Entrance with 45° beveled edges
Concrete - Beveled Edge (1.5:1)	0.20	Entrance with 33.7° beveled edges
Concrete - Mitered to Slope	0.70	Concrete pipe cut to match embankment slope
CMP - Headwall	0.50	Corrugated metal pipe with headwall
CMP - Thin Wall Projecting	0.90	Thin-wall pipe projecting from embankment
CMP - Mitered to Slope	0.70	Metal pipe cut to match embankment slope

Box Culverts

Entrance Type	Ke	Description
Box - Square Edge	0.50	Square-edged box with 90° headwall
Box - Beveled Edge (1.5:1)	0.20	Box with 33.7° beveled entrance edges
Box - Beveled Edge (1:1)	0.20	Box with 45° beveled entrance edges
Box - Wingwall 30-75	0.40	Box with wingwalls flared 30° to 75°
Box - Wingwall 90/15	0.50	Box with wingwalls at 90° or flared 15°, square-edged crown
Box - Wingwall 0 (Side Ext.)	0.70	Box with parallel wingwalls (extension of sides)

Inlet vs. Outlet Control

Both inlet control and outlet control headwater depths are computed independently; the higher value governs. This follows the HDS-5 dual-analysis approach used by FHWA HY-8.

Inlet Control (HY-8 Polynomial Method)

Inlet control headwater is computed using the FHWA HY-8 fifth-order polynomial equations rather than the traditional HDS-5 K/M two-equation approach. This provides a single continuous curve that smoothly transitions between unsubmerged and submerged conditions without requiring regime interpolation.

Flow parameter:

Headwater depth:

Where:

• poly(X) = A + BX + CX² + DX³ + EX⁴ + FX⁵, a fifth-order polynomial fit to FHWA nomographs
• S_R = slope factor (entrance-type dependent: +0.5 for conventional entrances, −0.7 for mitered-to-slope, so a mitered inlet gains headwater as the barrel steepens)
• S₀ = barrel slope (ft/ft)
• D = barrel rise (diameter for circular, height for box)

Each of the 15 entrance types carries a set of six polynomial coefficients (A–F) and a slope reduction factor S_R, calibrated against HY-8 v7.7. A few entrance pairs share one curve because HY-8 itself uses the same curve for both (for example, a square-edged 90° headwall and 90°/15° wingwalls on a box). Above each polynomial's fitted range, headwater follows HY-8's submerged-orifice continuation so results remain valid at deeply submerged inlets.

Outlet Control (Backwater Analysis)

Outlet control uses a direct-step backwater analysis to compute the water surface profile through the barrel, rather than the simplified single-equation HDS-5 energy method alone. The approach adapts to flow regime:

Mild Slopes (normal depth > critical depth)

A Gradually Varied Flow (GVF) M1 profile is computed from the outlet upstream using the direct-step method. The starting depth at the outlet is max(TW, d_c). If the profile reaches the barrel crown, it transitions to full-pipe pressure flow for the remaining upstream length:

Steep Slopes with TW > d_c

Both an S2 (supercritical) profile from the inlet and an S1 (subcritical) profile from the outlet are computed. A hydraulic jump forms where the sequent depth of the S2 profile exceeds the S1 depth. The inlet headwater is determined from whichever profile governs at the inlet.

Steep Slopes with TW ≤ d_c

Supercritical flow persists throughout the barrel (S2n profile). The simplified HDS-5 energy equation is used:

Where H = (1 + K_e + 29n²L/R^4/3) × V²/(2g) and h_o = max(TW, d_c).

Full-Pipe (Submerged Outlet)

When TW ≥ D (outlet submerged), the full-pipe energy equation is used for the entire barrel length:

Critical Depth

Circular: solved iteratively from the critical-flow condition using the exact partial-circle geometry:

Box:

Road Overtopping

When headwater exceeds the road crest elevation, road overtopping flow is computed using FHWA HDS-5's Figure 3.11 discharge-coefficient charts. The discharge coefficient is read from the head over the crest, the crest width, and the road surface type, with a submergence reduction applied when the downstream water surface rises over the crest.

Parameter	Units	Description
Crest Elevation	ft	Elevation of the road surface at the crossing
Weir Crest Length L	ft	Length of road crest along the crossing (weir length)
Crest Width Lr	ft	Width of the roadway in the flow direction
DS Water Surface	ft	Optional downstream water surface elevation, used for submergence reduction
Surface	—	Paved or Gravel — HDS-5 publishes separate coefficient curves for each
Crest Shape	—	Level, or Sag Vertical Curve when the road dips over the crossing

Total flow = culvert flow + overtopping flow (when headwater > crest elevation).

Manual Flow Mode

The culvert can accept manual flow inputs instead of computing from an upstream hydrograph:

• Enable “Enable Manual Flows”
• Enter up to 2 manual flows with custom labels (e.g., “25-yr Pre-Dev”, “100-yr Post-Dev”)

In hydrograph mode, the Analyze Storms checklist picks which storms the culvert is evaluated for; it is disabled while manual flows are on.

Input Parameters

Parameter	Units	Description
Barrel Shape	—	Circular or Box
Diameter (circular)	ft	Pipe diameter
Width (box)	ft	Box culvert span
Height (box)	ft	Box culvert rise
Length	ft	Barrel length
Slope	%	Barrel slope (max 55% per HY-8)
Manning's n	—	Barrel roughness
Entrance Type	—	One of 15 types (see Entrance Types above)
Number of Barrels	—	Parallel identical barrels
Flowline Elev	ft	Barrel invert at the inlet; the outlet invert follows from slope and length
Tailwater Condition	—	Free Outfall, Specified Elevation, or Downstream Channel (the normal depth of the channel named in Drains To)
Tailwater Elevation	ft	Downstream water surface (if specified)

Results

Output	Units	Description
Headwater Elevation	ft	Water surface elevation upstream of culvert
HW/D Ratio	—	Headwater depth / barrel height (key adequacy metric)
Control Type	—	Inlet Control or Outlet Control
Culvert Discharge	cfs	Flow through the barrel(s)
Overtopping Discharge	cfs	Flow over the road (if applicable)
Total Discharge	cfs	Culvert + overtopping
Outlet Velocity	ft/s	Exit velocity for erosion assessment
Status	—	PASSES, HIGH HW/D RATIO (above 1.5), or ROAD OVERTOPPED

HydraLink flags an HW/D ratio above 1.5 and any headwater over the road crest in the results verdict; tighter local limits are the engineer's call.

The Culvert Results dialog presents the same run as a profile, a rating curve, and a summary table.

Tips & Best Practices

• HW/D ≤ 1.0 is generally considered adequate for most jurisdictions.
• Some jurisdictions allow HW/D up to 1.2 or 1.5; check local standards.
• If headwater exceeds the road crest, the culvert is overtopping. Evaluate whether this is acceptable for the design storm.
• Use a lower Manning's n for concrete (0.012–0.013) and higher for corrugated metal (0.024–0.027).
• Multiple barrels are modeled as parallel identical barrels sharing the total flow equally.
• Always verify that the road overtopping parameters are set correctly, since overtopping flow can be a significant portion of total flow during extreme events.
• The entrance type significantly affects inlet control capacity: beveled and groove-end entrances provide substantially better performance than square-edge.

HY-8 Comparison

HydraLink's culvert engine has been compared against FHWA HY-8 v7.7 across a range of flow conditions, barrel sizes, entrance types, and slope regimes. The following summarizes the key alignments.

Methodology Alignment

Feature	HY-8 Approach	HydraLink Implementation
Inlet control	Fifth-order polynomial per entrance type	Fifth-order polynomials calibrated to HY-8 v7.7 program output
Outlet control	Direct-step backwater with crown transition	Direct-step backwater with crown transition detection
Slope classification	Compare yn to dc	Same (steep when yn < dc)
Steep slope outlet control	S2/S1 profiles with hydraulic jump detection	Same dual-profile approach with sequent depth check
Maximum slope	55% (0.55 ft/ft)	55% enforced by validation

References

• FHWA (2012). Hydraulic Design of Highway Culverts, HDS-5, Third Edition.
• FHWA. HY-8: Culvert Hydraulic Analysis Program, v7.7. Federal Highway Administration.