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 11 entrance configurations with pre-calibrated HDS-5 coefficients. Each entrance type has calibrated coefficients K, M, c, Y (for inlet control) and K_e (entrance loss for outlet control).

Circular Culverts

Entrance Type	Ke	Description
Square Edge with Headwall	0.50	Standard headwall with square-edged entrance
Groove End with Headwall	0.20	Corrugated metal pipe with groove end in headwall
Groove End Projecting	0.20	Corrugated metal pipe projecting from fill
Beveled Edge	0.25	Entrance with beveled edges (33.7° or 45°)
Thin Wall Projecting	0.90	Thin-wall pipe projecting from embankment
Mitered to Slope	0.70	Pipe cut to match embankment slope

Box Culverts

Entrance Type	Ke	Description
Box Square Edge	0.50	Square-edged box with headwall
Box Groove End	0.20	Box with groove-end connection to headwall
Box Beveled Edge	0.25	Box with beveled entrance edges
Box Wingwall Flare 30°–75°	0.40	Box with wingwalls flared 30° to 75°
Box Wingwall Flare 90° or 15°	0.70	Box with wingwalls at 90° (parallel) or 15°

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 — fifth-order polynomial fit to FHWA nomographs
• S_R = slope reduction factor (entrance-type dependent; typically −0.5 for conventional entrances, +0.7 for mitered-to-slope)
• S₀ = barrel slope (ft/ft)
• D = barrel rise (diameter for circular, height for box)

Each of the 11 entrance types has a unique set of six polynomial coefficients (A–F) and a slope reduction factor S_R, sourced from HY-8 v7.7 Appendix A.

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 (empirical):

Box:

Road Overtopping

When headwater exceeds the road crest elevation, road overtopping flow is computed. This is a required input on every culvert element.

Parameter	Units	Description	Default
Road Crest Elevation	ft	Elevation of the road surface at the crossing	Required
Road Length	ft	Length of road perpendicular to flow (weir length)	Required
Road Width	ft	Width of road in flow direction	Required
Weir Coefficient	—	Broad-crested weir coefficient	2.6 (paved)

Overtopping discharge:

Where H = headwater elevation − road crest elevation.

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

Manual Flow Mode

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

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

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 11 types (see Entrance Types above)
Number of Barrels	—	Parallel identical barrels
Invert Elevation (inlet)	ft	Upstream invert
Invert Elevation (outlet)	ft	Downstream invert
Tailwater Condition	—	Free Outfall or Specified Elevation
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

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 — 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	Same polynomials (HY-8 v7.7 Appendix A coefficients)
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 (2005). HY-8: Culvert Hydraulic Analysis Program, v7.7. Federal Highway Administration.