Evaluate a proposed channel lining using the FHWA HEC-15 normal-depth and maximum-tractive-force procedure. The calculator reconciles the design discharge with the channel hydraulics before checking bottom, side-slope, and optional bend shear.
Lining Property Guidance
| Lining Type | n | Vmax (fps) | taumax (psf) |
|---|---|---|---|
| Bare Soil | 0.025 | 2 | 0.02 |
| Grass | Varies | 4 | Varies |
| Riprap | Varies | 14 | Varies |
| Gabion | Varies | 15 | Varies |
| Concrete | 0.015 | 20 | 10 |
Grass Retardance Classes (HEC-15)
| Class | Height | Condition |
|---|---|---|
| A | 36 inches | SCS retardance class A |
| B | 24 inches | SCS retardance class B |
| C | 8 inches | SCS retardance class C |
| D | 4 inches | SCS retardance class D |
| E | 1.6 inches | SCS retardance class E |
Ready to Calculate
Select lining type and enter channel parameters to check adequacy.
For educational purposes only. Not a substitute for professional engineering judgment.
How the HEC-15 calculation works
1. Solve normal depth from the design discharge. The entered depth is an initial estimate. At each iteration the calculator determines area, wetted perimeter, hydraulic radius, lining roughness, and Manning capacity:
- A = (B + Zd)d
- P = B + 2d√(1 + Z2)
- R = A/P
- Q = (k/n)AR2/3S01/2
Iteration continues to a tighter numerical tolerance than the five-percent hand-calculation stopping criterion in HEC-15. The reported velocity is V = Q/A at the solved depth.
2. Recompute material-dependent roughness. Grass Manning roughness changes with applied mean shear according to HEC-15 Equation 4.2, n = αCnτo-0.4. Riprap and gabion roughness changes with relative submergence and uses the HEC-15 Blodgett or Bathurst relationship. These values are recalculated as depth changes.
3. Calculate the two shear measures for their proper purposes.
- Mean boundary shear: τo = γRS0, used by material resistance equations.
- Maximum bottom shear: τd = γdS0, used for the HEC-15 stability check.
A supplied bend factor Kb increases the critical applied shear. For a straight channel, Kb = 1.0.
4. Check the channel sides.
- τs = K1τd
- K1 follows the HEC-15 Equation 3.4 piecewise relationship with side slope Z.
- Riprap and gabion resistance on the bank is additionally adjusted by K2 for the bank angle and rock angle of repose.
5. Apply the safety factor. The lining is acceptable when the permissible value is at least the required safety factor times the governing applied value. The results report both the available factor of safety and the required factor.
Material models used
HEC-15 flexible-lining properties are hydraulic-condition dependent. Values labeled as material inputs should come from site testing, an agency specification, or manufacturer performance data for final design.
| Lining | Hydraulic resistance | Stability resistance |
|---|---|---|
| Vegetation | Dynamic n from HEC-15 Equations 4.1 and 4.2 | Vegetation/soil permissible shear from Equation 4.7 |
| Riprap, cobble, or gravel | Blodgett Equation 6.1 or Bathurst Equations 6.2-6.6 | Shields-based permissible shear, Equation 6.7 |
| Gabion mattress | Rock-fill D50 using the Chapter 6 roughness relations | Larger of Equations 7.1 and 7.2 |
| Bare soil | Selected soil roughness | Selected soil permissible shear |
| Rigid or tested manufactured lining | Specified or reference Manning n | Specified or reference permissible shear |
Grass roughness presets
HEC-15 Table 4.4 supplies Cn, not a constant Manning n. The calculator uses Cn with mean shear to calculate the final Manning n during the depth iteration.
| SCS retardance class | Reference stem height | Cn |
|---|---|---|
| A | 36 in | 0.605 |
| B | 24 in | 0.418 |
| C | 8.0 in | 0.220 |
| D | 4.0 in | 0.147 |
| E | 1.6 in | 0.093 |
Published HEC-15 check
The HEC-15 customary-unit grass example uses Q = 17.5 cfs, B = 3.0 ft, Z = 3, S0 = 0.03, a 0.25 ft maintained good sod stand, and an initial trial depth of 1.0 ft.
- Published converged depth: 0.70 ft
- Published final Manning n: 0.032
- Maximum bottom shear: 1.31 lb/ft2
- Vegetation/soil permissible shear: 2.7 lb/ft2
- Conclusion at SF = 1.0: acceptable
The site solves to a tighter discharge tolerance than the rounded hand iteration while reproducing the published values at their stated precision.
Frequently asked questions
What is the difference between the permissible-velocity and tractive-force methods?
The permissible-velocity method compares mean channel velocity with an empirical velocity limit. The FHWA HEC-15 tractive-force method first solves normal depth for the design discharge, then compares maximum applied shear with the lining resistance and required safety factor. HEC-15 generally favors the shear method for flexible linings because it accounts directly for depth and slope.
Does the calculator use the flow depth I enter as the final design depth?
No. The entered value is the initial trial depth required by the HEC-15 iteration. The calculator repeatedly evaluates channel geometry, Manning roughness, and discharge until the computed normal-flow capacity equals the design discharge. Results use that solved design depth, not the initial estimate.
Which shear stress is used for the lining stability check?
The stability check uses HEC-15 maximum bottom shear, tau_d = gamma*d*S0, where d is the solved maximum flow depth. Mean boundary shear, tau_o = gamma*R*S0, is still calculated where HEC-15 needs it to determine flow resistance, including the grass Manning n relation, but it is not substituted for maximum shear in the adequacy check.
How are grass roughness and permissible shear determined?
Grass roughness is not treated as a single constant. The calculator obtains the HEC-15 vegetation coefficient Cn from maintained height and condition, then recomputes Manning n from n = alpha*Cn*tau_o^-0.4 during the normal-depth solution. Grass permissible shear combines the underlying-soil resistance, vegetation cover factor, soil grain roughness, and final Manning n using HEC-15 Equation 4.7.
How are channel side slopes checked?
Maximum side shear is tau_s = K1*tau_d. HEC-15 Equation 3.4 defines K1 as 0.77 for Z <= 1.5, 0.066Z + 0.67 for 1.5 < Z < 5, and 1.0 for Z >= 5. For noncohesive riprap and gabion linings, the calculator also reduces side-slope resistance with the K2 tractive-force ratio based on bank angle and rock angle of repose.
Standards & related tools
What This Solves
Evaluates channel lining adequacy by comparing applied shear stress against permissible shear for grass, riprap, concrete, and other lining materials.
Best Used When
- You need to select an appropriate channel lining to prevent erosion at the design flow velocity
- You are checking whether an existing grass-lined or riprap-lined channel is stable under design conditions
- You want to compare permissible velocity or tractive force for different lining materials
Do NOT Use When
- You need to size riprap stone specifically using Isbash, USACE, or Maynord methods — Use Riprap Sizing Calculator
- You need to calculate flow capacity rather than lining stability — Use Manning's Channel Calculator
Key Assumptions
- Applied shear stress is calculated from channel geometry and flow depth (τ = γRS)
- Permissible shear values are from FHWA HEC-15 or equivalent design guides
- Channel geometry is uniform at the cross-section being analyzed
- Vegetation is fully established (for grass-lined channels)
- No significant wave action or turbulence beyond uniform flow conditions
Input Quality Notes
Permissible shear for grass varies significantly with grass species, density, and establishment. Use lower values for new plantings. Riprap permissible shear depends on stone quality and gradation.
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Last verified: August 2026