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.
Check whether a proposed channel lining — grass, riprap, gabion, concrete, geosynthetic, turf reinforcement mat or bare soil — is stable for your design flow. The tool compares the actual velocity and boundary shear stress against permissible values from FHWA HEC-15 using the permissible-velocity and tractive-force methods.
Lining Properties
| Lining Type | n | Vmax (fps) | taumax (psf) |
|---|---|---|---|
| Bare Soil | 0.025 | 2 | 0.02 |
| Grass | 0.05 | 4 | 1 |
| Riprap | 0.04 | 14 | 4 |
| Gabion | 0.028 | 15 | 5 |
| Concrete | 0.015 | 20 | 10 |
Grass Retardance Classes (HEC-15)
| Class | Height | Condition |
|---|---|---|
| A | > 30 inches | Excellent stand, tall vegetation |
| B | 11-24 inches | Good stand, tall vegetation |
| C | 6-10 inches | Good stand, moderate length |
| D | 2-6 inches | Good stand, short |
| E | < 2 inches | Good stand, burned or very short |
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 it works
For a trapezoidal channel the calculator first derives the hydraulic geometry, then evaluates flow velocity with Manning's equation and the boundary shear stress, and finally compares each against the permissible value for the chosen lining.
1. Hydraulic geometry (bottom width b, flow depth y, side slope z:1 H:V):
- Flow area: A = (b + zy)·y
- Wetted perimeter: P = b + 2y·√(1 + z²)
- Hydraulic radius: R = A / P
2. Actual velocity — Manning's equation:
- V = (k / n)·R2/3·S1/2
- where k = 1.486 (US customary) or 1.0 (SI), n is Manning's roughness for the lining, and S is the channel slope.
3. Boundary (bed) shear stress — tractive force:
- τ₀ = γ·R·S (multiplied by a sinuosity factor for bends)
- where γ is the unit weight of water (62.4 lb/ft³ or 9810 N/m³).
4. Adequacy check. The lining passes when the governing condition is met:
- Permissible-velocity method: V ≤ Vpermissible
- Tractive-force method: τ₀ ≤ τpermissible
The factor of safety is the ratio of the permissible value to the actual value. Side slopes are checked separately using the shear ratio Kₛ = √(1 − sin²θ / sin²φ), where θ is the bank angle and φ is the material angle of repose (≈ 40°), with the bank shear taken as about 0.75·τ₀.
Lining properties (HEC-15)
Typical Manning's roughness, permissible velocity and permissible shear stress used by the calculator. Values for riprap and gabions vary with stone size — treat these as starting points and confirm against the manufacturer or HEC-15 design charts.
| Lining type | Manning's n | Permissible velocity (fps) | Permissible shear (psf) |
|---|---|---|---|
| Bare soil | 0.025 | 2.0 | 0.02 |
| Grass | 0.030 – 0.20 | 4.0 | 1.0 |
| Turf reinforcement mat | 0.030 | 15.0 | 6.0 |
| Geosynthetic | 0.022 | 12.0 | 3.0 |
| Riprap | 0.04 | 14.0 | 4.0 |
| Gabion | 0.028 | 15.0 | 5.0 |
| Concrete | 0.015 | 20.0 | 10.0 |
Source: FHWA HEC-15 (2005), Design of Roadside Channels with Flexible Linings. Grass Manning's n spans Class E (≈ 0.03) to Class A (≈ 0.20) and varies with the n-VR relationship. Multiply psf by 47.88 to convert to Pa.
Grass retardance classes & permissible shear
For grass linings the permissible shear and roughness depend on the vegetation retardance class, which reflects stand height, density and condition.
| Class | Typical stand height | Permissible shear (psf) | Typical Manning's n |
|---|---|---|---|
| A | > 30 in | 3.7 | 0.20 |
| B | 11 – 24 in | 2.1 | 0.10 |
| C | 6 – 10 in | 1.0 | 0.05 |
| D | 2 – 6 in | 0.6 | 0.04 |
| E | < 2 in | 0.35 | 0.03 |
Source: FHWA HEC-15 (2005), Table 3.1 (permissible shear) and Table 2-1 (Manning's n). Retardance depends on season and maintenance — design for the lowest expected class.
Worked example
Grass-lined trapezoidal channel (Class C), bottom width b = 4 ft, side slope z = 3:1, flow depth y = 1.5 ft, channel slope S = 0.02 ft/ft:
- Flow area A = (4 + 3 × 1.5) × 1.5 = 12.75 ft²
- Wetted perimeter P = 4 + 2 × 1.5 × √(1 + 3²) = 13.49 ft
- Hydraulic radius R = 12.75 ÷ 13.49 = 0.945 ft
- Bed shear τ₀ = 62.4 × 0.945 × 0.02 = 1.18 psf
- Permissible shear for Class C grass = 1.0 psf → actual (1.18) exceeds permissible, so plain Class C grass is inadequate here; a turf reinforcement mat or higher retardance class is indicated.
Frequently asked questions
What is the difference between the permissible velocity and tractive force methods?
The permissible velocity method limits the mean channel velocity to a maximum value for the lining (for example about 4 ft/s for grass or 14 ft/s for riprap) and is quick to apply. The tractive force (shear stress) method instead compares the actual boundary shear stress, τ₀ = γRS, to a permissible shear for the lining. The shear approach is generally preferred in modern flexible-lining design (FHWA HEC-15) because it accounts for flow depth and slope, not just velocity.
How is the boundary shear stress calculated?
The calculator uses the maximum (bed) shear stress for steady uniform flow: τ₀ = γRS, where γ is the unit weight of water (62.4 lb/ft³ or 9810 N/m³), R is the hydraulic radius (flow area ÷ wetted perimeter), and S is the channel slope. A sinuosity factor can increase this for bends. The lining is adequate when the actual shear is less than or equal to the permissible shear for that lining.
What permissible shear stress can a grass lining take?
Permissible shear depends on the grass retardance class (HEC-15 Table 3.1): roughly 3.7 psf for Class A, 2.1 psf for Class B, 1.0 psf for Class C, 0.6 psf for Class D and 0.35 psf for Class E. Taller, denser, well-established vegetation (higher class) resists more shear. Where grass alone is exceeded, a turf reinforcement mat (about 6 psf), riprap (about 4 psf) or gabions (about 5 psf) are typically used.
Why does the calculator reduce the allowable shear on the side slopes?
On a sloping channel bank, gravity helps drag particles downhill, so a lining there fails at a lower tractive force than on the flat bed. The tool applies a side-slope shear ratio Kₛ = √(1 − sin²θ / sin²φ), where θ is the bank angle and φ is the lining material angle of repose (taken as about 40°). The permissible bank shear is the bed permissible shear multiplied by Kₛ, and the side slope shear is taken as roughly 0.75 τ₀ for a typical trapezoidal section.
Standards & related tools
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Last verified: February 2026