Channel Lining Design Calculator

Shear stress method

The FHWA HEC-15 procedure (3rd ed., 2005), which TxDOT Hydraulic Design Manual Ch. 7 §3 follows. Normal depth is solved with the lining’s n recomputed at each trial depth. Applied shear on the bottom is τ_d = γyS; on side slopes K₁τ_d; in bends K_bτ_d. A location is within permissible shear when τ_p ≥ SF·τ.

Grass

n = 0.213 C_n τ₀^−0.4 with C_n from cover condition and stem height. Permissible shear combines soil and cover: τ_p = τ_p,soil/(1 − C_f)·(n/n_s)². Non-cohesive soil: τ_p,soil = 0.4 D₇₅; cohesive soil: you enter it.

Riprap, cobble and gravel

Blodgett roughness for d_a/D₅₀ from 1.5 to 185. τ_p = F*(γ_s − γ)D₅₀ with Shields’ parameter and the least safety factor from the particle Reynolds number; stable D₅₀ for the bottom and the side slopes.

Other linings and concrete

Enter n and, for mats or gabions, the manufacturer’s permissible shear. For a rigid lining leave it blank: shear, Froude number and depth are still reported.

Bends and freeboard

K_b from R_c/T, length of protection below the bend L_p = 0.60 R^7/6/n, superelevation Δd = V²T/(gR_c). Freeboard is your criterion.

Ranges

Outside a published range the calculator stops and says why: d_a/D₅₀ below 1.5 (Bathurst), riprap slopes above 10% (HEC-15 Eq. 6.11), soil D₇₅ above 2 in.

The calculator is tested against the cases below every time its code changes.

Tolerance: 1% or half a unit of the last printed digit; a wider tolerance is used only where a published example rounds an intermediate value, with the reason recorded. Hydraulic Toolbox lining runs are scored at the depth of its second run (owner decision O8).

• Steep-slope riprap sizing (HEC-15 Eq. 6.11) and the Bathurst roughness for shallow flow over large stone are not included; the calculator stops instead.
• The angle of repose of riprap is an input (HEC-15 Fig. 6.1). The permissible shear of cohesive soils is an input (HEC-15 Eq. 4.6 or Fig. 4.1).
• Composite linings (for example a riprap bottom with grass sides) are not combined yet.
• The FHWA Hydraulic Toolbox computes the grass effective shear with soil grain roughness 0.016 even for coarser soils; this calculator follows HEC-15 Eq. 4.4, and that value is not scored.
• Your city, county or TxDOT may set the design frequency, freeboard and lining types. Those criteria decide the design.

What is permissible shear?

The largest shear stress a lining resists without eroding, from the FHWA HEC-15 tables and equations for grass, riprap and other linings. The check compares the maximum bed shear, γ d S, times your safety factor with the permissible shear (HEC-15 Eq. 3.2), on the channel bottom and on the side slopes.

What if the lining fails the check?

Use a stronger lining (for example larger riprap), reduce the slope with drops, or widen the channel so the flow runs shallower. The results show the shear next to the permissible value at each location checked, so you can try each option.

Does this check bends and steep channels?

Bends are checked with the HEC-15 bend factor and the superelevation of the water surface. Slopes steeper than 10% are outside the HEC-15 riprap method used here, and the calculator refuses them rather than extend it.

Can I attach the calculation sheet to a design report?

You can print it and include it as a supporting calculation that you have checked. It is a calculation aid, not a sealed engineering document: the engineer of record reviews it and is responsible for the design, and the criteria of the reviewing agency decide which methods and values apply.