Queendom Tools

Incipient Motion Armoring Calculator

For a coarse, well graded bed, this calculator applies FHWA HEC-20 (HIF-12-004, 2012), Equations 6.13, 6.15 and 6.16, to estimate the boundary shear stress, the critical particle size Dc that the flow can just no longer move, and the degradation depth Ys at which an armor layer of particles coarser than Dc could form. The inputs are preloaded with the US values of Example Problem 1 (pp. 6.36 to 6.38).

Inputs

0.03 to 0.10 for natural sediments (p. 6.27)

Leave empty for the first pass; read it at Dc from your gradation curve.

Formulas used

ks = 3.5 × D84

τ = ρ V² / [5.75 × log10(12.27 R / ks)]² (Equation 6.15, lb/ft²)

Dc = τ / [Ks × γ × (Gs − 1)] (Equation 6.13, ft)

ya = 3 × Dc (armor layer thickness, as in Example Problem 1)

Ys = ya × (1 / Pc − 1) (Equation 6.16, ft)

ρ = 1.94 slugs/ft³, γ = 62.4 lb/ft³ (HEC-20 Table 1.1)

SI inputs: 1 ft = 0.3048 m; SI results: 1 lb/ft² = 47.88025898033584 Pa

How to use it

  1. Choose the unit system, US or SI.
  2. Enter the hydraulic radius R, the mean velocity V, the D84 of the bed material, the specific gravity Gs and the Shields parameter Ks.
  3. Leave Pc empty and press Calculate to get the boundary shear stress τ and the critical particle size Dc.
  4. On your own gradation curve, read the fraction of bed material coarser than this Dc and enter it as Pc, as a decimal.
  5. Press Calculate again to get the degradation depth Ys at which an armor layer could form.

Limits of the method

  • Equation 6.15 with ks = 3.5 × D84 is for gravel and coarser, well graded bed material.
  • Poorly graded beds can have ks as low as 1.0 to 2.0 times D84.
  • The armor layer thickness ranges from 1 to 3 times Dc; this page assumes 3 × Dc.
  • The hydraulic depth can replace R when the width to depth ratio exceeds 10.

These estimates support preliminary sediment analysis. Whether an armor layer actually forms depends on site conditions and future flows.