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Launching apron, 5000 m3/s, HFL 225 m

Short answer

With f=1.76, t=0.06×5000^(1/3)=1.03 m, R=0.47(5000/1.76)^(1/3)=6.66 m. Scour below bed D'=1.5R−3=6.98 m. Apron length=1.5D'=10.48 m, launched thickness=1.5t=1.54 m (laid √5 t≈2.29 m).

Determine the length and thickness of launching apron for the straight portion of a guide bund in a river: Design flood = 5000 m³/s; av. dia. of bed material = 1 mm; HFL = 225.00 m; River bed level = 222.00 m.

Data and design basis

  • Silt factor (Lacey): f=1.76dmm=1.761.0=1.76f = 1.76\sqrt{d_{mm}} = 1.76\sqrt{1.0} = 1.76
  • Flood depth above bed: h=225.0−222.0=3.00h = 225.0 - 222.0 = 3.00 m
  • Design discharge for scour/apron: Q=5000Q = 5000 m³/s

1. Pitching thickness

t=0.06 Q1/3=0.06×50001/3=0.06×17.10=1.03 mt = 0.06\,Q^{1/3} = 0.06\times 5000^{1/3} = 0.06\times 17.10 = 1.03\ \text{m}

2. Scour depth and launching apron

Lacey's normal scour depth:

R=0.47(Qf)1/3=0.47(50001.76)1/3=6.66 mR = 0.47\left(\frac{Q}{f}\right)^{1/3} = 0.47\left(\frac{5000}{1.76}\right)^{1/3} = 6.66\ \text{m}

Maximum scour below HFL: 2R2R at the upstream nose, 1.5R1.5R at the shank (straight portion). The apron must launch to the slope 2H:1V2H:1V, so its horizontal width is 1.5D′1.5D' and, when launched, it covers a slope length 5 D′\sqrt5\,D' with thickness 1.5t1.5t.

PortionScour factorScour depth below HFLDepth below bed D′D'Apron length 1.5D′1.5D'
Shank (straight)1.5R9.98 m6.98 m10.48 m

Thickness: pitching t=1.03t = 1.03 m, so the launched apron thickness is 1.5t=1.5×1.03=1.541.5t = 1.5\times1.03 = 1.54 m. Equating volumes per metre, the thickness as laid over 1.5D′1.5D' width is T=1.5t×5D′1.5D′=5 t=2.29T = \dfrac{1.5t\times\sqrt5 D'}{1.5D'} = \sqrt5\,t = 2.29 m (about 2.25t2.25t).

Answer (straight portion): length of launching apron =1.5D′=10.48=1.5D' = 10.48 m, thickness =1.5t=1.54=1.5t = 1.54 m launched (about 2.29 m as laid).

✓ Answer checked by Claude Opus 5.5 (high effort)

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