Launching apron, 6000 m3/s, HFL 330 m

Data and design basis

• Silt factor (Lacey): $f = 1.76\sqrt{d_{mm}} = 1.76\sqrt{1.0} = 1.76$
• Flood depth above bed: $h = 330 - 326 = 4.00$ m
• Design discharge for scour/apron: $Q = 6000$ m³/s

1. Pitching thickness

$$t = 0.06\,Q^{1/3} = 0.06\times 6000^{1/3} = 0.06\times 18.17 = 1.09\ \text{m}$$

2. Scour depth and launching apron

Lacey's normal scour depth:

$$R = 0.47\left(\frac{Q}{f}\right)^{1/3} = 0.47\left(\frac{6000}{1.76}\right)^{1/3} = 7.07\ \text{m}$$

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

Thickness: pitching $t = 1.09$ m, so the launched apron thickness is $1.5t = 1.5\times1.09 = 1.64$ m. Equating volumes per metre, the thickness as laid over $1.5D'$ width is $T = \dfrac{1.5t\times\sqrt5 D'}{1.5D'} = \sqrt5\,t = 2.44$ m (about $2.25t$).

Answer (straight portion): length of launching apron $=1.5D' = 9.92$ m (horizontal), thickness $=1.5t = 1.64$ m when launched (about 2.44 m as laid).