Guide bund: length, curved head, apron; 4500 m3/s

Data and design basis

• Silt factor (Lacey): $f = 1.76\sqrt{d_{mm}} = 1.76\sqrt{0.1} = 0.557$
• Flood depth above bed: $h = 154 - 150 = 4.00$ m
• Design discharge for scour/apron: $Q = 4500$ m³/s

1. Waterway and length of guide bund

Lacey's regime waterway: $W = 4.75\sqrt{Q} = 4.75\sqrt{4500} = 318.64$ m. Adopt $W \approx 319$ m. Length of guide bund (Garg): upstream shank $=1.0$ to $1.5\,W$, downstream tail $=0.2$ to $0.5\,W$. Adopt

$$\begin{aligned} L_{us} &= 1.25W = 1.25\times 319 = 399\ \text{m} \\ L_{ds} &= 0.25W = 80\ \text{m} \end{aligned}$$

Curved heads: upstream radius $R_u \approx 0.5W = 160$ m with sweep $120^\circ$ to $145^\circ$ (adopt $120^\circ$); downstream radius $R_d \approx 0.25W = 80$ m with sweep about $45^\circ$. Arc length of upstream head $= R_u\theta = 160\times 2.094 = 334$ m, so total length on the upstream side $\approx 733$ m.

2. Thickness of stone pitching

$$t = 0.06\,Q^{1/3} = 0.06\times 4500^{1/3} = 0.06\times 16.51 = 0.99\ \text{m}$$

Adopt $t \approx 1.0$ m (pitching on the river side slope 2:1, over a 0.15 to 0.3 m graded filter).

3. Scour depth and launching apron

Lacey's normal scour depth:

$$R = 0.47\left(\frac{Q}{f}\right)^{1/3} = 0.47\left(\frac{4500}{0.557}\right)^{1/3} = 9.43\ \text{m}$$

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 $t = 0.99$ m, so the launched apron thickness is $1.5t = 1.5\times0.99 = 1.49$ m. Equating volumes per metre, the thickness as laid over $1.5D'$ width is $T = \dfrac{1.5t\times\sqrt5 D'}{1.5D'} = \sqrt5\,t = 2.21$ m (about $2.25t$).

Summary