Bell's waterway and guide bund, 7500 m3/s

Desired waterway of the barrage

Lacey's regime waterway (wetted perimeter) is

$$W = 4.75\sqrt{Q} = 4.75\sqrt{7500} = 411.4\ \text{m}$$

For a barrage the waterway is generally kept equal to this regime width (1.0 to 1.2 times); adopt $W = 411$ m between abutments. Flood depth $h = 238.0 - 232.0 = 6.0$ m.

Data and design basis (Bell's guide bund)

• Bell's guide bund is designed on Lacey's regime width; bed material is gravel (5.07 mm).
• Silt factor (Lacey): $f = 1.76\sqrt{d_{mm}} = 1.76\sqrt{5.07} = 3.96$
• Flood depth above bed: $h = 238.0 - 232.0 = 6.00$ m
• Design discharge for scour/apron: $Q = 7500$ m³/s

1. Waterway and length of guide bund

Lacey's regime waterway: $W = 4.75\sqrt{Q} = 4.75\sqrt{7500} = 411.36$ m. Adopt $W \approx 411$ m. Length of guide bund (Garg): upstream shank $=1.0$ to $1.5\,W$, downstream tail $=0.2$ to $0.5\,W$. Adopt

$$\begin{aligned} L_{us} &= 1.25W = 1.25\times 411 = 514\ \text{m} \\ L_{ds} &= 0.25W = 103\ \text{m} \end{aligned}$$

Curved heads: upstream radius $R_u \approx 0.5W = 206$ m with sweep $120^\circ$ to $145^\circ$ (adopt $120^\circ$); downstream radius $R_d \approx 0.25W = 103$ m with sweep about $45^\circ$. Arc length of upstream head $= R_u\theta = 206\times 2.094 = 430$ m, so total length on the upstream side $\approx 944$ m.

2. Thickness of stone pitching

$$t = 0.06\,Q^{1/3} = 0.06\times 7500^{1/3} = 0.06\times 19.57 = 1.17\ \text{m}$$

Adopt $t \approx 1.2$ 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:

$$R = 0.47\left(\frac{Q}{f}\right)^{1/3} = 0.47\left(\frac{7500}{3.96}\right)^{1/3} = 5.81\ \text{m}$$

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 $t = 1.17$ m, so the launched apron thickness is $1.5t = 1.5\times1.17 = 1.76$ m. Equating volumes per metre, the thickness as laid over $1.5D'$ width is $T = \dfrac{1.5t\times\sqrt5 D'}{1.5D'} = \sqrt5\,t = 2.63$ m (about $2.25t$).

Summary

Sketches

Plan of guide bunds:

 U/S                                          D/S
                       bridge / weir axis
   Shank (straight)                |
 ________________________________  |  ___
/  1.0-1.5 W upstream            \ | /   \  tail
\________________________________/=|=\___/  0.25 W
 curved head                       |
 R, sweep 120 deg    <-- waterway W -->
 ________________________________  |  ___
/                                \ | /   \
\________________________________/=|=\___/

Section at the shank (straight portion):

           top width 6 m
         ___________  <- HFL + 1.5 m
        /           \
 HFL ---/-------------\---  2:1 slopes
       / pitching t    \
 bed__/__ filter ______ \___
      \_ launching apron _/ (launches at 2:1)