Guide bund and apron, 13,100 m3/s

Data and design basis

• Total waterway $W = 658.88$ m (given). The flood depth is not given, so Lacey's regime depth for the intensity $q = Q/W = 13100/658.88 = 19.88$ m²/s is used: $R_L = 1.35(q^2/f)^{1/3} = 10.03$ m. $f = 1.76\sqrt{0.3} = 0.964$.
• Discharge is increased by 20 % for the apron design: $Q_a = 1.2\times13100 = 15720$ m³/s.
• Silt factor (computed, not given): $f \approx 0.96$
• Flood depth (assumed Lacey regime depth): $h = 10.03$ m
• Design discharge for scour/apron: $Q = 15720$ m³/s; for pitching, $Q = 13100$ m³/s

1. Waterway and length of guide bund

Waterway between abutments $W = 658.88$ m (given). Length of guide bund (Garg): upstream shank $=1.0$ to $1.5\,W$, downstream tail $=0.2$ to $0.5\,W$. Adopt

$$\begin{aligned} L_{us} &= 1.25W = 1.25\times 659 = 824\ \text{m} \\ L_{ds} &= 0.25W = 165\ \text{m} \end{aligned}$$

Curved heads: upstream radius $R_u \approx 0.5W = 330$ m with sweep $120^\circ$ to $145^\circ$ (adopt $120^\circ$); downstream radius $R_d \approx 0.25W = 165$ m with sweep about $45^\circ$. Arc length of upstream head $= R_u\theta = 330\times 2.094 = 690$ m, so total length on the upstream side $\approx 1514$ m.

2. Thickness of stone pitching

$$t = 0.06\,Q^{1/3} = 0.06\times 13100^{1/3} = 0.06\times 23.57 = 1.41\ \text{m}$$

Adopt $t \approx 1.5$ 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:

$$R = 0.47\left(\frac{Q}{f}\right)^{1/3} = 0.47\left(\frac{15720}{0.96}\right)^{1/3} = 11.92\ \text{m}$$

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 $t = 1.41$ m, so the launched apron thickness is $1.5t = 1.5\times1.41 = 2.12$ m. Equating volumes per metre, the thickness as laid over $1.5D'$ width is $T = \dfrac{1.5t\times\sqrt5 D'}{1.5D'} = \sqrt5\,t = 3.16$ 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)