Procedure for designing a Sarda type fall

A Sarda-type fall is a vertical-drop fall with a raised rectangular or trapezoidal crest wall. The crest is designed with Sarda's formula, the energy is dissipated in a cistern, and the floor is designed by Bligh's or Khosla's theory. The design steps are as follows.

Part 1. Hydraulic design (7 marks)

Data: $Q$, u/s and d/s FSL, bed levels, bed width $B_c$, side slopes, soil.

1. Crest length: usually equal to the bed width of the canal, $L = B_c$ (it may be made slightly longer to allow for a future increase in discharge).
2. Head over crest (Sarda's formula): for a rectangular crest $Q = 1.835\,L\,H^{3/2}\left(\dfrac{H}{B}\right)^{1/6}$, and for a trapezoidal crest $Q = 1.99\,L\,H^{3/2}\left(\dfrac{H}{B}\right)^{1/6}$, where $B$ is the crest top width. Assume $B$, then solve for $H$ by trial. A rectangular crest is used for small discharges (up to about 14 m³/s) and a trapezoidal crest for larger ones.
3. Crest level $=$ u/s TEL $- H$ (u/s FSL $+ \dfrac{v^2}{2g} - H$).
4. Crest dimensions ($d$ = height of the crest above the d/s bed, $G$ = specific gravity of masonry):
   • Rectangular crest: top width $B = 0.55\sqrt{d}$, base width $= \dfrac{H + d}{\sqrt{G}}$ for stability.
   • Trapezoidal crest: top width $B = 0.55\sqrt{H + d}$, with u/s batter about 1:3 and d/s batter about 1:8.
5. Cistern: with $E$ = total head over the crest and $H_L$ = drop in water level, length of cistern $L_c = 5\sqrt{E\,H_L}$ and depth of cistern below the d/s bed $X = \dfrac{1}{4}\left(E\,H_L\right)^{2/3}$.
6. Cistern level $=$ d/s bed $- X$.

Part 2. Floor and protection (6 marks)

7. Bligh's theory: total creep length $L = C\,H_L$, with $H_L$ = difference of u/s and d/s FSL. Provide cut-offs u/s ($d_1$) and d/s ($d_2$).
8. Length of floor: d/s floor length $L_d = 2.21C\sqrt{H_L\sqrt{q/75}}$ (not less than the cistern length); u/s floor from the balance of creep: $b_u = CH_L - 2(d_1 + d_2) - B_w - L_d$. If Khosla's method is used, find the total floor length from the safe exit gradient: $G_E = \dfrac{H}{d}\dfrac{1}{\pi\sqrt{\lambda}}$.
9. Floor thickness: at any section $t = \dfrac{4}{3}\dfrac{h}{G-1}$, where $h$ is the residual uplift head obtained from the creep line.
10. Protection works: d/s block protection of length about $2D$ to $3D$ with an inverted filter, and u/s block protection; wing walls splayed at 45° upstream and at 1:1 or 2:1 downstream, with the wings ending in the bank.
11. Check: stability of the crest wall (no tension, base pressure within the safe bearing capacity) and the exit gradient.
12. Draw the longitudinal section and plan.

 FSL u/s ~~~~~~~~~|
 u/s bed __________|crest         FSL d/s ~~~~
   cut-off d1 |   |  \___cistern X___ d/s bed
   u/s floor  |wall| Lc |  d/s floor  | d2