Cross drainage: Q 25, uplift on roof of barrel

The canal (25 m³/s, bed 160.00 m, FSL 161.50 m) crosses a drain of 800 m³/s with HFL 160.50 m, which is above the canal bed. The canal bed (160.00 m) is above the drain bed (158.00 m), so the structure is a siphon aqueduct: the drain flows through rectangular barrels under the canal trough, partly under pressure.

1. Drainage waterway (Lacey)

$$P = 4.75\sqrt{Q} = 4.75\sqrt{800} = 134.4\ \text{m}$$

Barrels of clear span 4.0 m with walls 0.4 m thick: 32 barrels give a clear width of 32×4.0 = 128 m (about the regime width, accepted as the obstruction is by walls only) and overall width 141.2 m.

Barrel height: bed 158.00 m to the roof soffit $= 160.00 - 0.40 = 159.60$ m, so the clear height is 1.6 m (roof 0.4 m thick, whose top is the canal bed). Area $= 128\times1.6 = 205$ m²; velocity $V = 800/205 = 3.91$ m/s; $V^2/2g = 0.778$ m.

Head loss (entry + exit $\approx 1.5V^2/2g$ plus Manning friction, $n = 0.015$, $R = 0.571$ m, length 34.5 m):

$$h_L = 1.5\times0.778 + \frac{n^2V^2L}{R^{4/3}} = 1.167 + 0.250 = 1.42\ \text{m}$$

(the afflux is absorbed by the flood bank and a flared u/s wing).

2. Canal waterway

Canal width in the trough is kept equal to the bed width of 30 m, depth 1.5 m (FSL 161.50 m), so the canal waterway is 30 m; the trough is a rectangular concrete section, with transitions (not needed since full width is kept). Barrel length along the canal axis $= 30 + 2\times1.5\times1.5 = 34.5$ m (including the canal side slopes of 1.5:1).

3. Uplift pressure on the roof of the barrel

Worst case: drain at HFL (160.50 m) and barrel full, canal empty. Pressure head at the roof soffit $= 160.50 - 159.60 = 0.90$ m.

$$\begin{aligned} \text{Uplift} &= 9.81\times0.90 = 8.83\ \text{kN/m}^2 \\ \text{Roof weight} &= 0.4\times24 = 9.6\ \text{kN/m}^2 \\ \text{FOS (canal empty)} &= 9.6/8.83 = 1.09 \end{aligned}$$

With the canal running at FSL, the water on the roof is $1.5\times9.81 = 14.7$ kN/m², so FOS $= (9.6+14.7)/8.83 = 2.75$ (safe). The roof is also checked against flow conditions: when the barrel runs full at Q = 800 m³/s the pressure at the soffit is negative (energy level 160.50 m is used in 1.17 m of entry loss and velocity head), so no uplift occurs; the still-water case governs. As FOS with empty canal is only 1.09, the roof should be reinforced and tied to the walls.

4. Impervious floor

Maximum seepage head (drain at HFL u/s, d/s dry): $H_s = 160.50 - 158.00 = 2.50$ m. Scour: $q = 800/134.4 = 5.95$ m²/s, $R = 1.35(q^2/f)^{1/3} = 4.44$ m ($f = 1$), scour level $= 160.50 - 1.5R = 153.85$ m, so d/s cut-off $d_2 = 4.2$ m below the floor; u/s cut-off $d_1 = 2.5$ m.

Creep path (Bligh): $2d_1 + 4 + 34.5 + 8 + 2d_2 = 59.9$ m. Uplift head at points on the floor (linear loss):

With $G = 2.24$, the barrel floor slab of the box is designed together with the weight of the walls, roof and canal water. The required thickness at the start of the floor from uplift alone is $t = \dfrac{4}{3}\dfrac{h}{G-1} = 2.28$ m; the box action (walls, roof, canal water) and the u/s cut-off carry the uplift, so the floor slab is made 0.6 m with pressure relief by weep holes at the d/s end.

Answer: drainage waterway 128 m clear (32 barrels of 4.0×1.6 m), canal waterway 30 m, uplift on the roof $= 8.8$ kN/m² (head 0.9 m, FOS 1.09 canal empty), and floor uplift heads 2.12 m (start) to 0.68 m (end).

 canal FSL 161.5 ~~~~~~~~~~~~~~~~~~~~
 canal bed 160.0 ==roof 0.4 m==========
 HFL 160.5 ~~~~ | 4 m | 4 m |  barrels   1.6 m
 drain bed 158.0 |_____|_____|___________
   u/s cut-off 2.5 m   floor    d/s cut-off 4.2 m