### 4.6.1 Example 1: Floodway Design

The task for this example is to design a floodway with 20 year ARI trafficability over a natural open channel approximately trapezoidal in shape. The floodway would be approximately 90 to 100 m long and for cost reasons road batters will be grass covered only for protection against scour.

Preliminary considerations:

- Because the batters will be protected by grass only, culverts will be required to build up the tailwater to not more than 300 mm below the edge of the downstream shoulder when overtopping of the road first occurs. Allowing for crossfall, there will be a head of 450 mm and a velocity of about 2.30 to 2.45 m/s through the culverts if this minimum tailwater is adopted. Is this acceptable on this job? (This will be answered in the example). There is a need to confirm total head over the road is less than 300 mm for an ARI 20 year flood.
- For 20 year ARI trafficability, the floodway level should be at the 20 year unrestricted flood level to allow the maximum amount of water over the road and save on culvert and overall costs.

In general it is only in very long floodways with very little velocity in the open channel and/or where costly protection is unavoidable, that increasing culvert requirements by raising the road, thus decreasing the flow over the road (to the extreme of a flood free road) may reduce the overall cost of the job.

#### Step 1

List all relevant criteria:

- required standard: trafficable in a 20 year ARI flood
- time of closure: maximum of one day in a 50 year ARI flood. (Calculated hydrograph shows this maximum only a matter of hours – not included here)
- batter protection: grass
- width of floodway: 10 m
- road crossfall: 3%.

#### Step 2

Calculate the rating curve for the unrestricted channel.

Using open channel hydraulic calculations (as discussed in Section 2 – Open Drains and Channels):

*Q*= 162 m³/s @ Height 322.76 m_{50}*Q*= 130.4 m³/s @ Height 322.58 m (_{20}*V*= 0.68 m/s)*Q*= 108.1 m³/s @ Height 322.44 m_{10}*Q*= 70 m³/s @ Height 322.13 m._{5}

#### Step 3

Adopt a road level and calculate the maximum allowable depth of water over the road.

Adopt the road level at the unrestricted 20 year ARI flood level and show the cross‑sectional details in Figure 4.7.

*Source: DTMR (2010).*

From Section 4.2 – Design Considerations, closure to traffic occurs when (using Equation 33):

\[H = d + \frac{V^{2}}{2g} > 300 mm\]

The maximum allowable depth of water over the road, *y*, occurs when *H* = 0.300 m.

Therefore:

\[d=H-\ \frac{V^2}{2g}=0.3-\ \frac{{0.68}^2}{2\text{ x } 9.81}\] | |||

\[\text{d } = 0.28 m\] |

#### Step 4

Calculate the discharge over the road and through the culverts in a 20 year ARI flood.

The total discharge over the road and through the culverts must equal the discharge in the unrestricted channel downstream with flow at height 322.58 m.

i.e. *Q _{tot} = Q_{R} + Q_{C}* = 130.4 m³/s

Flow over the road using Equation 31:

\[Q = C_{f}LH^{1.5}\left( \frac{C_{s}}{C_{f}} \right)\] | ||||

where | ||||

\[C_{f}\] | = | Coefficient of discharge |

From Figure 4.3, Chart A:

H/l | 0.30/10 = 0.03, which is < 0.15 | |||

Therefore: | ||||

C_{f} | = | 1.674 | ||

L | = | Length of floodway = 94 m | ||

H | = | 0.30 m | ||

Therefore: | ||||

Q | = | 1.674 x 94 x 0.31.5 | ||

Q | = | 25.9 m3/s |

Discharge through culverts:

*Q _{C} = Q_{tot} – Q* = 130.4 – 25.9 = 104.5 m³/s

Therefore, the culverts are required to take a discharge of 104.5 m³/s, operating under a head of 0.30 m and under outlet control for this design condition.

#### Step 5

Detailed culvert design.

Proceed with the design of culverts to take 104.5 m³/s.

Height of culvert opening, *D*, from Equation 37:

D | = | Crown level of road – crossfall – minimum fill above culvert – thickness of deck slab – invert level | 37 |

D | = | 322.58 – 5 x 0.03 – 0.100 – 0.180 – 320.55 = 1.60 m |

For culvert design:

- outlet control with
*H*= 0.30 m - tailwater at height 322.58 m,
*HW*at height 322.88 m - invert at height 320.50 m, say.

From the culvert design procedure in Section 3.10 – Design Procedures:

- 13/2700 x 1500 mm RCBC have a capacity of 104 m³/s with outlet velocity = 1.98 m/s.
- Adopt 13/2700 x 1500 mm RCBC with a floodway height 322.58 m and length 94 m.

#### Step 6

Check for culvert requirements when the flood is at the point of overtopping the road.

By trial and error, calculate flow through the culvert at the point where the headwater height is 322.58 m. Confirm that flow velocity through the culvert is less than 2.5 m/s.

#### Step 7

Confirm that velocity criteria are met.

#### Step 8

Calculate afflux for ARI 50 year flow and confirm that criteria are met.