Floodplain and Roadway Overtopping

Roadway designs must accommodate extreme flood events without causing hazardous roadway overtopping or flooding adjacent properties. When a flood event exceeds the capacity of cross-culverts or bridges, the roadway embankment acts as a weir, and water spills over the pavement.

FEMA Floodplain Definitions

FEMA (Federal Emergency Management Agency) regulates development within flood-prone areas.

  • Base Flood Elevation (BFE): The computed water surface elevation resulting from a flood that has a $1\%$ chance of occurring in any given year (also called the 100-year flood or “Base Flood”).
  • Regulatory Floodway: The channel of a river or stream plus the adjacent land area that must be kept free of development so that the 100-year flood can be discharged without increasing the water surface elevation by more than a designated height (typically 1.0 foot under FEMA standards).
  • Floodway Fringe: The portion of the 100-year floodplain outside of the regulatory floodway. Development is permitted here if structures are elevated above the BFE.

Roadway Overtopping Hydraulics

When water level exceeds the highest point of a roadway cross-section (the crown or shoulder elevation), the roadway behaves as a broad-crested weir.

Weir Flow Equation (USCS):

$$Q_{overtop} = C_w \cdot L \cdot H^{1.5}$$

Where:

  • $Q_{overtop}$ = Overtopping discharge (cfs)
  • $C_w$ = Weir discharge coefficient (dimensionless; for roadway overtopping, $C_w$ typically ranges from 2.5 to 3.0 depending on the pavement roughness and shoulder shape. A standard value of 2.63 or 3.0 is common; check your NCEES handbook or problem parameters).
  • $L$ = Length of roadway overtopped (feet), measured along the roadway centerline.
  • $H$ = Headwater depth above the roadway crest (feet), measured at a point upstream of the drawdown.

Combined Flow Capacity:

If a culvert or bridge is located beneath the overtopped road, the total discharge is the sum of the conduit capacity and the overtopping flow:

$$Q_{total} = Q_{conduit} + Q_{overtop}$$

Worked Example: Combined Culvert and Overtopping Discharge

A two-lane highway crosses a creek via a $4.0\text{-foot}$ diameter concrete culvert. During a major flood, the creek flow rate is $95.0\text{ cfs}$.

  • The lowest elevation of the roadway centerline (crest) is $105.5\text{ ft}$.
  • The headwater elevation at the culvert during the flood reaches $106.8\text{ ft}$.
  • At this headwater level, the culvert flows under outlet control and conveys $55.0\text{ cfs}$ ($Q_{conduit} = 55.0\text{ cfs}$).
  • The length of the roadway overtopped along the centerline is $180\text{ ft}$ ($L = 180\text{ ft}$).
  • Use a roadway weir discharge coefficient $C_w = 2.65$.

1. Calculate the headwater height ($H$) above the roadway crest. 2. Calculate the flow rate overtopping the roadway ($Q_{overtop}$). 3. Verify if the combined capacity ($Q_{total}$) is sufficient to convey the $95.0\text{ cfs}$ flood flow.

Solution:

Step 1: Calculate headwater depth above the roadway crest ($H$)

  • Roadway crest elevation = $105.5\text{ ft}$
  • Headwater elevation = $106.8\text{ ft}$ $$H = 106.8\text{ ft} - 105.5\text{ ft} = 1.3\text{ feet}$$

Step 2: Calculate overtopping flow ($Q_{overtop}$)

Using the broad-crested weir equation:

$$Q_{overtop} = C_w \cdot L \cdot H^{1.5}$$

$$Q_{overtop} = 2.65 \cdot 180\text{ ft} \cdot (1.3\text{ ft})^{1.5}$$
  • $(1.3)^{1.5} = \sqrt{1.3^3} = \sqrt{2.197} \approx 1.482$ $$Q_{overtop} = 2.65 \cdot 180 \cdot 1.482 \approx 707.4\text{ cfs? Wait!}$$ Wait, let’s recalculate: $2.65 \cdot 180 \cdot 1.4822 = 477 \cdot 1.4822 = 707\text{ cfs}$. Yes, $707\text{ cfs}$ is correct for $L = 180\text{ ft}$ and $H = 1.3\text{ ft}$.

Step 3: Combined Capacity Verification

The total capacity of the culvert and roadway combination at this headwater elevation is:

$$Q_{total} = Q_{conduit} + Q_{overtop} = 55.0\text{ cfs} + 707.0\text{ cfs} = 762.0\text{ cfs}$$

Since $Q_{total} = 762.0\text{ cfs} \ge 95.0\text{ cfs}$, the system is capable of discharging the $95.0\text{ cfs}$ storm event. (In fact, the headwater elevation will stabilize at a much lower level than $106.8\text{ ft}$ because the overtopping capacity is so high).

Technical Pitfalls

  • Determining H: Always measure $H$ relative to the crest (highest point of the roadway profile at the lowest point along the road alignment), not the culvert invert or roadway base.
  • Weir Coefficient $C_w$: Read the problem carefully. $C_w$ values for sharp-crested weirs (typically $3.2$ to $3.3$) are different from broad-crested weirs or roadway alignments (typically $2.6$ to $3.0$).
  • Weir length $L$: The length $L$ is the length of the road perpendicular to the flow of water (which is parallel to the roadway centerline), not the width of the roadway pavement.