Solutions to Provide Flood Relief to Residents of this watershed area included a stream diversion to deflect high flows From the Lower Reach of the Main Tributary.

The city of Charlotte in North Carolina contracted

## Stream Diversion Concept

One of the major elements of the McAlway-Churchill flood mitigation project is a stream diversion to deflect high flows from the lower reach of the main tributary, thereby providing flood relief to seven residences along the stream corridor. The stream diversion will consist of a low weir^{1} wall, 18 feet in length and 1.5 feet above the stream bed invert, that will act as the hydraulic control. Immediately downstream of the weir will be a bypass trunk line consisting of a 4 foot high x 18.5 foot wide reinforced concrete box culvert about 373 feet in length that will convey the diverted flow under Meadowbrook Road which runs along the stream, and discharge it to an large open area for energy dissipation and flow dispersion (see Figure 1). The discharged flow will pass over a concrete overflow wall 125 feet in length that will be constructed at grade to promote a wide dispersal of the flow into the existing undeveloped floodplain within the Catawba Lands Conservancy preserve adjacent to Briar Creek. The design of the diversion and bypass trunk line involved a number of technical challenges including an unavoidable conflict between the bypass trunk line and a gravity sanitary sewer main, and a diversion structure that was hydraulically complex to model.

## Design Challenges

### Gravity Sanitary Sewer

The existing 8-inch gravity sanitary sewer main in Meadowbrook Road could not be horizontally or vertically relocated. Therefore, the bypass trunk line was designed to accommodate the conflict by allowing the sanitary main to pass through the new box culvert. A 12-inch steel casing will be provided to protect the sewer main within the culvert opening. The vertical alignment of the bypass trunk line was set so that the sewer main will be located within the upper part of the box culvert trunk line. Hydraulic calculations were performed to confirm that the sewer main will be above the flow in the culvert. Design of this conflict was coordinated with Charlotte-Mecklenburg Utilities Department, the owner of the sewer main.

### Modeling a Diversion Structure

A hydraulic model of the watershed stream system was created for the project using the HEC-RAS program (Hydraulic Engineering Center – River Analysis System) developed by the U.S. Army Corps of Engineers. To determine the flood mitigation benefits that would be obtained using the stream diversion, the diversion was modeled in HEC-RAS as a “lateral structure” that removed flow from the main tributary. An “inline” weir is constructed across a watercourse, while a “lateral” weir is constructed along one of the stream banks, parallel to the flow of the water, such that flow over the weir is removed from the watercourse. The diversion was defined in HEC-RAS as a water surface elevation (WSE) vs. discharge (Q) rating curve. The main challenge in designing this diversion was to take into account the many factors that influence the hydraulic performance of the weir. Each of these factors is discussed below.

#### End contractions

The formula for calculating flow over a weir is generally expressed as:

Where Q is the calculated discharge, C is the coefficient of discharge, L is the effective length of the weir, and H is the head over the weir. Since the approach flow to the weir is wider than the weir itself, the weir will perform as a “contracted” weir, such that the effective length of the weir decreases as the head increases. To mitigate this effect such that L will equal the actual length of the weir for all values of H, the diversion was designed as a “Cipolletti” weir, which is trapezoidal in shape with end walls at each side that are not vertical but constructed at a slope of 1:4 inclining outward from the base, horizontal to vertical (Brater & King, 1976). See Figure 2.

#### Coefficient of discharge

The coefficient of discharge is a critical parameter in evaluating the hydraulic performance of a weir since the discharge over the weir is directly proportional to the coefficient of discharge. The value of this coefficient can vary significantly depending on whether the weir will function as a “broad-crested” or “sharp-crested” weir. When flow over the weir is supported by the weir crest, it is considered “broad-crested”. When the head over a weir becomes one to two times the breadth (thickness) of the weir crest, the flow separates from the crest and the weir performs as a sharp-crested weir. This ratio ranges from 1.5 to 3.5 for the proposed diversion weir. Therefore, the Rehbock formula for sharp-crested weirs (Chow, 1959) was used to determine the coefficient of discharge:

Where H is the head over the weir, and h is the height of the weir over the stream bed. As the above formula indicates, the coefficient of discharge varies with the head at the weir. Therefore, in developing the performance rating curve for the diversion, the coefficient of discharge needed to be calculated at each successive WSE.

#### Weir submergence

Headwater at the upstream end of the box culvert under Meadowbrook Road will be higher than the weir crest elevation for the design discharges, causing the weir to be “submerged”. Submergence of a weir reduces its hydraulic capacity such that the discharge under submerged conditions is less than the discharge calculated assuming no submergence. In order to calculate the actual discharge during submerged conditions, the Villemonte equation (Brater & King, 1976) was used:

Where Q is the submerged discharge, Q1 is the unsubmerged discharge, H1 is the head on the weir on the upstream side, and H2 is the head on the downstream side. To determine the value of H2, HEC-RAS was used to analyze the box culvert downstream of the weir over a range of discharges to establish the WSE vs. Q rating curve immediately upstream of the culvert (see Figure 3). Since the value of H2 can thus be determined for any discharge, the unsubmerged and submerged values of Q can be calculated through iterative methods. This was accomplished using a spreadsheet to compute the final WSE vs. Q rating curve for the diversion weir. This rating curve information was then used to define the lateral structure in the HEC-RAS model so that the amount of flow diverted from the stream for the 2, 10, 25, 50, and 100-year storms could be calculated.

#### Model Stability

The final challenge in designing the diversion was overcoming the inherent instability of the HEC-RAS model, which used an iterative process to determine the flow split at the diversion for each storm event scenario. Initial attempts to run the model were not successful since HEC-RAS was not able to converge on a solution at the diversion. This problem was solved by recognizing the information provided by the diversion rating curve need not be evenly distributed throughout the range of possible water surface elevations, but should be concentrated in “clusters” of information near the likely occurrences of the peak water surface elevations (see Figure 4). Once this was done, the HEC-RAS model converged on a solution for each storm event without any problems.

## Summary

Although much more challenging to design than a traditional stream widening approach, the stream diversion and bypass trunk line will not only provide flood mitigation benefits to the neighborhood, but will do so with less impact to the environment and local residents, and much less cost to the city than the competing alternative of widening the existing channel for a distance of 1300 feet. It is estimated that the stream diversion option saved over $1 million in comparison to the stream widening alternative. The project also enhances the resiliency of the city’s infrastructure in several ways. First, the project reduces flood impacts to Meadowbrook Road, reducing the frequency of road closures due to flooding and maintaining access for both residents and emergency personnel. Second, the project reduces flood impacts to several residential structures, which reduces risks to local residents as well as emergency responders. Third, the project reduces financial losses for the city that result from repetitive flood impacts.

^{1}A weir is a typically horizontal structure used for controlling or measuring the flow of water. In most cases, weirs take the form of obstructions smaller than most conventional dams, pooling water behind them while also allowing it to flow steadily over their tops.