12.2 Stormwater Collection Systems and Inlet Capacities

Stormwater Collection Systems and Inlet Capacities

Pavement Drainage and Stormwater Collection

Stormwater collection systems are critical for highway safety. Standing water on pavement (spread) can cause hydroplaning, reduce visibility due to spray, and compromise structural integrity of the subgrade. Design guidelines, such as FHWA HEC-22 (Circular 22), establish limits on the allowable spread ($T$) of stormwater onto the shoulder or travel lanes during a design storm (typically a 10-year or 5-year event).

Gutter Flow and Spread Calculations

Gutter flow is considered open-channel flow in a shallow, triangular channel formed by the pavement cross slope and the curb. Because the hydraulic radius of a shallow triangular flow section is not representative of typical open channels, Manning's equation is modified (Manning's modified formula or Izzard's equation) to calculate the gutter flow capacity:

$$Q = \frac{0.56}{n} S_x^{1.67} S_L^{0.5} T^{2.67}$$

Where:

• $Q$ = Gutter flow rate (cfs)
• $n$ = Manning's roughness coefficient (typically $0.015$ to $0.016$ for smooth concrete pavement)
• $S_x$ = Pavement cross slope (ft/ft)
• $S_L$ = Longitudinal slope of the roadway (ft/ft)
• $T$ = Width of flow or pavement spread (ft)

Solving for the pavement spread ($T$) for a given design runoff $Q$:

$$T = \left( \frac{Q \cdot n}{0.56 \cdot S_x^{1.67} \cdot S_L^{0.5}} \right)^{0.375}$$

If the cross-section has a depressed gutter (where the cross slope near the curb is steeper than the pavement cross slope), the flow is divided into the gutter section and the pavement section. The total flow is $Q = Q_w + Q_s$, where $Q_w$ is the flow in the depressed gutter width ($W$) and $Q_s$ is the flow on the remaining pavement spread.

Inlet Types and Hydraulics

Inlets are placed at low points (sumps/sags) and on continuous grades to intercept gutter flow and convey it into the underground storm sewer system. The capacity of an inlet depends on its type, location, and geometry.

Inlets on Continuous Grade

On a continuous grade, inlets rarely intercept 100% of the gutter flow. The performance is defined by its interception efficiency ($E$):

$$E = \frac{Q_i}{Q}$$

Where $Q_i$ is the intercepted flow (cfs) and $Q$ is the total gutter flow (cfs). The remaining flow that bypasses the inlet is the bypass or carryover flow ($Q_b = Q - Q_i$).

1. Grate Inlets on Grade: Grate capacity depends on the portion of flow passing directly over the grate (frontal flow) and the flow passing along the side (side flow).
   • Frontal Flow Ratio ($E_o$): The ratio of frontal flow ($Q_w$) to total gutter flow ($Q$): $$E_o = \frac{Q_w}{Q} = 1 - \left( 1 - \frac{W}{T} \right)^{2.67}$$ Where $W$ is the grate width (ft) and $T$ is the spread (ft).
   • Interception Efficiency ($E$): $$E = R_f E_o + R_s (1 - E_o)$$ Where $R_f$ is the frontal flow interception efficiency (drops from 1.0 to less if velocity exceeds the splash-over velocity) and $R_s$ is the side flow interception efficiency (typically $0.1$ to $0.2$).
2. Curb Inlets on Grade: Curb inlets are highly effective at intercepting flow and are less prone to clogging. The length of curb opening required for 100% interception ($L_T$) is given by: $$L_T = 0.6 Q^{0.42} S_L^{0.3} \left( \frac{1}{n S_x} \right)^{0.6}$$ If the actual length of the curb inlet ($L$) is less than $L_T$, its efficiency is calculated as: $$E = 1 - \left( 1 - \frac{L}{L_T} \right)^{1.8}$$
3. Combination Inlets on Grade: Consist of a curb opening and a grate. On grade, their capacity is generally assumed to be equal to the grate alone if the grate is placed adjacent to the curb opening. However, placing the curb opening upstream of the grate increases total capacity and reduces clogging.

Inlets in a Sump (Sag)

In a sump or sag, water pools around the inlet. The inlet operates under two distinct hydraulic regimes depending on the depth of ponding ($d$):

1. Grate Inlets in Sump:
   • Weir Flow (Shallow Depths, $d \le 0.4\text{ ft}$): Capacity is limited by the perimeter of the grate ($P$, excluding the side against the curb): $$Q_i = C_w P d^{1.5} = 3.0 P d^{1.5}$$
   • Orifice Flow (Deep Depths, $d \ge 1.4\text{ ft}$): Capacity is limited by the clear opening area ($A_g$): $$Q_i = C_o A_g \sqrt{2 g d} = 0.67 A_g \sqrt{2 g d}$$
   • Transition ($0.4\text{ ft} < d < 1.4\text{ ft}$): Flow is transitional, and the lesser of the weir and orifice capacities is typically used.
2. Curb Inlets in Sump:
   • Weir Flow ($d \le h$, where $h$ is curb opening height): $$Q_i = C_w L d^{1.5} = 3.0 L d^{1.5}$$ (Or $2.3 L d^{1.5}$ for undepressed curb inlets).
   • Orifice Flow ($d \ge 1.4 h$): $$Q_i = C_o A_i \sqrt{2 g \left( d - \frac{h}{2} \right)} = 0.67 L h \sqrt{2 g \left( d - \frac{h}{2} \right)}$$

Storm Sewer Pipe Design and Velocities

Once intercepted, stormwater flows through a network of pipes (laterals and trunks) and manholes/junctions to an outfall.

• Design Flow ($Q$): Pipe diameters are sized using the Rational Method ($Q = C I A$) where the time of concentration ($t_c$) is computed for the critical pathway.
• Capacity Sizing: Manning's equation is used to size the pipe to flow gravity full under gravity flow conditions: $$Q = \frac{1.486}{n} A R^{2/3} S_0^{0.5}$$
• Velocity Criteria:
  • Minimum Velocity (Self-Cleansing): Pipes must be designed to maintain a full-flow velocity of at least $2.0\text{ fps}$ to prevent the deposition of sand, grit, and silt.
  • Maximum Velocity: Velocities must not exceed $15.0\text{ fps}$ to prevent concrete pipe scour and joints from separating due to high shear forces.

Hydraulic and Energy Grade Lines

Calculations of the Hydraulic Grade Line (HGL) and Energy Grade Line (EGL) are performed starting from the downstream outfall and working upstream.

• Energy Grade Line (EGL): Represents the total energy head of the water: $$EGL = \text{Elevation} + \text{Depth} + \frac{V^2}{2g}$$
• Hydraulic Grade Line (HGL): Represents the potential and pressure head: $$HGL = \text{Elevation} + \text{Depth} = EGL - \frac{V^2}{2g}$$ If the pipe is flowing under pressure (surcharged), the depth term represents the pressure head ($P/\gamma$) above the pipe soffit (top of pipe).
• Junction and Manhole Head Losses: Minor losses occur at bends, expansions, contractions, and junction manholes. The loss ($H_j$) is calculated as: $$H_j = K \frac{V_o^2}{2g}$$ Where $K$ is the junction loss coefficient (typically $0.2$ to $0.9$ depending on flow deflection angle and pipe diameter ratios) and $V_o$ is the velocity in the outlet pipe.
• Starting HGL: The backwater analysis begins at the outfall. If the outfall discharges into a body of water with a known water surface elevation (tailwater), the HGL starts at that tailwater elevation. If the tailwater is below the critical depth of the pipe, the starting HGL is $\max(TW, (d_c + D)/2)$.