8.2 Runoff Analysis

Once the drainage boundaries are established, the next step in site stormwater management is runoff analysis. The primary goal of runoff analysis is to determine the peak discharge rate and total volume of water that will run off a site during a specific rainfall event. This information is vital for sizing storm sewers, culverts, and detention basins. For the PE Construction exam, two of the most frequently tested runoff models are the Rational Method and the Soil Conservation Service (SCS) Curve Number method. Furthermore, managing this runoff during construction requires a solid understanding of erosion and sediment control systems to comply with environmental regulations.

The Rational Method (Q = CiA)

The Rational Method is widely used for estimating peak runoff rates from small, urban watersheds (typically less than 200 acres). The method is based on the assumption that the peak flow occurs when the entire watershed is contributing to the runoff, which happens after the rain has been falling for a duration equal to the time of concentration ($t_c$). The Rational Equation is:

$Q = C i A$

Where:

• $Q$ = Peak runoff rate (cfs)
• $C$ = Runoff coefficient (dimensionless, ranging from 0 to 1)
• $i$ = Rainfall intensity (inches/hour)
• $A$ = Drainage area (acres)

The runoff coefficient ($C$) represents the fraction of rainfall that becomes runoff. Impervious surfaces like asphalt or concrete have high $C$ values (0.70-0.95), whereas forested or grassy areas have low $C$ values (0.10-0.30). The rainfall intensity ($i$) is obtained from Intensity-Duration-Frequency (IDF) curves provided by local meteorological data. To use an IDF curve, you must know the design storm frequency (e.g., a 10-year or 25-year return period) and the storm duration, which is set equal to the watershed's time of concentration.

It is important to note the assumptions inherent in the Rational Method. It assumes that rainfall intensity is uniform over the entire watershed and constant throughout the duration of the storm. Furthermore, it assumes that the runoff coefficient $C$ remains constant, ignoring the fact that soils may become saturated over time, which would increase runoff. Because of these simplifications, the Rational Method is strictly limited to small drainage areas. The PE exam will often test your ability to calculate a weighted $C$ value for a site with mixed land uses before applying the Rational formula.

Worked Example: Rational Method

Problem: A 15-acre commercial development is being planned. The site consists of 10 acres of paved parking lot ($C = 0.90$) and 5 acres of landscaped grass ($C = 0.25$). The time of concentration for the site is 15 minutes. Based on the local 10-year IDF curve, a 15-minute duration corresponds to a rainfall intensity of 4.2 in/hr. Calculate the peak 10-year runoff from this site.

Solution: First, calculate the composite (area-weighted) runoff coefficient: $C_{comp} = \frac{(C_1 A_1) + (C_2 A_2)}{A_{total}}$ $C_{comp} = \frac{(0.90 \times 10) + (0.25 \times 5)}{15} = \frac{9.0 + 1.25}{15} = \frac{10.25}{15} \approx 0.683$

Now, apply the Rational Equation: $Q = C_{comp} \times i \times A$ $Q = 0.683 \times 4.2 \text{ in/hr} \times 15 \text{ acres}$ $Q \approx 43.0 \text{ cfs}$

The estimated peak runoff for the 10-year storm is 43.0 cubic feet per second.

SCS/NRCS Curve Number Method

For larger or more complex watersheds, the SCS (now NRCS) Curve Number (CN) method is preferred. Instead of just calculating peak flow, this method estimates the total volume of direct runoff. The method relies on the Curve Number, an empirical parameter (ranging from 30 to 100) based on soil type, land use, and antecedent moisture conditions. Higher CN values indicate greater runoff potential.

The Curve Number is a function of Hydrologic Soil Groups (HSG), designated as A, B, C, and D. Group A soils (like sands and gravels) have high infiltration rates and low runoff potential, while Group D soils (like heavy clays) have very low infiltration rates and high runoff potential. The antecedent runoff condition (ARC)—whether the soil is dry, average, or saturated from recent rains—also adjusts the CN value.

The method calculates runoff depth ($Q_{depth}$) based on total precipitation ($P$) and the initial abstraction ($I_a$), which accounts for interception, infiltration, and surface depression storage before runoff begins. The core equations are:

$S = \frac{1000}{CN} - 10$ $Q_{depth} = \frac{(P - 0.2S)^2}{P + 0.8S}$

(where $I_a$ is assumed to be $0.2S$). By tracking the volume over time, this method can generate a complete runoff hydrograph, essential for routing flows through storage basins.

Erosion Control Systems

Construction activities strip vegetation and expose soil, massively increasing erosion potential. A Stormwater Pollution Prevention Plan (SWPPP) is a federally mandated document that outlines how a construction site will manage runoff and prevent sediment from polluting nearby water bodies. Common Best Management Practices (BMPs) include:

• Silt Fences: Temporary, permeable fabric barriers trenched into the ground to intercept sediment-laden sheet flow. They allow water to pond and sediment to settle but are not designed for concentrated channel flow.
• Turbidity Curtains: Floating barriers deployed in water bodies to contain sediment plumes caused by construction activities in or near the water.
• Check Dams: Small, temporary dams constructed across a swale or drainage ditch to reduce the velocity of concentrated flow, thereby reducing channel erosion and promoting sediment deposition.

Beyond these, construction sites rely on stabilized construction entrances to prevent track-out of mud onto public roads. This usually involves a thick pad of large aggregate underlain by geotextile fabric. Additionally, temporary seeding and mulching are used to quickly stabilize exposed soils when grading operations pause. Understanding the application, limitations, and maintenance requirements of these BMPs is a frequent focus of PE Construction questions regarding site management and environmental compliance.