3.4 Erosion, Scour Protection & Slope Protection During Construction

Soil Erosion Physics & RUSLE Modeling

Construction activities disturb natural vegetative cover, expose bare soil matrix, and alter natural drainage paths, increasing soil erosion rates by up to $100 \text{ to } 1,000 \text{ times}$ baseline agricultural conditions. Controlling erosion and sediment runoff is a regulatory requirement under the Clean Water Act.

The Four Stages of Soil Erosion by Water

1. Raindrop (Splash) Detachment: High-velocity raindrops hit bare soil, dislodging fine soil particles and destroying soil structure.
2. Sheet Erosion: Shallow, uniform overland runoff transports detached particles down un-vegetated slopes in thin sheets.
3. Rill Erosion: Runoff concentrates into small micro-channels (rills) a few inches deep, accelerating flow velocity and soil detachment.
4. Gully Erosion: Rills coalesce into large, deep channels (gullies) that cannot be smoothed over by normal earthmoving equipment.

                      Progression of Soil Erosion
                      
   [Raindrop Splash] ---> [Sheet Flow] ---> [Rill Formation] ---> [Gully Erosion]
   (Particle Detachment)  (Thin Overland)   (Micro-Channels)      (Deep Channels)

The Revised Universal Soil Loss Equation (RUSLE)

The Revised Universal Soil Loss Equation (RUSLE) calculates average annual sheet and rill soil loss ($A$):

$A = R \cdot K \cdot LS \cdot C \cdot P$

where:

• $A$ = computed spatial soil loss per unit area (typically $\text{tons / acre / year}$ or $\text{metric tonnes / hectare / year}$).
• $R$ = Rainfall-Runoff Erosivity Factor: Quantifies kinetic energy and peak intensity of storm events.
• $K$ = Soil Erodibility Factor: Measures inherent soil susceptibility to erosion ($K$ ranges from $0.05$ for coarse gravels to $0.65$ for highly erodible silts).
• $LS$ = Topographic Factor: Combined factor for slope length ($L$) and slope steepness ($S$).
• $C$ = Cover Management Factor: Ratio of soil loss from land under specific vegetation/mulch relative to bare soil ($C = 1.0$ for bare tilled soil; $C = 0.005 - 0.05$ for erosion control blankets).
• $P$ = Support Practice Factor: Ratio of soil loss with erosion control practices (contouring, silt fences, terracing) relative to straight up-and-down slope cultivation.

Construction SWPPP & Temporary Best Management Practices (BMPs)

Under EPA National Pollutant Discharge Elimination System (NPDES) Construction General Permits (CGP), any project disturbing $1.0 \text{ acre}$ or more of land must implement a written Stormwater Pollution Prevention Plan (SWPPP).

Temporary Erosion & Sediment Control BMP Categories

                                  SWPPP BMPs
                                      |
        +-----------------------------+-----------------------------+
        |                                                           |
  [Erosion Control BMPs (Source Control)]        [Sediment Control BMPs (Trapping)]
  - Prevent soil particle detachment              - Traps detached sediment on site
  - Temporary seeding & Hydroseeding              - Silt Fences (ASTM D6459/D6462)
  - Erosion Control Blankets (ECBs)               - Straw Wattles & Fiber Rolls
  - Hydraulic Mulch / Bonded Fiber Matrix         - Sediment Basins & Sediment Traps
  - Interceptor Swales & Slope Drains             - Inlet Protection & Construction Entrances

Silt Fence Specification Rules (ASTM D6459 / D6462)

Silt fences are temporary sediment barriers consisting of synthetic geotextile fabric mounted on wooden or steel posts. They filter runoff and promote ponding so sediment settles out.

• Maximum Tributary Slope Length: Silt fences are limited to sheet flow applications with maximum slope length tributary of $100 \text{ ft}$ ($30 \text{ m}$).
• Trench Key-In Depth: The bottom flap of the geotextile MUST be buried in a trench at least $6 \text{ inches}$ ($150 \text{ mm}$) deep and backfilled with compacted soil to prevent undercutting flow ('washouts').
• Post Spacing: Maximum post spacing is $6 \text{ ft}$ ($1.8 \text{ m}$) for un-backed fabric, or $10 \text{ ft}$ ($3.0 \text{ m}$) if reinforced with wire mesh backing.

Slope Protection Materials & Hydroseeding

Turf Reinforcement Mats (TRMs) vs. Erosion Control Blankets (ECBs)

• Erosion Control Blankets (ECBs): Temporary degradable organic mats composed of straw, wood coconut fibers, or jute matrix stitched between photodegradable polypropylene netting. Designed to protect slopes ($3H:1V \text{ to } 2H:1V$) for 6 to 24 months while vegetation establishes.
• Turf Reinforcement Mats (TRMs): Permanent, non-degradable synthetic 3D matrices engineered to reinforce plant root zones. TRMs sustain high hydraulic shear stresses ($\tau > 10 \text{ psf}$ or $480 \text{ Pa}$) and flow velocities ($V > 15 \text{ ft/s}$ or $4.5 \text{ m/s}$), providing a flexible green alternative to rigid concrete lining.

Hydroseeding & Bonded Fiber Matrix (BFM)

Hydroseeding applies a slurry of seed, fertilizer, tackifier, and mulch pneumatically. Bonded Fiber Matrix (BFM) uses thermally refined wood fibers combined with cross-linked hydro-colloid tackifiers. Upon drying, BFM forms a water-resistant, breathable crust over steep, inaccessible slopes ($1H:1V$), reducing $C$-factors to $< 0.01$.

Scour Protection & Riprap Armoring Design

Channel scour and slope erosion occur when hydrodynamic bed shear stress ($\tau_0$) exerted by flowing water exceeds the critical shear stress ($\tau_c$) of soil particles.

Hydrodynamic Shear Stress Equation

For open channel flow with hydraulic radius $R_h$ and slope $S_0$:

$\tau_0 = \gamma_w \cdot R_h \cdot S_0$

where $\gamma_w = 62.4 \text{ pcf}$ ($9.81 \text{ kN/m}^3$).

Riprap Sizing Equation (FHWA HEC-11 / HEC-23)

To prevent scour around bridge abutments, culvert outlets, and drainage channels, angular stone riprap is sized based on median particle diameter ($d_{50}$):

$d_{50} = C \cdot \frac{V^2}{2 g (S_s - 1)}$

where:

• $V$ = mean channel velocity ($\text{ft/s}$ or $\text{m/s}$)
• $g$ = acceleration due to gravity ($32.2 \text{ ft/s}^2$ or $9.81 \text{ m/s}^2$)
• $S_s$ = specific gravity of stone (typically $2.65$)
• $C$ = stability coefficient ($C = 1.2$ for straight channels; $C = 1.5$ for steep bends or severe turbulence)

Filter Layer Criteria Beneath Riprap

Riprap MUST be underlain by a geotextile filter fabric or graded granular filter layer to prevent high-velocity water from piping and washing out fine subgrade soil particles beneath the stone. The Terzaghi retention criteria must be met:

$\frac{D_{15,\text{filter}}}{D_{85,\text{soil}}} \le 5 \quad \text{(Retention Criteria; prevents piping)}$ $\frac{D_{15,\text{filter}}}{D_{15,\text{soil}}} \ge 5 \quad \text{(Permeability Criteria; prevents excess uplift pore pressure)}$

Sediment Basin Hydraulics & Stokes' Law Settling

Sediment retention basins retain sediment-laden stormwater, reducing flow velocity so suspended soil solids settle out before effluent discharges off site.

Particle Settling Velocity (Stokes' Law)

For spherical soil particles falling through laminar fluid, settling velocity ($v_s$) is:

$v_s = \frac{g \cdot D_p^2 \cdot (\rho_s - \rho_w)}{18 \mu}$

where:

• $D_p$ = particle diameter ($\text{m}$ or $\text{ft}$)
• $\rho_s$ = density of soil solids ($2,650 \text{ kg/m}^3$)
• $\rho_w$ = density of water ($1,000 \text{ kg/m}^3$)
• $\mu$ = dynamic viscosity of water ($1.002 \times 10^{-3} \text{ N}\cdot\text{s/m}^2$ at $20^\circ\text{C}$)

Sediment Basin Surface Area Sizing

To capture particles with settling velocity $v_s$ at peak design inflow rate $Q_{\text{design}}$:

$A_s = \frac{Q_{\text{design}}}{v_s}$

where $A_s$ is the minimum required basin surface area at the outlet crest elevation.

Worked PE Engineering Example

Problem Statement

A construction site contractor is excavating a temporary discharge channel to convey stormwater runoff around an earthwork site. The channel hydraulic parameters for the peak 10-year storm design flow are:

• Mean channel velocity ($V$) = $11.5 \text{ ft/s}$
• Channel bed slope ($S_0$) = $0.025 \text{ ft/ft}$
• Hydraulic radius ($R_h$) = $2.2 \text{ ft}$
• Specific gravity of available angular granite riprap ($S_s$) = $2.65$
• Stability factor for channel bend ($C$) = $1.40$

Additionally, stormwater runoff draining into a temporary sediment basin has a peak flow rate of $Q = 15.0 \text{ cfs}$. The basin must capture silt particles down to $D_p = 0.02 \text{ mm}$ ($0.00002 \text{ m}$).

• Acceleration of gravity $g = 9.81 \text{ m/s}^2$ ($32.2 \text{ ft/s}^2$)
• Water density $\rho_w = 1,000 \text{ kg/m}^3$, soil density $\rho_s = 2,650 \text{ kg/m}^3$
• Dynamic viscosity of water $\mu = 1.00 \times 10^{-3} \text{ Pa}\cdot\text{s}$

Evaluate:

1. Hydrodynamic shear stress ($\tau_0$) along the channel bed.
2. Minimum required median riprap diameter ($d_{50}$) in inches.
3. Settling velocity ($v_s$) of the target silt particle in $\text{ft/s}$.
4. Minimum required sediment basin surface area ($A_s$) in $\text{square feet}$ and in $\text{acres}$.

Step-by-Step Solution

Step 1: Calculate Channel Hydrodynamic Shear Stress ($\tau_0$)

$\tau_0 = \gamma_w \cdot R_h \cdot S_0 = (62.4 \text{ pcf}) \times (2.2 \text{ ft}) \times (0.025) = 3.432 \text{ psf} \quad (164.3 \text{ Pa})$ Because $\tau_0 = 3.43 \text{ psf}$ exceeds the allowable shear stress of bare soil ($\approx 0.1 - 0.4 \text{ psf}$), riprap armoring is mandatory.

Step 2: Calculate Riprap Median Diameter ($d_{50}$)

Using the FHWA HEC-11 riprap sizing equation: $d_{50} = C \cdot \frac{V^2}{2 g (S_s - 1)} = 1.40 \times \frac{(11.5)^2}{2 \times 32.2 \times (2.65 - 1)} = 1.40 \times \frac{132.25}{64.4 \times 1.65} = 1.40 \times \frac{132.25}{106.26}$ $d_{50} = 1.40 \times 1.2446 \text{ ft} = 1.7424 \text{ ft}$ $\text{In Inches: } d_{50} = 1.7424 \text{ ft} \times 12 \text{ in./ft} = 20.91 \text{ inches} \approx 21 \text{ inches}$

Step 3: Calculate Particle Settling Velocity ($v_s$) using Stokes' Law

Convert inputs to SI units:

• $D_p = 0.02 \text{ mm} = 2.0 \times 10^{-5} \text{ m}$
• $\Delta \rho = \rho_s - \rho_w = 2,650 - 1,000 = 1,650 \text{ kg/m}^3$

$v_s = \frac{9.81 \times (2.0 \times 10^{-5})^2 \times 1,650}{18 \times 1.00 \times 10^{-3}} = \frac{9.81 \times (4.0 \times 10^{-10}) \times 1,650}{0.018} = \frac{6.4746 \times 10^{-6}}{0.018} = 3.597 \times 10^{-4} \text{ m/s}$

Convert settling velocity $v_s$ to $\text{ft/s}$: $v_s = 3.597 \times 10^{-4} \text{ m/s} \times 3.28084 \text{ ft/m} = 0.00118 \text{ ft/s}$

Step 4: Determine Minimum Sediment Basin Surface Area ($A_s$)

$A_s = \frac{Q}{v_s} = \frac{15.0 \text{ cfs}}{0.00118 \text{ ft/s}} = 12,711.86 \text{ ft}^2$

Convert surface area to acres ($1 \text{ acre} = 43,560 \text{ ft}^2$): $A_s = \frac{12,711.86 \text{ ft}^2}{43,560 \text{ ft}^2/\text{acre}} = 0.2918 \text{ acres} \approx 0.29 \text{ acres} \quad (12,712 \text{ sq ft})$

Design Summary: Specify Class III riprap with median diameter $d_{50} = 21 \text{ inches}$ underlain by a geotextile filter fabric, and construct a sediment basin with a minimum water surface area of $12,712 \text{ sq ft}$ ($0.29 \text{ acres}$).