4.1 Fundamentals of Erosion & the Sedimentation Cycle

4.1 Fundamentals of Erosion & the Sedimentation Cycle

Quick Summary: Soil erosion and sedimentation represent a continuous, three-phase physical cycle: detachment, transport, and deposition. While natural (geologic) erosion slowly shapes landscapes at rates balanced by pedogenesis (soil formation), human land disturbance causes accelerated erosion, generating sediment yields 20 to 1,000 times higher than native background levels. Suspended sediment is the single largest non-point source water pollutant by volume in North America, degrading aquatic habitats, attenuating light penetration, and acting as a primary transport vector for nutrients and heavy metals. Understanding soil particle physics—specifically Stokes' Law, Reynolds numbers, and colloidal zeta potential—is essential for designing effective sediment traps, basins, and chemical flocculation systems.

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The Three-Phase Erosion & Sedimentation Cycle

Every erosion event, regardless of whether it is driven by falling rain, concentrated stormwater runoff, streamflow, or wind, progresses through three distinct, interrelated physical phases:

Phase 1: Detachment  ➔  Phase 2: Transport  ➔  Phase 3: Deposition

[Raindrop / Shear Forces]    [Moving Fluid Energy]       [Quiescent Conditions]
  Dislodges particles         Conveys suspended mass      Gravitational settling
  from soil aggregate         along flow pathway          exceeds drag & lift

1. Detachment (The Initiation Phase)

Detachment is the mechanical dislodging of individual soil grains, mineral aggregates, or organic fragments from the consolidated soil matrix. On bare construction sites, detachment is initiated primarily by the kinetic impact of falling raindrops or by the tractive boundary shear stress ($\tau$) exerted by moving surface water or wind. For detachment to occur, the applied mechanical force must overcome the internal shear strength of the soil, which is governed by inter-particle cohesion ($c$), internal friction angle ($\phi$), biological root anchoring, and chemical cementing agents (such as iron oxides and organic matter).

2. Transport (The Conveyance Phase)

Once detached, soil particles become mobile and are transported across the landscape by a fluid medium—predominantly stormwater runoff or air currents. The capacity of the moving fluid to transport detached sediment is known as the sediment transport capacity ($T_c$). Transport capacity is a direct mathematical function of fluid velocity ($V$), flow depth ($y$), turbulence, and hydraulic gradient ($S$). Transport continues as long as the fluid's kinetic energy maintains sufficient hydrodynamic drag and vertical lift forces to keep particles in motion (either in suspension, saltation, or bedload rolling).

3. Deposition (The Sedimentation Phase)

Deposition occurs when the hydraulic energy of the conveying fluid drops below the threshold required to sustain transport—specifically, when gravitational body forces ($F_g$) exceed the combined fluid drag ($F_d$) and lift ($F_l$) forces. This occurs when overland flow enters a flat grade, encounters dense vegetative filtration, spreads out across a wide floodplain, or enters an engineered impoundment (such as a temporary sediment trap or sediment basin). As flow decelerates ($V \to 0$), the largest, densest particles settle out first, followed progressively by smaller fractions.

The Relationship Between Transport Capacity and Sediment Load

The dynamics of erosion and sedimentation along any flow path are governed by the dynamic balance between Sediment Load ($L$) (the mass of detached soil currently moving in the flow) and Transport Capacity ($T_c$):

• Detachment Dominant ($T_c > L$): When the energy of the flow exceeds the current sediment load, the excess fluid energy attacks the channel boundary or bare slope face, causing active scouring, rilling, and downcutting.
• Dynamic Equilibrium ($T_c = L$): The flow is fully saturated with sediment; neither net erosion nor net deposition occurs.
• Deposition Dominant ($T_c < L$): When runoff decelerates (e.g., passing through a compost filter sock, entering a vegetative buffer, or discharging into a basin), transport capacity plunges below the sediment load ($T_c < L$), compelling excess suspended particles to settle out as sediment deposits.

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Geologic (Natural) Erosion vs. Accelerated Erosion

A central premise of erosion science is the fundamental distinction between natural background rates of soil denudation and human-induced land degradation.

Geologic Erosion (Natural Background)

Geologic erosion is the normal, continuous geomorphic weathering and denudation process that has operated throughout Earth's history without anthropogenic disruption. Over centuries, natural geologic erosion is roughly in dynamic equilibrium with pedogenesis (the natural formation of new soil through mineral rock weathering and organic matter decomposition). In undisturbed temperate forests, undisturbed prairies, and mature scrublands, geologic erosion rates typically generate less than 0.01 to 0.5 tons of soil loss per acre per year (0.02 to 1.1 metric tons/hectare/year). Dense vegetative canopies, thick organic leaf litter (duff), and deep root systems absorb raindrop impacts, promote rapid infiltration, and anchor soil particles.

Accelerated (Anthropogenic) Erosion

Accelerated erosion occurs when human intervention—such as urban construction, highway grading, mining, agricultural tillage, or silvicultural clear-cutting—strips the protective vegetative mantle, compacts the subgrade, and alters natural hydrologic flow patterns. When soil is stripped bare and subjected to heavy equipment compaction, infiltration capacity plummets, surface runoff volumes multiply by 200% to 500%, and soil aggregates are directly exposed to the violent forces of rainfall impact and concentrated runoff.

Quantifying Accelerated Construction Erosion Rates

Empirical research across North America consistently confirms that active construction sites generate the highest specific sediment yields of any major land-use category:

• Mass Construction Sites: Actively graded, un-stabilized construction sites regularly yield 20 to 200 tons of sediment per acre per year, and under extreme storm conditions on steep slopes with erodible soils, sediment yields can exceed 500 to 1,000 tons per acre per year.
• Comparative Ratio: Construction sites routinely generate sediment at rates 20 to 1,000 times greater than undisturbed agricultural croplands, and up to 2,000 to 10,000 times greater than undisturbed mature forested watersheds.
• Cumulative Impact: Although construction activities typically occupy less than 5% of a regional watershed's total geographic area, construction runoff frequently contributes more than 50% of the total annual sediment load delivered to downstream receiving waters during periods of rapid urban expansion.

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Environmental Impacts of Sedimentation on Aquatic Ecosystems

Suspended and deposited sediment is legally classified as a pollutant under the federal Clean Water Act (CWA). When sediment-laden runoff escapes construction perimeters, it inflicts severe physical, biological, chemical, and economic damage on receiving water bodies.

1. Physical and Optical Degradation: Turbidity & PAR Attenuation

• Turbidity Spikes: Suspended mineral particles scatter and absorb light, causing high turbidity (measured in Nephelometric Turbidity Units, NTU). While pristine streams often exhibit turbidities below 5 to 10 NTU, construction runoff regularly discharges effluent exceeding 1,000 to 5,000+ NTU.
• Reduction of Photosynthetically Active Radiation (PAR): Turbid water blocks PAR from penetrating the water column. Submerged aquatic vegetation (SAV)—such as eelgrass, wild celery, and pondweeds—is deprived of sunlight and dies off. The loss of SAV eliminates critical nursery habitat for juvenile fish and drastically reduces dissolved oxygen ($DO$) generation through photosynthesis.
• Thermal Modification: Suspended dark mineral particles absorb solar radiation, warming the surface water column. Elevated water temperatures decrease oxygen solubility and trigger severe physiological thermal stress in cold-water fish species (e.g., brook trout, salmon).

2. Biological Smothering: Benthic Invertebrates & Spawning Gravels

• Clogging of Interstitial Gravel Spaces: Clean, coarse gravel beds in riffle environments contain open interstitial spaces that circulate oxygenated water. Fine sediment settling onto stream bottoms infiltrates these voids (interstitial sedimentation or embeddedness).
• Smothering Salmonid Redds: Salmonids (trout and salmon) excavate depressions (redds) in clean gravels to deposit eggs. Fine silt and clay infiltration blankets the redds, creating an impermeable cap that blocks intragravel water exchange. This deprives developing embryos of dissolved oxygen and physically traps newly hatched alevins, resulting in 90% to 100% mortality.
• Decimation of Benthic Macroinvertebrates: Benthic insects (such as mayflies [Ephemeroptera], stoneflies [Plecoptera], and caddisflies [Trichoptera]—the "EPT" clean-water index taxa) dwell within interstitial gravel voids. Deposited sediment eliminates their clinging habitat and smothers their breathing gills, collapsing the primary food web supporting sport and commercial fisheries.
• Abrasive Gill Damage: Suspended angular quartz silt and sand particles act as an abrasive slurry, scouring and tearing the delicate gill lamellae of fish, inducing chronic mucus secretion, respiratory impairment, fungal infections, and direct asphyxiation.

3. Hydraulic and Infrastructure Siltation

• Reservoir Capacity Depletion: Sediment accumulation displaces active storage volume in municipal water supply and flood-control reservoirs across the nation, reducing drought resilience and flood buffering capacity.
• Navigation Channel Shoaling: Deposition in navigable rivers, estuaries, and commercial shipping channels forces continuous, multi-million-dollar maintenance dredging operations funded by the U.S. Army Corps of Engineers.
• Storm Sewer Clogging: Infilled storm drain pipes, culverts, and bridge openings severely restrict hydraulic conveyance ($Q = A \cdot V$), inducing premature urban street flooding and infrastructure washouts.

4. Chemical Vectors: Adsorption of Toxins and Nutrients

Soil particles—specifically cohesive clay platelets and colloidal organic matter—carry high specific surface areas and strong chemical surface charges. Fine sediment acts as a chemical sponge, adsorbing and transporting non-point source pollutants:

• Phosphorus Transport: Phosphorus, the primary limiting nutrient in freshwater lakes and rivers, binds tightly to fine sediment particles (iron and aluminum mineral oxides). When sediment discharges into lakes, phosphorus desorbs, fueling massive eutrophication, toxic cyanobacteria (blue-green algae) blooms, and subsequent deep-water hypoxia / anoxia.
• Heavy Metals and Hydrocarbons: Hydrophobic organic pollutants, polycyclic aromatic hydrocarbons (PAHs), vehicle oils, and heavy metals (copper, lead, zinc, nickel) bind electrostatically to sediment surfaces, concentrating toxic compounds in downstream estuarine muds.

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Soil Particle Physics: Settling Velocity & Stokes' Law

Designing sediment capture devices—such as temporary sediment traps, detention basins, and baffle chambers—requires a precise mathematical understanding of particle sedimentation physics.

The Mathematical Derivation of Stokes' Law

Under quiescent (still water) conditions, an individual spherical particle settling through a viscous fluid accelerates until the downward gravitational body force is exactly balanced by the upward buoyant force and hydrodynamic viscous drag force. For small particles settling in a laminar regime, this equilibrium is expressed by Stokes' Law:

$v_s = \frac{g (\rho_p - \rho_w) d^2}{18 \mu}$

Where:

• $v_s$ = Settling velocity of the particle ($\text{cm/s}$ or $\text{m/s}$)
• $g$ = Acceleration due to gravity ($981\text{ cm/s}^2$ or $9.81\text{ m/s}^2$)
• $\rho_p$ = Mass density of the soil particle (standard quartz soil mineral density is typically taken as $2.65\text{ g/cm}^3$ or $2,650\text{ kg/m}^3$)
• $\rho_w$ = Mass density of the fluid ($1.00\text{ g/cm}^3$ or $1,000\text{ kg/m}^3$ for water at 68°F / 20°C)
• $d$ = Effective spherical particle diameter ($\text{cm}$ or $\text{m}$)
• $\mu$ = Dynamic viscosity of water ($0.01002\text{ poise}$ or $1.002 \times 10^{-3}\text{ Pa}\cdot\text{s}$ at 68°F / 20°C)

Critical Insights from Stokes' Law

1. The Diameter-Squared Relationship ($v_s \propto d^2$): Settling velocity is proportional to the square of the particle diameter. If a particle's diameter decreases by a factor of 10 (e.g., from a fine sand of 0.1 mm down to a medium silt of 0.01 mm), its settling velocity decreases by a factor of $10^2 = 100$. If diameter drops by a factor of 100 (from 0.1 mm sand to 0.001 mm clay), its settling velocity drops by a factor of $10,000$.
2. Viscosity and Water Temperature Dependence: Dynamic viscosity ($\mu$) is highly temperature-dependent. Cold water is significantly more viscous than warm water. In near-freezing winter stormwater (35°F / 1.7°C, where $\mu \approx 1.79 \times 10^{-3}\text{ Pa}\cdot\text{s}$), settling velocities are approximately 44% slower than in summer stormwater (77°F / 25°C, where $\mu \approx 0.89 \times 10^{-3}\text{ Pa}\cdot\text{s}$). Consequently, sediment basins designed for summer storm parameters perform poorly during winter conditions.

The Reynolds Number Limit of Stokes' Law

Stokes' Law is valid only when the settling flow around the particle remains strictly laminar. The boundary flow regime is defined by the Particle Reynolds Number ($Re_p$):

$Re_p = \frac{\rho_w v_s d}{\mu}$

Stokes' Law strictly applies when $Re_p < 0.5$ to $1.0$. This laminar condition holds true for fine sands, silts, and clays ($d < 0.1\text{ mm}$). For larger coarse sand grains ($d > 0.5\text{ mm}$) and gravels, flow separation generates turbulent wake eddies ($Re_p \gg 1$), causing hydrodynamic drag to exceed viscous drag. These larger particles settle at rates lower than predicted by Stokes' Law, requiring empirical transition-flow or Newton's law drag equations.

Critical Shear Stress ($\tau_c$) & The Shields Criterion

While Stokes' Law governs particle settling in still water, entrainment (resuspension) in flowing water is governed by the boundary shear stress ($\tau$). The threshold boundary shear stress required to initiate detachment and movement of a particle resting on the bed is the critical shear stress ($\tau_c$), calculated using the dimensionless Shields parameter ($\theta_c$):

$\tau_c = \theta_c (\gamma_s - \gamma_w) d$

Where $\gamma_s$ is the unit weight of the soil, $\gamma_w$ is the unit weight of water, and $d$ is particle diameter. Coarse non-cohesive sands and gravels resist scour purely through submerged particle weight and inter-locking friction angle. Conversely, cohesive clays resist scour through chemical electrochemical bonds, exhibiting much higher critical shear stress values than would be predicted based solely on their tiny physical diameter.

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The Colloid Challenge: Zeta Potential & Brownian Motion

Conventional sediment basins and silt fences rely exclusively on passive gravitational settling. While highly effective at capturing sand and coarse silt, gravity-alone sediment basins are physically incapable of settling fine colloidal clay particles within practical field retention times.

Why Colloidal Clays Remain in Permanent Suspension

1. Microscopic Mass vs. Fluid Viscosity: Colloidal clay platelets ($d < 0.002\text{ mm}$ or $< 2\text{ \mu m}$) have near-zero physical mass. Their Stokes settling velocity is less than $10^{-6}\text{ m/s}$ (requiring months to years to settle through a single foot of water).
2. Brownian Motion: At colloidal scales, the kinetic thermal energy of ambient water molecules bombarding the clay platelet exceeds the minuscule downward gravitational body force. This continuous, random molecular bombardment—known as Brownian motion—keeps colloidal particles in permanent suspension.
3. Electrostatic Repulsion and Zeta Potential: Clay minerals (such as montmorillonite, illite, and kaolinite) consist of tetrahedral silica and octahedral alumina crystalline sheets. Isomorphous substitution within the crystal lattice imparts a permanent net negative electrical surface charge to the planar faces of the clay platelets. In water, these negative charges attract a tightly bound layer of positive counter-ions (the Stern layer) surrounded by a diffuse ionic cloud, collectively termed the electric double layer (EDL). The electrical potential measured at the slipping boundary of this double layer is called the Zeta Potential ($\zeta$) (typically ranging from $-15\text{ mV}$ to $-50\text{ mV}$ in turbid stormwater). Because like charges repel, approaching clay particles experience powerful electrostatic repulsive forces that prevent them from colliding and aggregating into larger, settleable flocs.

Chemical Coagulation and Flocculation

To settle colloidal clay turbidity, practitioners must introduce chemical treatment agents:

• Coagulation (Charge Neutralization): Adding trivalent metal salts (such as aluminum sulfate [alum, $\text{Al}_2(\text{SO}_4)_3$] or ferric chloride [$\text{FeCl}_3$]) introduces high-valence cations ($\text{Al}^{3+}$, $\text{Fe}^{3+}$) that compress the diffuse electric double layer, collapsing the zeta potential toward zero and eliminating the electrostatic repulsion barrier.
• Flocculation (Polymer Bridging): Introducing long-chain synthetic polymers, primarily anionic or cationic Polyacrylamides (PAM), creates physical polymer bridges between neutralized clay platelets. These bridges bind microscopic colloids into large, visible aggregates (flocs) with effective diameters exceeding $0.5\text{ to }2.0\text{ mm}$. The flocs settle rapidly out of the water column in accordance with Stokes' Law within minutes rather than months.

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Comprehensive Comparison: Soil Particle Settling Characteristics

The following engineering table details the physical dimensions, surface characteristics, theoretical Stokes settling velocities, and practical field settling durations across the complete spectrum of mineral soil fractions in standard 68°F (20°C) water.

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On-Site Impacts: What Erosion Costs the Soil Resource

Downstream impacts get the regulatory attention, but the CPESC body of knowledge lists impacts of erosion on soil resources as its own competency, separate from impacts on water and air. Erosion is selective: raindrop splash and shallow sheet flow preferentially remove the finest, lightest, most chemically active fraction — clay, silt, and particulate organic matter — and leave the coarse sand and gravel behind. Every consequence follows from that selectivity.

The practical CPESC conclusion. Because the eroded fraction is the fraction that made the soil productive, the standard remedies — stripping, stockpiling, and replacing topsoil; keeping ground covered; and amending with compost — are not landscaping niceties. They are the only economical way to preserve a growing medium once it has been lost, which is why topsoil management is a specification item and not a field decision.