Chapter 2: Transportation and Deposition of

Siliciclastic Sediment

• Fluid Flow

• Particle transportation in a fluid

• Particle transport by sediment gravity flows

Mass-wasting processes such as slides and slumps often provide an initial role in moving sediment short distances down steep slopes to sites where other transport processes take over.

Types of fluids

•Newtonian: No strength and no change in viscosity as shear rate increases (i.e. water).

•Non-Newtonian: No strength, viscosity does change with shear rate (i.e. water-saturated non-compacted muds)

•Bingham plastics: Has strength with a yield point. After yield strength is exceeded, behaves as a Newtonian fluid with a constant viscosity. (i.e. Debris flow)

Fundamentals of Fluid Flow

Fluid Density (ρ) = mass/unit volume (g/cm2).

For water at 4°C, ρ = 1 g/cm2.

Fluid Dynamic Viscosity (μ) = τ/(du/dy)

For water at 20°C μ = 1 poise = dyne · s/cm2.

Fluid Kinematic Viscosity (ν) = μ/ρ

Figure 2.1.1

Shear Stress (τ) = μ(du/dy) unit = dyne = g·cm/s2 (unit of force).

A

B

Laminar versus Turbulent Flow

Laminar flow: sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers.

Turbulent flow: faster moving, highly distorted flowing fluid. Fluid moves in a series of constantly changing & deforming masses (eddies) in which there is sizable transport of fluid perpendicular to the mean direction of flow.

Laminar Flow

The beginning of turbulent flow

Turbulent Flow

The flow is more turbulent above the streambed as friction is strongest in contact with the bed – resulting in laminar flow.

http://www.biophysics.uwa.edu.au/turbulence/animations/Miko_1.gif

Eddy viscosity (apparent viscosity) (η): refers to the internal friction generated as laminar (smooth, steady) flow becomes irregular and turbulent.

If we take into consideration the effects of eddy viscosity, Shear stress (τ) for a turbulent flow becomes:

τ = (μ + η)du/dy

Most flow of water and air, under natural conditions, is turbulent, although flow of ice and mud are essentially laminar.

Why?

How do we determine if a flow is laminar or turbulent?

Reynolds number (Re) = UL/ν

Where U = mean flow velocity. L = some length that characterizes the scale of flow (commonly water depth) & ν = kinematic viscosity.

The transition from laminar to turbulent flow takes place above a critical value of Re. Depending on the boundary conditions (channel depth and geometry), the critical value is usually between 500 & 2000.

Boundary layer: the region of fluid next to the boundary across which the fluid velocity grades from that of the boundary (usually zero) to that of the unaffected part of the flow.

Boundary (Bed) Shear Stress (τo) = γρghs = γRhs

Where γ = the specific gravity of the fluid, ρ = fluid density, g = gravitational acceleration, h = flow depth, s = slope & Rh = hydraulic radius (cross section area/wetted perimeter).

Boundary shear stress: a force that opposes the motion of the fluid at the bed surface. It is a function of the density of the fluid, slope of the bed and the fluid depth.

The effects of gravity also play an important part in the role of fluid flow. Gravity influences the way in which a fluid transmits surface waves.

The ratio between inertial and gravity forces is the Froude number (Fr)

Fr = U/√(gL)

Where U = the mean velocity of flow, g = acceleration of gravity & L = fluid depth.

When Fr < 1 gravity waves can travel upstream. The flow is tranquil, streaming or subcritical.

When Fr > 1 gravity waves cannot be propagated upstream. The flow is rapid, shooting or supercritical.

Particle Transport by Fluids

Entrainment: the process involved in lifting resting grains from the bed or otherwise putting them into motion.

Critical threshold: the point at which the downcurrent transport of the grains on the bed is common everywhere on the bed.

Figure 2.2

A. Forces acting during fluid flow on a grain resting on a channel bed with grains of similar size.

B. Flow pattern of fluid moving over a grain.

Bernoulli Effect

Faster air,

lower pressure

Lift Force

Slower air, higher pressure

Hjulström Diagram

Illustrates the velocity at which specific-size grain movement begins. This is a general estimation assuming water depth of 1 meter and constant grain

densities and fluid viscosity.

The Shields Diagram

Another illustration of initiation of sediment grain movement that is more specific and more widely used (not limited to 1 meter depth.)

*Dimensionless bed shear stress: (θt) = τo/((ρs – ρ)gD)

Where τo = Boundary Shear Stress, g = gravity acceleration, and D = particle diameter.

*An increase in dimensionaless shear stress indicates either an increase in flow velocity or a decrease in grain size or density.

†Grain Reynolds number: (Reg) = U*d/ν

Where U* = Shear Velocity, d = particle diameter & ν = kinematic viscosity

†A measure of turbulence at the grain-fluid boundary.

The Shields Diagram

No motion

Grains in motion

Hjulström

Shields

Settling Velocity and Stoke’s Law

Terminal fall velocity (Settling Velocity (Vs) ): a steady rate of fall achieved by a particle settling in a fluid. It is a function of the viscosity of the fluid and the size, shape and density of the particles.

Stokes Law: Vs = 2/9(g(ρs – ρ)r2)/μ

Sediment Transport

Bedload transport: coarse sediment, such as sand and gravel that moves on or very close to the bed during transport.

Suspended load transport: finer material carried higher up in the main flow above the bed.

When U* > Vs the sediment will be suspended load

When U* < Vs the sediment will be bedload

Traction: transport in continuous contact with the bed. This includes rolling of large or elongated grains, sliding of grains past each other and creep.

Saltation: bedload transport in which grains tend to move in intermittent contact with the bed by a series of jumps or hops.

Intermittent suspension: when suspended particles subject to erratic lift forces drop back to the bed from time to time.

Continuous suspension: smaller particles that are carried along close to the same velocity as the fluid flow.

Wash load: sediment that is derived either from upstream source areas or by erosion of the bank and travels in continuous suspension.

Wave action transport … (not in book)

μt = (πH)/(Tsinh((2πh)/L)

Where μt = orbital velocity, H = wave height, h = water

depth, L = wave length, T = wave period.

Deposits of Fluid Flows

Major types of mass-transport processes, their mechanical behavior and transport sediment

mechanisms

Grain Orientation can be used to determine a general character to the water that deposited the grains and also to the porosity of the deposit.

Imbricated particles: where particles lie atop one another as fallen dominoes, or shingles on a roof, where the alignment tends to be parallel to the direction of flow.

Debris Flow character varies with water content and consolidation of sediment

Turbidity Currents

Low-density flows contain < 20 to 30% grains, whereas high-density flows contain greater concentrations.

First known investigated in 1938 with Grand Banks Earthquake

Uhead = 0.7gh√(ρ/ρ)

Uhead = velocity of the turbidity current head, h = height of the head, g = gravitational acceleration, ρ = density contrast between turbidity current and ambient water, ρ = density of ambient water

U body = hs(ρ/ρ) √(8g/fo + f1)

Ubody = velocity of the turbidity current body, s = slope of the bottom, fo = frictional resistance at the bottom of the flow, f1 = frictional resistance at the upper interface of the flow in contact with ambient water.

Turbidites: deposits of turbidity currents. High-density deposits tend to form thick-bedded turbidite successions containing coarse-grained sandstones or gravels. Low density deposits form thin bedded successions with good vertical size gradings and well-developed laminations.

Grain flow deposit: deposition occurs quickly and en masse resulting in a deposit that is massively bedded, with little or no lamination and with single grain size.

Liquified flow deposit: deposits are typically thick, poorly sorted sand units characterized by fluid escape structures.

Debris flow deposit: deposits are thick, poorly sorted units that lack internal layering. Grading, although not common, can be either normal or reverse.

Grain Settling and Water expulsion

Lab 2: Mechanical Size Analysis of Sediments