Lecture 23
Sand transport by wind
The estimation of the annual volume of sand transported
along the coast is crucial for the planning and construction of coastal
structures. One of the primary drivers of sand transport is the well-known
littoral current, generated by wave action. Another significant factor is wind.
The movement of sand due to wind has been extensively studied by various
researchers.
- Aeolian processes refer to the erosion,
transport, and deposition of sediment by wind.
- These processes are particularly important in coastal
environments, where wind interacts with loose sand on beaches and dunes.
Types
of Sediment Transport:
o Suspension: Fine particles
(e.g., silt and clay) are lifted high into the air and carried over long
distances. Example: Dust storms.
o Saltation: Sand grains
(0.1–0.5 mm) bounce along the surface. This is the primary mode of sand
transport.
o Creep: Larger grains roll
or slide along the surface due to the impact of saltating grains.
Factors
Influencing Wind Transport:
o Wind Velocity: Higher wind speeds
increase the capacity for sediment transport.
o Grain Size and Shape: Smaller, rounder
grains are more easily transported.
o Surface Moisture: Wet sand is harder
to move because moisture increases cohesion between grains.
o Vegetation: Plants stabilize
sand and reduce wind speed near the surface.
Several investigators have developed expressions for the
rate of sand movement as a function of certain variables. Some of these
expressions are as follows:
Bagnold Formula:
The rate of sand movement per unit width and unit time q, is
given by
Where,
D = the grain
diameter of standard 0.25 mm sand,
d = the grain
diameter of sand in question,
ɣ = the specific
weight of air,
U*
= the shear velocity, and
c has the following
values:
·
1.5 for a nearly uniform sand
·
1.8 for a naturally graded sand
·
2.8 for sand with a very wide range of grain
diameter
Kawamura Formula
The rate of sand movement, q, is given by:
Where,
ɣ = the specific
weight of air,
U* =
the shear velocity,
U*t
= the threshold shear velocity, and
K is a constant
which must be determined by experiment.
O'Brien and Rindlaub Formula:
O'Brien and Rindlaub proposed the following formula from
data derived by field tests
Where,
G = the rate
of transport in pounds per day per foot width, and
U5
= the wind velocity at 5 feet above the sand surface in ft/sec.
However, the use of this formula should be limited to sand
having the same grain diameter of that existing in the field tests (0.195 mm).
Wind velocity above a sand surface
The shear stress, 𝝉,
produced at the sand surface by wind is one of the most important factors in
investigating sand movement by wind action. When the shear stress exceeds a
certain critical value, the sand particles start to move. As long as there is
no sand movement, the wind-velocity distribution can be described adequately by
the general equation:
U = C Log (Z/ZO)
Where, U is the
velocity at height Z above the sand surface and Zo is a reference
parameter.
The coefficient, C, according to von Karman's development,
C = (2.3/K)*U*
where K is the Karman constant,
U* = √(𝝉/ρ)
U* = the shear velocity, and
ρ= the density of air.
For K = 0.40, the von Karman equation becomes
U = 5.75 U* Log (Z/ZO)
Concerning the roughness factor, Zo, Zingg
proposed an equation:
Zo = 0.081 Log (d/0.18)
where Zo and the sand grain diameter, d, are
expressed in mm.
Once the wind velocity reaches a level sufficient to move
sand particles, the velocity profiles for varying wind speeds converge at a
specific point, referred to as a "focus." The height of
this focus, Z′, seems to be linked to the height of the ripples that
develop on the sand surface. Research conducted by Zingg provides a formula
that enables the prediction of the focus height.
Z′ =
10 d mm
U′
=20 d miles/hour
where the grain diameter, d, is expressed in millimeters.
Thus, using the component of the focus, Z', U', the
wind-velocity distribution can be expressed by
U = C Log (Z/ Z′) + U′
Bagnold assumed a coefficient C of 5.75 U*, which
corresponds to the value of 0.40 for the Karman constant. But the experiments
by Zingg yielded the equation
U = 6.13 U* Log (Z/ Z′) + U′
which indicates values of 0.375 for the Karman constant.
Transport Calculations:
At this stage, the question
arises: what method should be used to calculate the transport rate? Previous
research indicates that the Bagnold formula is more effective than other
formulas for the following reasons:
1.
Grain-Size Consideration: Bagnold's
equation incorporates the grain-size diameter. Given the significant variation
in d50 (median grain size) across different reaches, the
Bagnold formula is better suited for accurate calculations.
2.
Well-Defined Coefficient: The
coefficient C in the Bagnold formula is more precisely defined
and has a narrower range compared to the coefficient K in the
Kawamura formula, reducing uncertainty in the calculations.
3.
Threshold Shear Velocity: The
Kawamura formula includes the threshold shear velocity, which introduces
additional uncertainty in transport rate calculations. This factor is
particularly sensitive to variations in the moisture content of the sand,
further complicating its use.
4.
Limitations of O'Brien and Rindlaub Formula: The
O'Brien and Rindlaub formula is not suitable here, as it has been demonstrated
that their equation should only be applied to sand with the same grain diameter
as that tested in their field studies (specifically, d=0.195mm).
So, the Bagnold formula is preferred due to its adaptability to varying grain sizes, well-defined coefficients, and reduced uncertainties compared to other methods.
Accordingly, the Bagnold formula
will be used in the following calculations for sand transport.
Above equation of the Bagnold
formula gives the transport in pounds per second per one-foot length. Rewriting
the Bagnold formula in a more general way:
Q = total transport in pounds per year
C = Bagnold constant
l= length of reach in feet perpendicular
to direction of wind considered
d = average grain diameter of sand
considered (d50 mm)
D = average grain diameter of standard
0.25 mm sand
ɣ
= specific weight of air = (0.076 lbs/ft3)
U* = shear velocity in ft/sec
T = duration of wind in seconds per year
g = acceleration due to gravity = 32.2
ft/sec2
(A reach is a distinct segment or arm of
the sea of the coastline that exhibits relatively uniform characteristic)
Now substituting the values of ɣ, g and choosing C =1.8, since the sand considered
has a natural grading, the equation:
In pounds per year. t is in hours per year.