2.6
Grain Shape
We distinguish between three parameters:
1. Roundness is a property of surface shape – whether
it is smooth or angular. A visual scale is most
commonly used.
2. Sphericity is an expression for how much a particle
deviates from a spherical form, and is defined as the
ratio between the diameter of a circumscribed circle round the grain and the diameter of a sphere of
the same volume (the nominal diameter).
3. We also use various expressions for grain shape
such as (a) discoid or bladed for grains which are
flat, (b) Prolate or roller for grains with one dimension considerably greater than the two others,
(c) equant for grains with three relatively equal
dimensions and (d) oblate for grains with one
large, one medium and one small dimension.
4. Surface textures are concerned with the nature of the
surface itself, whether it is rough, smooth, pitted,
scratched etc. Some textures are diagnostic of specific modes of transport, and superimposed texture
features may reveal the transport history of a grain.
The surface texture of grains can best be studied
under the scanning electron microscope. Aeolian
sand grains may develop fine pitting on their
surfaces due to the collisions of grains during transport, clearly visible under a binocular microscope.
Large grains become rounded far more rapidly than
smaller ones because the impact energy released in
collisions with other grains declines in proportion to
the cube root of the radius. Blocks may be rounded
after only a few hundred metres or several kilometres
of transport. Grains less than 0.1 mm in diameter
undergo little rounding even when carried very long
distances in water, for example by tidal currents.
The grain size and sorting of sand grains at the time
of deposition play an important role determining the
rate of compaction with increasing overburden stress
(See chapters 4 and 6). The grain-size distribution may
also change due to grain crushing during compaction
and chemical alterations e.g. dissolution of felspar and
precipitation of clay minerals like kaolinite.
2.7
Sediment Transport
Sedimentary grains can be transported by water or by
air. In order to understand the transportation processes
we must know a little about the hydrodynamic
(or aerodynamic) principles involved. When a liquid
or gas flows in a channel or pipe it exerts a force (shear
stress) against the walls or bottom. This force is
counteracted by friction from the walls.
Pure water without suspended sediment is a Newtonian fluid which obeys Newton’s law:
τ ¼ μ dv=dh
A Newtonian fluid has no shear strength, so it will
be deformed even by an infinitely small shear stress
dv=dh
ð
Þ.
τ ¼ shear stress, which is an expression of force per
unit area (N/m
2
). μ is the dynamic viscosity expressed
in poise (g/cm/s or 0.1 N s/m
2
), dv=dh is the change in
velocity (dv) or velocity gradient (deformation velocity)
as a function of distance from the boundary (dh). The
viscosity of pure water decreases with increasing temperature. Suspended material may also affect viscosity,
but the concentration of suspended material must be
quite high (15–25%) before the viscosity increases significantly. If the water contains a large percentage of
swelling clay minerals (smectite), however, the viscosity will increase at lower concentrations. The kinematic
viscosity v is the dynamic viscosity (μ) divided by
density ρ, i.e. v ¼ μ=ρ and units are cm
2
/s.
We distinguish between laminar flow, where each
point in the liquid moves along a straight line parallel
to the bed, and turbulent flow, where each point
follows an irregular path so that eddies form
(Fig. 2.6). Reynold’s number (Re) is a dimensionless
number which describes flow in channels and pipes.
It is defined as:
Re ¼ vhρ=μ
Here v is the mean velocity, h is the depth of a
channel or the diameter of a pipe in which fluid is
flowing, ρ is the fluid density and μ its viscosity. If
Reynold’s number exceeds a certain value, about
2,000, the flow changes from laminar to turbulent.
The density of water is 1 g/cm
3 and the viscosity is
one centipoise (0.01 Ps ¼ 0.01 g/cm/s). We see that
the boundary between laminar and turbulent flow
corresponds to 20 cm/s.
This means that for the flow of water to be laminar
the product of velocity (cm/s) and depth (cm) must not
exceed 20. If the velocity is 1 cm/s, there will be
turbulence if the depth (h) is greater than 20 cm. In
practice, then, flow in rivers and channels is always
40
K. Bjørlykke
Grain Shape
We distinguish between three parameters:
1. Roundness is a property of surface shape – whether
it is smooth or angular. A visual scale is most
commonly used.
2. Sphericity is an expression for how much a particle
deviates from a spherical form, and is defined as the
ratio between the diameter of a circumscribed circle round the grain and the diameter of a sphere of
the same volume (the nominal diameter).
3. We also use various expressions for grain shape
such as (a) discoid or bladed for grains which are
flat, (b) Prolate or roller for grains with one dimension considerably greater than the two others,
(c) equant for grains with three relatively equal
dimensions and (d) oblate for grains with one
large, one medium and one small dimension.
4. Surface textures are concerned with the nature of the
surface itself, whether it is rough, smooth, pitted,
scratched etc. Some textures are diagnostic of specific modes of transport, and superimposed texture
features may reveal the transport history of a grain.
The surface texture of grains can best be studied
under the scanning electron microscope. Aeolian
sand grains may develop fine pitting on their
surfaces due to the collisions of grains during transport, clearly visible under a binocular microscope.
Large grains become rounded far more rapidly than
smaller ones because the impact energy released in
collisions with other grains declines in proportion to
the cube root of the radius. Blocks may be rounded
after only a few hundred metres or several kilometres
of transport. Grains less than 0.1 mm in diameter
undergo little rounding even when carried very long
distances in water, for example by tidal currents.
The grain size and sorting of sand grains at the time
of deposition play an important role determining the
rate of compaction with increasing overburden stress
(See chapters 4 and 6). The grain-size distribution may
also change due to grain crushing during compaction
and chemical alterations e.g. dissolution of felspar and
precipitation of clay minerals like kaolinite.
2.7
Sediment Transport
Sedimentary grains can be transported by water or by
air. In order to understand the transportation processes
we must know a little about the hydrodynamic
(or aerodynamic) principles involved. When a liquid
or gas flows in a channel or pipe it exerts a force (shear
stress) against the walls or bottom. This force is
counteracted by friction from the walls.
Pure water without suspended sediment is a Newtonian fluid which obeys Newton’s law:
τ ¼ μ dv=dh
A Newtonian fluid has no shear strength, so it will
be deformed even by an infinitely small shear stress
dv=dh
ð
Þ.
τ ¼ shear stress, which is an expression of force per
unit area (N/m
2
). μ is the dynamic viscosity expressed
in poise (g/cm/s or 0.1 N s/m
2
), dv=dh is the change in
velocity (dv) or velocity gradient (deformation velocity)
as a function of distance from the boundary (dh). The
viscosity of pure water decreases with increasing temperature. Suspended material may also affect viscosity,
but the concentration of suspended material must be
quite high (15–25%) before the viscosity increases significantly. If the water contains a large percentage of
swelling clay minerals (smectite), however, the viscosity will increase at lower concentrations. The kinematic
viscosity v is the dynamic viscosity (μ) divided by
density ρ, i.e. v ¼ μ=ρ and units are cm
2
/s.
We distinguish between laminar flow, where each
point in the liquid moves along a straight line parallel
to the bed, and turbulent flow, where each point
follows an irregular path so that eddies form
(Fig. 2.6). Reynold’s number (Re) is a dimensionless
number which describes flow in channels and pipes.
It is defined as:
Re ¼ vhρ=μ
Here v is the mean velocity, h is the depth of a
channel or the diameter of a pipe in which fluid is
flowing, ρ is the fluid density and μ its viscosity. If
Reynold’s number exceeds a certain value, about
2,000, the flow changes from laminar to turbulent.
The density of water is 1 g/cm
3 and the viscosity is
one centipoise (0.01 Ps ¼ 0.01 g/cm/s). We see that
the boundary between laminar and turbulent flow
corresponds to 20 cm/s.
This means that for the flow of water to be laminar
the product of velocity (cm/s) and depth (cm) must not
exceed 20. If the velocity is 1 cm/s, there will be
turbulence if the depth (h) is greater than 20 cm. In
practice, then, flow in rivers and channels is always
40
K. Bjørlykke