acceleration term g in Stokes’ Law. There are also
“sedimentation balances”. Sediments suspended in a
cylinder fall through the water column and accumulate
on a balance pan at the bottom of the cylinder. This
balance records and writes out the increase in weight,
which is the precipitation from suspension, as a function of time. This gives a direct cumulative curve.
Other methods are based on the refraction or dispersion of a laser beam passed through suspensions
producing a characteristic “scatter” which is calibrated
against samples of known grain size. These machines
use very small samples and have a high degree of
repeatability. Equipment has also been developed
which uses X-rays instead of light to produce the
characteristic scatter patterns.
It is important to note that no method measures the
nominal diameter. In methods which measure settling
velocity, grain shape is a significant factor. A large,
thin mica flake has a settling velocity which
corresponds to that of a considerably smaller spherical
grain. The diameter of a spherical grain with the same
volume and settling velocity is called the effective
diameter (d e ). With the scatter method, flaky grains
are assigned a different, probably greater, diameter
than that indicated by the settling velocity method.
2.2
Grain-Size Distribution in Solid
Rocks
Lightly-cemented sandstones can be disintegrated by
means of ultrasound in the laboratory and then analysed
as loose sediment in the normal manner. Carbonatecemented rocks may be disintegrated using acids. However, we must bear in mind that new clay minerals may
have formed through post-depositional alteration (diagenetic processes), and that some of the original
minerals may have been broken down mechanically or
dissolved chemically. Consequently it is not certain that
we are dealing with the original grain distribution.
Diagenesis must be taken into account.
Well-cemented rocks must be analysed in thin section by means of a petrographic microscope. It is
difficult to analyse the finer fractions (fine silt and
clay) in this manner and we must always remember
the “section effect”, i.e. that in most cases we will not
be seeing the greatest diameter of the grains. With
spherical grains, the relation between the real diameter, d r , and the observed diameter, d o , can be expressed
statistically: d r ¼ 4d o =π.
2.3
Presentation of Grain-Size
Distribution Data
Grain-size distribution is one of the many types of
natural data which must be presented on a logarithmic
scale for convenience. Wentworth’s scale is based on
logarithms to the base 2, and this is now the one most
widely found in geological literature (Fig. 2.1b).
For the sake of convenience, these data are commonly plotted against a linear scale. The phi (φ) scale,
where φ ¼ À log 2 d, allows convenient interpolation
of graphic data. The reason this negative logarithm is
used is that normally most of the sediment grain
diameters (d) are less than 1 mm, so these will have
a positive phi value (Fig. 2.3). It is convenient to plot
grain-size distribution data as a function of phi values,
especially on cumulative curves. In normal
descriptions of grain size, however, it is more helpful
to state grain size in mm, so the reader does not have to
calculate back from phi values.
The simplest, and visually most informative, way
of presenting grain-size distribution data is by means
of histograms (Fig. 2.3). These show the percentage,
by weight, of the grains falling within each chosen
Resistance due to
friction. Laminar flow;
6πRvμ (Stokes law)
Force of gravity:
4/3πR 3 Δρ
R
Fig. 2.2 The velocity of a falling grain in water is controlled by
the gravity forces directed downwards and the resistance to the
flow around the grain which is directed upwards (6πRvμ). The
force of gravity is a function of the volume of the grain
(4/3πgR
3
) and the density difference (△ρ) between the grain
and the fluid (ρ g – ρ f )
36
K. Bjørlykke
“sedimentation balances”. Sediments suspended in a
cylinder fall through the water column and accumulate
on a balance pan at the bottom of the cylinder. This
balance records and writes out the increase in weight,
which is the precipitation from suspension, as a function of time. This gives a direct cumulative curve.
Other methods are based on the refraction or dispersion of a laser beam passed through suspensions
producing a characteristic “scatter” which is calibrated
against samples of known grain size. These machines
use very small samples and have a high degree of
repeatability. Equipment has also been developed
which uses X-rays instead of light to produce the
characteristic scatter patterns.
It is important to note that no method measures the
nominal diameter. In methods which measure settling
velocity, grain shape is a significant factor. A large,
thin mica flake has a settling velocity which
corresponds to that of a considerably smaller spherical
grain. The diameter of a spherical grain with the same
volume and settling velocity is called the effective
diameter (d e ). With the scatter method, flaky grains
are assigned a different, probably greater, diameter
than that indicated by the settling velocity method.
2.2
Grain-Size Distribution in Solid
Rocks
Lightly-cemented sandstones can be disintegrated by
means of ultrasound in the laboratory and then analysed
as loose sediment in the normal manner. Carbonatecemented rocks may be disintegrated using acids. However, we must bear in mind that new clay minerals may
have formed through post-depositional alteration (diagenetic processes), and that some of the original
minerals may have been broken down mechanically or
dissolved chemically. Consequently it is not certain that
we are dealing with the original grain distribution.
Diagenesis must be taken into account.
Well-cemented rocks must be analysed in thin section by means of a petrographic microscope. It is
difficult to analyse the finer fractions (fine silt and
clay) in this manner and we must always remember
the “section effect”, i.e. that in most cases we will not
be seeing the greatest diameter of the grains. With
spherical grains, the relation between the real diameter, d r , and the observed diameter, d o , can be expressed
statistically: d r ¼ 4d o =π.
2.3
Presentation of Grain-Size
Distribution Data
Grain-size distribution is one of the many types of
natural data which must be presented on a logarithmic
scale for convenience. Wentworth’s scale is based on
logarithms to the base 2, and this is now the one most
widely found in geological literature (Fig. 2.1b).
For the sake of convenience, these data are commonly plotted against a linear scale. The phi (φ) scale,
where φ ¼ À log 2 d, allows convenient interpolation
of graphic data. The reason this negative logarithm is
used is that normally most of the sediment grain
diameters (d) are less than 1 mm, so these will have
a positive phi value (Fig. 2.3). It is convenient to plot
grain-size distribution data as a function of phi values,
especially on cumulative curves. In normal
descriptions of grain size, however, it is more helpful
to state grain size in mm, so the reader does not have to
calculate back from phi values.
The simplest, and visually most informative, way
of presenting grain-size distribution data is by means
of histograms (Fig. 2.3). These show the percentage,
by weight, of the grains falling within each chosen
Resistance due to
friction. Laminar flow;
6πRvμ (Stokes law)
Force of gravity:
4/3πR 3 Δρ
R
Fig. 2.2 The velocity of a falling grain in water is controlled by
the gravity forces directed downwards and the resistance to the
flow around the grain which is directed upwards (6πRvμ). The
force of gravity is a function of the volume of the grain
(4/3πgR
3
) and the density difference (△ρ) between the grain
and the fluid (ρ g – ρ f )
36
K. Bjørlykke