(c) The normal distribution is described by its mean and standard
déviation. Since the distribution of sand size is approximately lognormal,
then individual sand size distributions can be more easily described by
units based on the logarithm of the diameter rather than the absolute diameter. Comparison with the theoretical lognormal distribution is alsô a
convenient way of characterizing and comparing the size distribution of
different samples.
Of these three advantages, only (a) is unique to the phi units. The
other two, (b) and (c) , would be valid for any unit based on the logarithm
of size.
Disadvantages of phi units are:
(a) Phi units increase as absolute size in millimeters decreases.
(b) Physical appréciation of the size involved is easier when the
units are millimeters rather than phi units.
(c) The médian diameter can be easily obtained without phi units.
(d) Phi units are dimensionless, and are not usable in physically
related quantifies where grain size must hâve units of length such as
grain-size Reynolds number, or relative roughness.
Size distributions of samples of littoral materials vary widely.
Qualitatively, the size distribution of a sample may be characterized by
a diameter that is in some way typical of the sample, and by the way that
the sizes coarser and finer than the typical size are distributed. (Note
that size distributions are generally based on weight, rather than number
of particles.)
A size distribution is described qualitatively as vell-sorted if al
particles hâve sizes that are close to the typical size. If ail the particles hâve exactly the same size, then the sample is perfeatly eorted.
If the particle sizes are distributed evenly over a wide range of sizes
then the sample is said to be well-graded. A well-graded sample is poorly
sorted; a well-sorted sample is poorly graded.
The médian (M
mon measure of sand size
the mean (M) define typical sizes of a sample of
médian size,
in millimeters, is the most comIt may be defined as
in engineering reports.
~ ^5 0
(4-2)
*•’ vo» OU.X.C
millimeters that divides the sample so that half
» by weight, has particles coarser than
ci
An eau
’’ —
«-ko r»hi
^ere ds0 is the size in
e sample,
ncignu,
----aient définition holds for the médian of the phi
the dso size. An equiv
size distribution, using
the symbol
instead of Mdapproximate mean
Several formulas hâve been
sample. (Otto, 1939,
(M) from the cumulative size distribution
4-15
déviation. Since the distribution of sand size is approximately lognormal,
then individual sand size distributions can be more easily described by
units based on the logarithm of the diameter rather than the absolute diameter. Comparison with the theoretical lognormal distribution is alsô a
convenient way of characterizing and comparing the size distribution of
different samples.
Of these three advantages, only (a) is unique to the phi units. The
other two, (b) and (c) , would be valid for any unit based on the logarithm
of size.
Disadvantages of phi units are:
(a) Phi units increase as absolute size in millimeters decreases.
(b) Physical appréciation of the size involved is easier when the
units are millimeters rather than phi units.
(c) The médian diameter can be easily obtained without phi units.
(d) Phi units are dimensionless, and are not usable in physically
related quantifies where grain size must hâve units of length such as
grain-size Reynolds number, or relative roughness.
Size distributions of samples of littoral materials vary widely.
Qualitatively, the size distribution of a sample may be characterized by
a diameter that is in some way typical of the sample, and by the way that
the sizes coarser and finer than the typical size are distributed. (Note
that size distributions are generally based on weight, rather than number
of particles.)
A size distribution is described qualitatively as vell-sorted if al
particles hâve sizes that are close to the typical size. If ail the particles hâve exactly the same size, then the sample is perfeatly eorted.
If the particle sizes are distributed evenly over a wide range of sizes
then the sample is said to be well-graded. A well-graded sample is poorly
sorted; a well-sorted sample is poorly graded.
The médian (M
mon measure of sand size
the mean (M) define typical sizes of a sample of
médian size,
in millimeters, is the most comIt may be defined as
in engineering reports.
~ ^5 0
(4-2)
*•’ vo» OU.X.C
millimeters that divides the sample so that half
» by weight, has particles coarser than
ci
An eau
’’ —
«-ko r»hi
^ere ds0 is the size in
e sample,
ncignu,
----aient définition holds for the médian of the phi
the dso size. An equiv
size distribution, using
the symbol
instead of Mdapproximate mean
Several formulas hâve been
sample. (Otto, 1939,
(M) from the cumulative size distribution
4-15