EM 1110-2-1100 (Part III)
30 Apr 02
( φ16 % φ50 % φ84 )
Mφ '
(III-1-2)
3
where Mφ is the estimated mean grain size of the sample in phi units. This can be converted to a linear
diameter using Equation 1-1b. The median and mean grain sizes are usually quite similar for most beach
sediments. For example, a study of 465 sand samples from three New Jersey beaches, the mean averaged
only 0.01 mm smaller than the median for sands having an average median diameter of 0.30 mm (1.74 phi)
(Ramsey and Galvin 1977). If the grain sizes in a sample are log-normally distributed, the two measures are
identical. Since the median is easier to determine and the mean does not have a universally accepted
definition, the median is normally used in coastal engineering to characterize the central tendency of a
sediment sample.
e. Higher order moments.
(1) Additional statistics of the sediment distribution can be used to describe how the sample varies from
a log-normal distribution. The standard deviation is a measure of the degree to which the sample spreads out
around the mean (i.e., its sorting). Following Folk (1974), the standard deviation can be approximated by:
( φ84 & φ16)
( φ95 & φ5)
σφ '
(III-1-3)
%
4
6
where σφ is the estimated standard deviation of the sample in phi units. For a completely uniform sediment
φ05, φ16, φ84, and φ95 are all the same, and thus, the standard deviation is zero. There are also qualitative
descriptions of the standard deviation. A sediment is described as well-sorted if all particles have sizes that
are close to the typical size (small standard deviation). 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.
(2) The degree by which the distribution departs from symmetry is measured by the phi coefficient of
skewness αφ defined in Folk (1974) as:
φ16 % φ84 & 2 (φ50 )
φ5 % φ95 & 2 (φ50)
αφ '
%
(III-1-4)
2 ( φ84 & φ16 )
2 (φ95 & φ5)
(3) For a perfectly symmetric distribution, the skewness is zero. A positive skewness indicates there is
a tailing out toward the fine sediments, and conversely, a negative value indicates more outliers in the coarser
sediments.
(4) The phi coefficient of kurtosis βφ is a measure of the peakedness of the distribution; that is, the
proportion of the sediment in the middle of the distribution relative to the amount in both tails. Following
Folk (1974), it is defined as:
φ95 & φ5
βφ '
(III-1-5)
2.44 (φ75 & φ25)
Values for the mean and median grain sizes are frequently converted from phi units to linear measures.
However, the standard deviation, skewness, and kurtosis should remain in phi units because they have no
corresponding dimensional equivalents. If these terms are used in equations, they are used in their
dimensionless phi form. Relative relationships are given for ranges of standard deviation, skewness, and
kurtosis in Table III-1-3.
III-1-10
Coastal Sediment Properties
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