EM 1110-2-1100 (Part III)
30 Apr 02
geologist's classification, sand is between 0.0625 and 2.0 mm. In describing a sediment, it is necessary to say
which classification system is being utilized.
c. Units of sediment size.
(1) Table III-1-2 lists three ways to specify the size of a sediment particle: U.S. Standard sieve numbers,
millimeters, and phi units. A sieve number is approximately the number of square openings per inch,
measured along a wire in the wire screen cloth (Tyler 1991). Available sieve sizes can be obtained from
catalogs on construction materials testing such as Soiltest (1983). The millimeter dimension is the length of
the inside of the square opening in the screen cloth. This square side dimension is not necessarily the
maximum dimension of the particle which can get through the opening, so these millimeter sizes must be
understood as nominal approximations to sediment size. Table III-1-2 shows that the Wentworth scale has
divisions that are whole powers of 2 mm. For example, medium sands are those with diameters between 2-2
mm and 2-1 mm. This property of powers of 2-mm class limits led Krumbein (1936) to propose a phi unit
scale based on the definition:
φ ' & log2 D
(III-1-1a)
where D is the grain diameter in millimeters. Phi diameters are indicated by writing φ after the numerical
value. That is, a 2.0-φ sand grain has a diameter of 0.25 mm. To convert from phi units to millimeters, the
inverse equation is used:
D ' 2& φ
(III-1-1b)
(2) The benefits of the phi unit include: (a) it has whole numbers at the limits of sediment classes in the
Wentworth scale; and (b) it allows comparison of different size distributions because it is dimensionless.
Disadvantages of this phi unit are: (a) the unit gets larger as the sediment size gets smaller, which is both
counterintuitive and ambiguous; (b) it is difficult to physically interpret size in phi units without considerable
experience; and (c) because it is a dimensionless unit, it cannot represent a unit of length in physical
expressions such as fall velocity or Reynolds number.
d. Median and mean grain sizes.
(1) All natural sediment samples contain grains having a range of sizes. However, it is frequently
necessary to characterize the sample using a single typical grain diameter as a measure of the central tendency
of the distribution. The median grain diameter Md is the sample characteristic most often chosen. The
definition of Md is that, by weight, half the particles in the sample will have a larger diameter and half will
have a smaller. This quantity is easily obtained graphically, if the sample is sorted by sieving or other
method, and the weight of the size fractions are plotted, as seen in Figures III-1-1 and III-1-2.
(2) The median diameter is also written as D50. Other size fractions are similarly indicated. For example,
D90 is the diameter for which 90 percent of the sediment, by weight, has a smaller diameter. An equivalent
definition holds for the median of the phi-size distribution φ50 or for any other size fraction in the phi scale.
(3) Another measure of the central tendency of a sediment sample is the mean grain size. Several
formulas have been proposed to compute this quantity, given a cumulative size distribution plot of the sample
(Otto 1939, Inman 1952, Folk and Ward 1957, McCammon 1962). These formulas are averages of 2, 3, 5,
or more symmetrically selected percentiles of the phi frequency distribution. Following Folk (1974):
Coastal Sediment Properties
III-1-9
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