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.

(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:

(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.

(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 M*d is the sample characteristic most often chosen. The

definition of *M*d 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 *D*50. Other size fractions are similarly indicated. For example,

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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