Grain size

Size ranges define limits of classes that are given names in the Wentworth scale (or Udden–Wentworth scale) used in the United States. The Krumbein phi (φ) scale, a modification of the Wentworth scale created by W. C. Krumbein[1] in 1934, is a logarithmic scale computed by the equation

${\displaystyle \varphi =-\log _{2}{\frac {D}{D_{0}}},}$

where

${\displaystyle \varphi }$ is the Krumbein phi scale,

${\displaystyle D}$ is the diameter of the particle or grain in millimeters (Krumbein and Monk's equation)[2] and

${\displaystyle D_{0}}$ is a reference diameter, equal to 1 mm (to make the equation dimensionally consistent).

This equation can be rearranged to find diameter using φ:

${\displaystyle D=D_{0}\cdot 2^{-\varphi }\,}$

In some schemes, gravel is anything larger than sand (comprising granule, pebble, cobble, and boulder in the table above).

ISO 14688-1:2017, establishes the basic principles for the identification and classification of soils on the basis of those material and mass characteristics most commonly used for soils for engineering purposes. ISO 14688-1 is applicable to natural soils in situ, similar man-made materials in situ and soils redeposited by people.[3]

An accumulation of sediment can also be characterized by the grain size distribution. A sediment deposit can undergo sorting when a particle size range is removed by an agency such as a river or the wind. The sorting can be quantified using the Inclusive Graphic Standard Deviation:[4]

${\displaystyle \sigma _{I}={\frac {\phi 84-\phi 16}{4}}+{\frac {\phi 95-\phi 5}{6.6}}}$

where

${\displaystyle \sigma _{I}}$ is the Inclusive Graphic Standard Deviation in phi units

${\displaystyle \phi 84}$ is the 84th percentile of the grain size distribution in phi units, etc.

The result of this can be described using the following terms:

Diameter (phi units)	Description
${\displaystyle \sigma _{I}}$ < 0.35	very well sorted
0.35 < ${\displaystyle \sigma _{I}}$ < 0.50	well sorted
0.50 < ${\displaystyle \sigma _{I}}$ < 1.00	moderately sorted
1.00 < ${\displaystyle \sigma _{I}}$ < 2.00	poorly sorted
2.00 < ${\displaystyle \sigma _{I}}$ < 4.00	very poorly sorted
4.00 < ${\displaystyle \sigma _{I}}$	extremely poorly sorted

• Deposition (geology)
• Feret diameter
• Martin diameter
• Orders of magnitude (volume)
• Soil texture
• Substrate (biology)
• Unified Soil Classification System (USCS)

• R D Dean & R A Dalrymple, Coastal Processes with Engineering Applications (Cambridge University Press, 2002)
• W C Krumbein & L L Sloss, Stratigraphy and Sedimentation, 2nd edition (Freeman, San Francisco, 1963).
• Udden, J. A. (1914). "Mechanical composition of clastic sediments". Geological Society of America Bulletin. 25 (1): 655–744. Bibcode:1914GSAB...25..655U. doi:10.1130/GSAB-25-655.
• Wentworth, C. K. (1922). "A Scale of Grade and Class Terms for Clastic Sediments". The Journal of Geology. 30 (5): 377–392. Bibcode:1922JG.....30..377W. doi:10.1086/622910. JSTOR 30063207. S2CID 128682870.