• Images
• Videos
• Documents
• Books
• Articles

Krumbein phi scale

Size ranges define limits of classes that are given names in the Wentworth scale (or Udden–Wentworth scale named after geologists Chester K. Wentworth and Johan A. Udden) used in the United States. The Krumbein phi (φ) scale, a modification of the Wentworth scale created by W. C. Krumbein¹ in 1934, is a logarithmic scale computed by the equation

φ = − log 2 ⁡ D D 0 , {\displaystyle \varphi =-\log _{2}{\frac {D}{D_{0}}},}

where

φ {\displaystyle \varphi } is the Krumbein phi scale, D {\displaystyle D} is the diameter of the particle or grain in millimeters (Krumbein and Monk's equation)² and D 0 {\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:

D = D 0 ⋅ 2 − φ {\displaystyle D=D_{0}\cdot 2^{-\varphi }\,}

φ scale	Size range(metric)	Size range(approx. inches)	Aggregate name(Wentworth class)	Other names
<−8	>256 mm	>10.1 in	Boulder
−6 to −8	64–256 mm	2.5–10.1 in	Cobble
−5 to −6	32–64 mm	1.26–2.5 in	Very coarse gravel	Pebble
−4 to −5	16–32 mm	0.63–1.26 in	Coarse gravel	Pebble
−3 to −4	8–16 mm	0.31–0.63 in	Medium gravel	Pebble
−2 to −3	4–8 mm	0.157–0.31 in	Fine gravel	Pebble
−1 to −2	2–4 mm	0.079–0.157 in	Very fine gravel	Granule
0 to −1	1–2 mm	0.039–0.079 in	Very coarse sand
1 to 0	0.5–1 mm	0.020–0.039 in	Coarse sand
2 to 1	0.25–0.5 mm	0.010–0.020 in	Medium sand
3 to 2	125–250 μm	0.0049–0.010 in	Fine sand
4 to 3	62.5–125 μm	0.0025–0.0049 in	Very fine sand
8 to 4	3.9–62.5 μm	0.00015–0.0025 in	Silt	Mud
10 to 8	0.98–3.9 μm	3.8×10−5–0.00015 in	Clay	Mud
20 to 10	0.95–977 nm	3.8×10−8–3.8×10−5 in	Colloid	Mud

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

International scale

ISO 14688-1:2017, establishes the basic principles for identifying and classifying soils based on those material and mass characteristics most commonly used for soils for engineering purposes. ISO 14688-1 applies to natural soils in situ, similar man-made materials in situ and soils redeposited by people.³

ISO 14688-1:2017

Name				Size range (mm)	Size range (approx. in)
Very coarse soil		Large boulder	lBo	>630	>24.8031
		Boulder	Bo	200–630	7.8740–24.803
		Cobble	Co	63–200	2.4803–7.8740
Coarse soil	Gravel	Coarse gravel	cGr	20–63	0.78740–2.4803
		Medium gravel	mGr	6.3–20	0.24803–0.78740
		Fine gravel	fGr	2.0–6.3	0.078740–0.24803
	Sand	Coarse sand	cSa	0.63–2.0	0.024803–0.078740
		Medium sand	mSa	0.2–0.63	0.0078740–0.024803
		Fine sand	fSa	0.063–0.2	0.0024803–0.0078740
Fine soil	Silt	Coarse silt	cSi	0.02–0.063	0.00078740–0.0024803
		Medium silt	mSi	0.0063–0.02	0.00024803–0.00078740
		Fine silt	fSi	0.002–0.0063	0.000078740–0.00024803
	Clay		Cl	≤0.002	≤0.000078740

Sorting

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

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

where

σ I {\displaystyle \sigma _{I}} is the Inclusive Graphic Standard Deviation in phi units ϕ 84 {\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:⁵

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

See also

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

External links

• 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.

References

1. Krumbein, W. C. (1934). "Size frequency distributions of sediments". Journal of Sedimentary Petrology. 2 (4). doi:10.1306/D4268EB9-2B26-11D7-8648000102C1865D. /wiki/Doi_(identifier) ↩

2. PetroWiki: Estimating permeability based on grain size https://petrowiki.org/Estimating_permeability_based_on_grain_size ↩

3. "ISO 14688-1:2017 – Geotechnical investigation and testing – Identification and classification of soil – Part 1: Identification and description". International Organization for Standardization (ISO). https://www.iso.org/standard/66345.html ↩

4. Folk, Robert L.; Ward, William C. (1957). "Brazos River bar: a study in the significance of grain-size parameters" (PDF). Journal of Sedimentary Petrology. 27 (1): 3–26. Bibcode:1957JSedR..27....3F. doi:10.1306/74d70646-2b21-11d7-8648000102c1865d. Archived from the original (PDF) on 12 May 2014. Retrieved 11 May 2014. https://web.archive.org/web/20140512213708/http://www.er.uqam.ca/nobel/aqqua1/articles/Folk_Ward_27%281%29-3.pdf ↩

5. Folk, Robert L. (1980). Petrology of sedimentary rocks. Austin, Tex: Hemphill Pub. Co. ISBN 978-0-914696-14-8. 978-0-914696-14-8 ↩