Udden-Wentworth Scale
The Udden-Wentworth scale is the grain-size classification used almost universally by sedimentologists to describe the sizes of particles in sediments and sedimentary rocks. [1] Particles in natural sediments span an enormous range - from the finest clay that requires an electron microscope to visualise up to boulders several metres across - and a classification scale must be designed to handle this breadth in a way that is practically useful. [1]
Why a Geometric Scale?
The wide range of particle sizes in nature makes a linear scale - where each step adds a fixed number of millimetres - impractical. A linear scale would require thousands of divisions to cover the clay-to-boulder range, and most of those divisions would be clustered at the coarse end where they provide little useful discrimination. [1]
A geometric scale solves this by defining each step as a fixed ratio rather than a fixed increment: each successive size boundary is either twice as large or half as large as the one before it, depending on direction. [1] This doubling/halving ratio means that each step on the scale represents the same relative change in grain size, which matches the way transport energy actually changes in natural systems. A current that can move 2 mm granules is not trivially different from one that moves 1 mm very coarse sand - it is meaningfully different in the same proportional sense that distinguishes a current moving 0.5 mm coarse sand from one moving 0.25 mm medium sand.
Major Size Classes and Subdivisions
The scale extends from less than 1/256 mm (0.0039 mm) at the finest end to greater than 256 mm at the coarsest end, and is divided into four major categories: clay, silt, sand, and gravel, each of which can be further subdivided. [1] Sand, for example, is subdivided into very fine, fine, medium, coarse, and very coarse fractions, each bounded at a doubling of grain diameter. Silt is similarly subdivided into very fine, fine, medium, and coarse silt.
The gravel fraction is divided into granules (2-4 mm), pebbles (4-64 mm), cobbles (64-256 mm), and boulders (>256 mm). [1] An extended classification proposed for the coarsest end of the scale adds the categories of block (4.1-65.5 m), slab (65.5 m to 1.0 km), monolith (1.0-33.6 km), and megalith (>33.6 km), though these divisions apply to geological landform-scale clasts rather than to typical sedimentary particles. [1]
The Phi Scale
Working directly with millimetre values over the clay-to-boulder range is cumbersome because the numbers span many orders of magnitude. The phi scale, a logarithmic transformation of millimetre diameter, was introduced to express grain-size data in units of equal value that are convenient for graphical plotting and statistical calculations. [1]
The relationship is: [1]
φ = -log₂(d) [1]
where φ is the phi size and d is the grain diameter in millimetres. [1] To take the worked examples directly: a grain 4 mm in diameter has a phi size of -2, because 2 must be raised to the power 2 to give 4, and the negative sign is then applied; a grain 8 mm in diameter has a phi value of -3. [1]
The phi scale yields both positive and negative numbers. Grain size expressed in millimetres decreases as phi values become more positive, and increases as phi values become more negative. [1] The negative logarithm was chosen deliberately: because sand-size and smaller grains are the most abundant particles in sedimentary rocks, making this the most commonly worked part of the scale, the negative sign ensures that the abundant fine and medium sands plot as positive phi values, avoiding the inconvenience of constantly working with negative numbers in the region of greatest practical interest. [1] This convention also aligns with the standard graphical practice of plotting coarse sizes to the left and fine sizes to the right on grain-size plots. [1]
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References & Citations
- 1.Principles of Sedimentology and Stratigraphy Boggs, Sam Jr.
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