Mineralogy & Petrology

Sedimentology & Grain Size

The Udden–Wentworth scale, phi units, sorting and Stokes settling — quantifying clastic sediments and their depositional energy.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Clastic sediments are described by grain size (Udden–Wentworth: clay <1/256 mm, silt 1/256–1/16 mm, sand 1/16–2 mm, gravel >2 mm), expressed on the logarithmic phi scale

ϕ = - lo g_{2} d_{mm}

. Sorting (the spread of grain sizes) and rounding record transport energy and distance: a well-sorted, well-rounded quartz arenite is mature. Settling of fine grains obeys Stokes' law, where velocity scales with the square of diameter.

The Core Formula Matrix

Phi scale:

ϕ = - lo g_{2} d_{mm}

(small/negative

ϕ

= coarse).

Stokes settling velocity:

v_{s} = \frac{g ( ρ _{s} - ρ _{w} ) d ^{2}}{18 μ}

Graphic sorting:

σ_{ϕ} \approx \frac{ϕ _{84} - ϕ _{16}}{2}

Uniformity coefficient:

C_{u} = d_{60} / d_{10}

The ‘IIT Traps’

⚠
Phi sign. Coarser grains have *smaller* (even negative) $ϕ$ ; $- lo g_{2}$ flips the order.
⚠
Stokes ∝ d². Halving grain diameter quarters the settling velocity.
⚠
Sorting vs grain size. Sorting is the *spread*, not the average size.

📚 Standard references

Sedimentary Petrology — Maurice E. Tucker
Principles of Sedimentology and Stratigraphy — Sam Boggs Jr.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

A sand grain is

0.25

mm in diameter. Its phi (

ϕ

) value is _____.

Q2MEDIUM1 Mark · MCQ

On the Udden–Wentworth scale, particles between 1/16 mm and 2 mm are

Q3HARD2 Marks · NAT

A sand has

d_{60} = 0.9

mm and

d_{10} = 0.3

mm. Its uniformity coefficient

C_{u}

is _____.