Soil Mechanics / Particle size, description and classification

Grading curves, D-values and coefficients

Read the distribution, then judge whether a soil is well, poorly or gap graded.

Lesson review: expert verification remains open

This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.

Corrections checked in this pass

Removed the inference that failing grading coefficients proves a gap-graded soil.

Checks needed for project use

A geotechnical reviewer must check laboratory interpretation, classification conventions and the limits of drained, undrained and one-dimensional idealisations.
Full classification needs fines/plasticity and applicable current BS/ISO or USCS system; gap interpretation requires whole curve.

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Why this matters

The grading curve condenses a soil's whole size distribution into one plot, and two numbers taken from it — the uniformity and curvature coefficients — tell you how the sizes are spread and therefore how the soil will pack and drain.

A grading curve plots the percentage of the sample (by mass) passing each size against particle size, on a logarithmic size axis. From it we read the D-values: $D_{10}$ , $D_{30}$ and $D_{60}$ are the sizes at which 10%, 30% and 60% of the sample is finer. $D_{10}$ is called the effective size because the fine tail controls permeability.

Uniformity and curvature coefficients

C_u = \dfrac{D_{60}}{D_{10}}, \qquad C_c = \dfrac{D_{30}^2}{D_{10}\,D_{60}}

What it calculates: how wide the size range is, and how smooth the distribution is

C_u: uniformity coefficient (dimensionless)
C_c: coefficient of curvature (dimensionless)
$D_{10}, D_{30}, D_{60}$: sizes at 10, 30 and 60% passing (mm)

In plain terms: A large Cu means a wide range of sizes. A well-graded soil has a high Cu AND a smoothly curved distribution (1 ≤ Cc ≤ 3), so small grains fill the gaps between large ones and it packs densely.

Try it

Grading-curve explorer

Percentage passing against particle size. Read the D-values and a limited USCS-style coarse grading screen; this is not a complete BS/ISO soil classification.

Soil

D₁₀: 0.100 mm
D₃₀: 0.500 mm
D₆₀: 1.500 mm
C_u = D60/D10: 15.0
C_c: 1.67

This soil is well graded (C_u = 15.0, C_c = 1.67). The coefficients meet the stated coarse grading screen. Density and permeability need separate assessment.

Worked example

Classifying a sand from its grading curve

Given

D10 = 0.10 mm
D30 = 0.50 mm
D60 = 1.50 mm

Find

The uniformity and curvature coefficients, and the gradation.

Assumptions

This example uses the USCS convention for a clean sand: Cu ≥ 6 and 1 ≤ Cc ≤ 3. Confirm fines content and classification rules before assigning a project classification.

Practice

A soil has D10 = 0.15 mm and D60 = 0.60 mm. What is its uniformity coefficient Cu?

Practice

For the same soil, D30 = 0.30 mm. What is the coefficient of curvature Cc?

Summary

The grading curve plots % passing against particle size on a log axis; read D10, D30, D60 from it.
Cu = D60/D10 measures the range of sizes; Cc = D30²/(D10·D60) measures the shape.
Well-graded (coarse): high Cu and 1 ≤ Cc ≤ 3. Uniform: low Cu. Gap-graded: a missing size range.