Module 4 · Lesson 4.2

Grading curves, D-values and coefficients

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

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} = \frac{D _{60}}{D _{10}}, C_{c} = \frac{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 the shape coefficients.

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). A wide range of sizes packs densely and drains moderately.

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

A coarse (sand) soil, so the well-graded threshold is Cu ≥ 6.

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.

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This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint