Particle size distribution describes the proportion of soil or aggregate passing nominated particle sizes. D-values read from a grading curve can be used to calculate the uniformity coefficient and coefficient of curvature.
These calculations summarise the shape of a grading curve. They do not, by themselves, establish material compliance, soil classification, permeability or engineering suitability.
Percent passing and percent retained
For a sieve test:
$$ P_{\mathrm{retained}} = \frac{M_{\mathrm{retained}}}{M_{\mathrm{total}}}\times100 $$Cumulative percent retained is the sum retained on the nominated sieve and all larger sieves.
$$ P_{\mathrm{passing}} = 100-P_{\mathrm{cumulative\ retained}} $$The mass basis, washing process, test fraction and any correction must follow the nominated test method. This page explains the derived grading calculations rather than the laboratory procedure.
Understanding D10, D30 and D60
A value \(D_P\) is the particle diameter at which \(P\) percent of the tested material is finer or passing.
| Value | Meaning |
|---|---|
| \(D_{10}\) | Particle diameter at 10 percent passing |
| \(D_{30}\) | Particle diameter at 30 percent passing |
| \(D_{60}\) | Particle diameter at 60 percent passing |
The values are read or interpolated from a particle-size distribution curve. Because particle size is conventionally plotted on a logarithmic horizontal axis, logarithmic interpolation should be used between measured points.
Uniformity coefficient
The uniformity coefficient is:
$$ C_u = \frac{D_{60}}{D_{10}} $$It is dimensionless, but both D-values must use the same length unit.
A value closer to 1 indicates a narrower range between D10 and D60. A larger value indicates a broader range over that part of the grading curve. Formal grading descriptions and soil group symbols must use the complete rules of the applicable classification system.
Coefficient of curvature
The coefficient of curvature is:
$$ C_c = \frac{D_{30}^2}{D_{10}D_{60}} $$It is also dimensionless.
Direct-input worked example
Assume:
- \(D_{10}=0.18\) mm
- \(D_{30}=0.42\) mm
- \(D_{60}=1.25\) mm
Uniformity coefficient:
$$ C_u = \frac{1.25}{0.18}=6.944 $$Coefficient of curvature:
$$ C_c = \frac{0.42^2}{0.18\times1.25}=0.784 $$The calculation should retain the source grading report, data unit and method used to obtain the D-values.
Logarithmic interpolation
Where the target percentage lies between two measured points:
$$ \log D = \log D_1+ \frac{P-P_1}{P_2-P_1} (\log D_2-\log D_1) $$Where:
| Symbol | Meaning |
|---|---|
| \(P\) | Target percent passing |
| \(P_1,P_2\) | Percent-passing values bracketing the target |
| \(D_1,D_2\) | Corresponding particle diameters |
| \(D\) | Interpolated target diameter |
Either base-10 or natural logarithms can be used consistently.
Interpolation example
Suppose the grading data contain:
- 20 percent passing at 0.20 mm
- 40 percent passing at 0.80 mm
To calculate \(D_{30}\), the target percentage is halfway between 20 and 40 percent on the logarithmic size scale:
$$ \log D_{30} = \log(0.20)+ \frac{30-20}{40-20} [\log(0.80)-\log(0.20)] $$ $$ D_{30}=0.40\ \mathrm{mm} $$The result is the geometric midpoint of 0.20 and 0.80 mm.
Interpolation rules
A calculation tool should:
- order points by particle diameter
- require positive diameters
- require percent passing between 0 and 100
- check that percent passing is monotonic
- identify the two points used for each interpolation
- reject duplicate or contradictory points for review
- avoid extrapolation outside measured data
- return D10, D30 or D60 as unavailable when the data do not bracket the target
- retain the meaningful precision of the source data
Extrapolating D10 from a curve that does not reach 10 percent passing can create a misleading Cu result.
Calculation validation
For direct D-values:
- require \(D_{10}>0\)
- require \(D_{10}\leq D_{30}\leq D_{60}\)
- require consistent units
- block division by zero
For grading datasets:
- reconcile the total retained mass with the nominated test basis
- retain raw and corrected values separately
- do not silently smooth non-monotonic data
- show whether each D-value is measured or interpolated
Interpreting Cu and Cc
Cu and Cc describe the grading curve, not the complete engineering behaviour of the material.
Interpretation may also require:
- fines content and plasticity
- particle shape and mineralogy
- density and fabric
- segregation
- moisture condition
- sample representativeness
- the applicable classification or material specification
Do not use Cu or Cc alone to assign design permeability or accept a pavement material.
Review checklist
Ask the reviewing geotechnical engineer to confirm:
- The logarithmic interpolation method is suitable.
- No extrapolation is permitted in the default calculation.
- D-values and units are labelled correctly.
- Monotonicity and duplicate-point rules are appropriate.
- The calculator avoids assigning a soil group automatically.
- Source-data precision and rounding are acceptable.
- The worked examples reproduce independently.
Related resources
- Soil Classification
- Soil Phase Relationships
- Atterberg Limits
- Darcy Flow and Hydraulic Gradient
- California Bearing Ratio Testing
Authoritative references
- AS 1289.0:2014, Standards Australia
- FHWA geotechnical publication library
- FHWA example using D-values, Cu and Cc
Use the current applicable test method and classification system for formal results.
This guide is an educational and checking aid. It does not replace project-specific testing, specifications or review by a suitably qualified geotechnical professional.