Atterberg Limits Indices: PI, LI and CI

Atterberg limits describe the water-content boundaries associated with changes in the consistency of a fine-grained soil. Once the liquid limit and plastic limit have been determined using the nominated test methods, three useful indices can be calculated: plasticity index, liquidity index and consistency index.

Required inputs

Input	Symbol	Meaning	Unit
Liquid limit	\(LL\)	Water content at the liquid-limit condition	%
Plastic limit	\(PL\)	Water content at the plastic-limit condition	%
Natural moisture content	\(w\)	Moisture content of the sample being assessed	%

All three values must be expressed using the same percentage basis.

The calculated indices do not replace the laboratory methods used to determine LL, PL or moisture content.

Plasticity index

The plasticity index is the numerical range between the liquid and plastic limits:

$$ PI = LL-PL $$

For:

• \(LL=52\%\)
• \(PL=24\%\)

$$ PI = 52-24=28 $$

The plasticity index is 28 percentage points.

If \(PL\) is greater than \(LL\), the input set is invalid and should be checked. If \(LL=PL\), then \(PI=0\), and the liquidity and consistency indices cannot be calculated because their denominator is zero.

Liquidity index

The liquidity index compares the natural moisture content with the plastic range:

$$ LI = \frac{w-PL}{PI} $$

Using \(w=35\%\), \(PL=24\%\) and \(PI=28\):

$$ LI = \frac{35-24}{28}=0.3929 $$

A negative liquidity index can occur when the natural moisture content is below the plastic limit. A value greater than 1 can occur when it is above the liquid limit. These values should not be automatically rejected, but the sample condition, representativeness and test data should be reviewed.

Consistency index

The consistency index is:

$$ CI = \frac{LL-w}{PI} $$

For the same example:

$$ CI = \frac{52-35}{28}=0.6071 $$

The two indices provide a useful arithmetic check:

$$ LI+CI=1 $$

Small differences from 1 may arise if displayed values have been rounded. The check should use unrounded values.

Complete worked example

Item	Value
Liquid limit	52%
Plastic limit	24%
Natural moisture content	35%
Plasticity index	28
Liquidity index	0.3929
Consistency index	0.6071

Calculation sequence:

1. Check that \(LL\), \(PL\) and \(w\) use the same basis.
2. Confirm that \(LL\) is greater than \(PL\).
3. Calculate \(PI=LL-PL\).
4. If PI is greater than zero, calculate LI and CI.
5. Check that \(LI+CI=1\) before rounding.
6. Record the source test reports and sample condition.

Plasticity chart relationship

Plasticity index and liquid limit may be plotted on a plasticity chart as part of a soil-classification process. The commonly used A-line is:

$$ PI = 0.73(LL-20) $$

A chart position is not a complete classification by itself. The applicable classification system, organic characteristics, particle-size information and current standard rules must also be considered.

Read Soil Classification for the distinction between a laboratory classification and a field description.

What the indices can help describe

The indices can support:

• comparison of fine-grained samples
• laboratory classification
• assessment of the sample state relative to its plastic range
• identification of inconsistent test results
• selection of additional testing
• engineering interpretation alongside mineralogy, grading, structure and stress history

They do not directly determine:

• characteristic surface movement
• residential site class
• shrink-swell behaviour
• shear strength
• compressibility
• CBR
• suitability as fill or pavement material

Those conclusions require the applicable project method, additional test data and professional judgement.

Important sample considerations

Atterberg results can be affected by:

• sample preparation
• material fraction tested
• drying and storage
• organic content
• particle breakdown
• mixing and conditioning
• operator and apparatus effects
• natural variability within the soil unit

The test report should identify the method and sample preparation used. Values from different methods or fractions should not be combined without review.

Calculation validation checks

A calculation tool should:

• require \(LL\) and \(PL\)
• block \(PL>LL\)
• return PI without LI or CI when natural moisture is absent
• return PI of zero but mark LI and CI undefined when \(LL=PL\)
• permit negative LI and LI above 1 with explanatory messages
• retain unrounded values for the arithmetic check
• avoid assigning a soil group automatically unless a separate validated classification method is selected

Review checklist

Ask the reviewing geotechnical engineer to confirm:

1. The terminology matches current Australian practice.
2. The LL and PL test methods are identified in the source report.
3. Percentage-point and dimensionless outputs are labelled correctly.
4. The treatment of \(PI=0\) is acceptable.
5. Negative LI and LI above 1 are handled appropriately.
6. No site classification or design property is inferred from PI alone.
7. The worked example and rounding are suitable.

Related resources

• Soil Phase Relationships
• Soil Classification
• Particle Size Distribution and Grading Coefficients
• Shrink-Swell Testing
• Shear Strength of Soil

Reference framework

• AS 1289.0:2014, Standards Australia
• AS 1726:2017, Standards Australia

Use licensed copies of the current applicable methods for formal test procedures and reporting requirements.

This guide is an educational and checking aid. It does not replace project-specific testing, applicable standards or review by a suitably qualified geotechnical professional.