Atterberg Limits Explained: Liquid, Plastic and Shrinkage Limits

Three limits, three state boundaries

Fine-grained soil behaves differently depending on its moisture content: as a brittle solid when very dry, as a plastic (moldable) material at intermediate moisture, and as a liquid-like slurry when very wet. The Atterberg limits (commonly tested per a standard such as ASTM D4318) mark the moisture-content boundaries between these states: the shrinkage limit, plastic limit, and liquid limit, in increasing order of moisture content.

The tests are run on the portion of the soil passing the No. 40 sieve, and each limit is reported as a water content. The table below lists the standard for each one, as given in the FHWA's Geotechnical Aspects of Pavements reference manual (NHI-05-037, Table 5-21), with the current ASTM shrinkage-limit method.

From test masses to LL and PL

Both limits are water contents, and each comes from three masses: the container, the container plus wet soil, and the container plus oven-dried soil. Water content (%) = (wet mass − dry mass) ÷ (dry mass − container mass) × 100 — the same calculation covered in How to Calculate Soil Moisture Content.

Liquid limit. The liquid limit is typically determined with a standardized device (the Casagrande cup), and it is defined as the water content at which the groove cut through the soil pat closes at 25 blows. With the one-point method, you measure the water content wN of a specimen whose groove closed at N blows and correct it to 25 blows. The Atterberg Limits Calculator makes that correction with LL = wN × (N ÷ 25)^0.121; take the correction and the blow-count range within which the one-point method is valid from the standard you are testing to (ASTM D4318 or AASHTO T 89), and check that range before relying on a single test. The multi-point method, which tests the soil at several water contents, is the alternative.

Plastic limit. The plastic limit is the water content of a soil thread rolled by hand until it just crumbles at a diameter of 3.2 mm (1/8 in). It uses the same water-content formula, applied to the thread's masses.

The Atterberg Limits Calculator runs these steps from the raw masses and returns the liquid limit, plastic limit and plasticity index.

The plasticity index

The plasticity index is simply the liquid limit minus the plastic limit — the range of moisture content over which the soil behaves plastically. A high plasticity index indicates a soil that stays workable/moldable over a wide moisture range (often a clay-rich soil); a low or zero plasticity index (the soil crumbles before it becomes plastic) is typical of silts or sands.

The liquidity index

Once LL and PL are known, the soil's natural moisture content, w, can be placed between them. The liquidity index is LI = (w − PL) ÷ PI. It equals 0 when the soil is at its plastic limit and 1 at its liquid limit.

Using the worked example below (PL = 25.0, PI = 5.4) and a natural moisture content of 28%: LI = (28 − 25.0) ÷ 5.4 = 0.56. The natural moisture content comes from a separate oven-dry test on the field sample, as in How to Calculate Soil Moisture Content. The Atterberg Limits Calculator does not compute the liquidity index, so do this step by hand.

Reporting the results

Report the liquid limit to the precision required by the standard you are testing to (ASTM D4318 or AASHTO T 89). The Atterberg Limits Calculator shows its results to one decimal place so that each step can be checked; that is a display choice, not a reporting rule.

The shrinkage limit

The shrinkage limit is the water content below which further drying no longer reduces the soil's volume — the boundary between semi-solid and solid behavior, and the lowest of the three limits.

It is a separate test from the liquid and plastic limits. ASTM D4943 determines it by the water submersion method, in which the volume of a dried soil pat is measured while it is submerged in water; AASHTO T 92 is the AASHTO shrinkage-limit test. The older ASTM D427 method, which used mercury to measure that volume, is reported to have been withdrawn in 2008, although some references, including the 2006 FHWA manual, still list it. The BuildNumerics Atterberg Limits Calculator does not calculate the shrinkage limit; it covers the liquid limit, plastic limit and plasticity index only.

Why it matters for construction

Atterberg limits are core inputs to the Unified Soil Classification System and AASHTO soil classification, which inform decisions about a soil's suitability as fill, subgrade, or foundation material, and how it's likely to behave with changes in moisture (shrink-swell potential). For what the numbers mean — plasticity bands, the plasticity chart and A-line, and the soil classes — see What Are Atterberg Limits?.