Theory: Atterberg Limits
What the liquid, plastic and shrinkage limits are, how they're found with the Casagrande cup, by rolling the soil to 3 mm and by drying a pat, and what the plasticity, consistency and liquidity indices say about the soil.
Atterberg limits
A fine-grained soil changes behavior with its water content: very dry, it's solid and brittle; with more water, it turns plastic and can be molded; with more still, it flows like a viscous liquid. Atterberg proposed the water contents between these states in 1911, and Casagrande standardized the tests in the 1930s.
The liquid limit (LL) divides the plastic and liquid states; the plastic limit (PL), the semisolid and plastic ones; the shrinkage limit (SL), the solid and semisolid ones. All are found on soil passing the 425 µm (No. 40) sieve.
Liquid limit
The soil, mixed with water into a uniform paste, is spread in the cup of the Casagrande device. A groove is cut through it with the standard tool, and the cup is dropped 10 mm onto the base, twice a second, until the groove closes over about 13 mm (½ in). The number of blows is recorded and the water content of soil from beside the groove measured. This is repeated at different water contents so the blows spread between 15 and 35.
Plotted as water content against the logarithm of the number of blows, the trials fall close to a straight line, the flow line. The liquid limit is, by definition, its water content at 25 blows.
ASTM D4318 method B also estimates the limit from a single trial between 20 and 30 blows, as LL = w (N / 25)^0.121. Method A, the multipoint line, is the reference method and the one this page uses.
Plastic limit
A moist portion of the soil is rolled with the palm on a ground-glass plate into a thread. When the thread crumbles as it reaches 3.2 mm (⅛ in) in diameter, the water content of the pieces is one determination. If it reaches that diameter whole, it's kneaded and rolled again, drying until it crumbles.
ASTM D4318 averages two determinations. ABNT NBR 7180 rolls to 3 mm, asks for at least three determinations, and accepts them when none is more than 5% of the mean away from it.
Shrinkage limit
As it dries, a soil loses volume along with water down to the shrinkage limit; below it, air enters the voids and the volume barely changes. The test molds a pat of wet soil in a dish of known volume, oven-dries it and measures the dry pat's volume — ASTM D4943 by coating it in wax and weighing it submerged, which replaced the mercury displacement of the withdrawn D427.
The shrinkage index, PL − SL, is the range of water contents of the semisolid state. A low SL with a large change in volume points to an expansive soil.
Casagrande noted that the A- and U-lines of the plasticity chart, extended, meet near (LL, PI) = (−43.5, −46.4), and that the line from there through the soil's point crosses the LL axis near its shrinkage limit. It's only an estimate, which this page shows when there's no pat:
Indices
When either limit can't be determined, or when PL ≥ LL, the soil is reported as nonplastic (NP).
The liquidity index places the natural water content between the limits: 0 at the plastic limit and 1 at the liquid limit. A clay with a liquidity index above 1 may turn to a viscous liquid when remolded. The ratio PI / FI, the toughness index, rises with the soil's strength at the plastic limit.
Plasticity and consistency
| Plasticity (Burmister) | PI (%) |
|---|---|
| Nonplastic | 0 |
| Slightly plastic | 1 to 5 |
| Low plasticity | 5 to 10 |
| Medium plasticity | 10 to 20 |
| High plasticity | 20 to 40 |
| Very high plasticity | over 40 |
| Consistency | CI |
|---|---|
| Very soft | below 0 |
| Soft | 0 to 0.50 |
| Medium | 0.50 to 0.75 |
| Stiff | 0.75 to 1.00 |
| Hard | over 1.00 |
Plasticity chart
On Casagrande's chart, PI against LL, the A-line (PI = 0.73 (LL − 20)) separates clays, above, from silts and organic soils, below, and LL = 50% separates low from high plasticity. No known soil plots above the U-line (PI = 0.9 (LL − 8)): a point there points to an error in the data. The soil's region gives the symbol of fine-grained soils in the USCS.
Limitations
- The results depend on the device (base hardness, drop height, tool wear), on hand pressure and on the operator; differences of a few points between labs are common.
- Outside 15 to 35 blows the line stops being reliable, and extrapolating to 25 blows is unsafe.
- Sandy or silty soils may slide in the cup or not form a thread; such a soil is nonplastic.
- Drying the soil before the test can lower the limits of organic soils and some tropical soils.
- The consistency ranges by CI apply to clays, not to cemented or sensitive soils.
References
- ASTM. D4318: Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils. West Conshohocken, 2017.
- ASTM. D4943: Standard Test Method for Shrinkage Factors of Cohesive Soils by the Water Submersion Method. West Conshohocken, 2018.
- Burmister, D. M. Principles and techniques of soil identification. Proceedings, Highway Research Board, v. 29, 1949.
- Casagrande, A. Research on the Atterberg limits of soils. Public Roads, v. 13, n. 8, 1932.
- Holtz, R. D.; Kovacs, W. D. An Introduction to Geotechnical Engineering. Englewood Cliffs: Prentice-Hall, 1981.
- Das, B. M.; Sobhan, K. Principles of Geotechnical Engineering. 9th ed. Boston: Cengage, 2018.