Atterberg Limits: Liquid Limit, Plastic Limit, Shrinkage Limit and Indices with Example
Short answer: the Atterberg limits are the water contents at which a fine-grained soil changes state. The liquid limit (wL) is where it changes from liquid to plastic, the plastic limit (wP) is where it changes from plastic to semi-solid, and the shrinkage limit (wS) is the water content below which drying no longer reduces its volume. The plasticity index PI = wL − wP is the range over which the soil stays plastic, and it is the key number used to classify clays and silts under IS 1498.
The four states and the three limits
| State | Boundary below it | How it is found |
|---|---|---|
| Liquid | Liquid limit wL | Casagrande cup: water content at which the groove closes over about 12 mm at 25 blows; or cone penetrometer: 20 mm penetration (IS 2720 Part 5) |
| Plastic | Plastic limit wP | Water content at which a soil thread just starts to crumble when rolled to 3 mm diameter (IS 2720 Part 5) |
| Semi-solid | Shrinkage limit wS | Mercury displacement / shrinkage dish test on a dried soil pat (IS 2720 Part 6) |
| Solid | — | Volume no longer changes as water is removed |
Indices you must know
| Index | Formula | What it tells you |
|---|---|---|
| Plasticity index | IP = wL − wP | Range of plastic behaviour; higher = more clayey |
| Liquidity index | IL = (w − wP) / IP | Where the natural water content w sits in the plastic range |
| Consistency index | IC = (wL − w) / IP | Stiffness of the soil in its natural state; IL + IC = 1 |
| Flow index | IF = (w1 − w2) / log10(N2/N1) | Slope of the flow curve (water content vs log blows) |
| Toughness index | IT = IP / IF | Shear strength at the plastic limit; usually between 0 and 3 |
| Shrinkage ratio | SR = Md / (Vd ρw) | Volume change per unit change in water content below wL |
| Activity (Skempton) | A = IP / (% clay finer than 2 µm) | < 0.75 inactive, 0.75–1.25 normal, > 1.25 active |
Consistency by IC: below 0 liquid, 0–0.25 very soft, 0.25–0.50 soft, 0.50–0.75 medium stiff, 0.75–1.00 stiff, above 1.00 very stiff (semi-solid).
Classification on the plasticity chart (IS 1498)
Fine soils are plotted with wL on the x-axis and IP on the y-axis. The A-line is IP = 0.73 (wL − 20). Soils above it are clays (C), below it silts (M) or organic soils (O). Compressibility is set by the liquid limit: L (low) for wL < 35%, I (intermediate) for 35–50%, and H (high) above 50%. So a soil with wL = 43% plotting above the A-line is CI.
Exam tip: remember the order wS < wP < wL. If the natural water content is above the liquid limit, IL > 1 and IC < 0 — the soil behaves like a liquid when disturbed. Many MCQs just test IL + IC = 1.
Worked example
In a Casagrande test a soil gave a water content of 46.5% at 15 blows and 40.2% at 40 blows. Its plastic limit is 22%, natural water content 35%, and clay fraction (< 2 µm) 30%. A shrinkage pat had a wet mass of 34.0 g and volume 19.0 cm³; after oven drying its mass was 24.0 g and volume 13.1 cm³. Find all the indices and classify the soil.
- Flow index: IF = (46.5 − 40.2) / log10(40/15) = 6.3 / 0.426 = 14.8.
- Liquid limit (water content at 25 blows on the flow line): wL = 46.5 − 14.8 × log10(25/15) = 43.2%.
- Plasticity index: IP = 43.2 − 22.0 = 21.2%.
- Liquidity index: IL = (35 − 22) / 21.2 = 0.61; consistency index: IC = (43.2 − 35) / 21.2 = 0.39 → soft clay (check: 0.61 + 0.39 = 1).
- Toughness index: IT = 21.2 / 14.8 = 1.43. Activity: A = 21.2 / 30 = 0.71 → inactive clay.
- A-line at wL = 43.2: IP = 0.73 × (43.2 − 20) = 16.9. Actual IP 21.2 is above it and wL is between 35 and 50 → CI (clay of intermediate compressibility).
- Shrinkage limit: initial water content = (34.0 − 24.0)/24.0 = 41.67%; wS = 41.67 − (19.0 − 13.1) × 1/24.0 × 100 = 17.1%. Shrinkage ratio SR = 24.0/13.1 = 1.83.
Why site engineers care
High-PI clays (black cotton soils often have wL above 50%) swell when wet and shrink when dry, cracking floors, plinth beams and pavements. The liquid limit also gives a rough idea of compressibility, so it shows up again in settlement and subgrade design. That is why every soil investigation report lists wL, wP and IP for each clay layer.
Frequently asked questions
What is the plasticity index of a soil?
Plasticity index is the liquid limit minus the plastic limit (IP = wL - wP). It is the range of water content over which the soil behaves plastically.
What is the relation between liquidity index and consistency index?
Liquidity index plus consistency index always equals 1, because IL = (w - wP)/IP and IC = (wL - w)/IP.
What is the A-line equation in the plasticity chart?
The A-line is IP = 0.73 (wL - 20). Fine soils plotting above it are classified as clays and those below it as silts or organic soils (IS 1498).
Which IS code covers the liquid and plastic limit test?
IS 2720 (Part 5) covers the liquid limit and plastic limit tests, and IS 2720 (Part 6) covers the shrinkage factors.
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