Atterberg Limits — Liquid Limit, Plastic Limit & Shrinkage Limit
Consistency limits of fine-grained soils, derived indices, IS 2720 test procedures, and the plasticity chart — with GATE-level worked examples
Last Updated: March 2026
Key Takeaways
- Atterberg limits define the water content boundaries between the four consistency states of fine-grained soil: solid, semi-solid, plastic, and liquid.
- Liquid Limit (LL or wL): water content at which soil transitions from plastic to liquid state — measured by Casagrande cup (IS 2720 Part 5) or cone penetrometer.
- Plastic Limit (PL or wP): water content at which soil transitions from semi-solid to plastic state — measured by thread-rolling method (IS 2720 Part 5).
- Shrinkage Limit (SL or wS): water content below which further drying causes no further volume decrease — measured by mercury displacement method (IS 2720 Part 6).
- Plasticity Index PI = LL − PL; it measures the range of water content over which soil behaves plastically.
- Liquidity Index LI = (w − PL) / PI and Consistency Index CI = (LL − w) / PI describe the current state of a natural soil relative to its limits.
- Activity A = PI / (% clay fraction) characterises the clay mineral type and expansion potential of the soil.
1. Consistency States of Fine-Grained Soils
Fine-grained soils (silts and clays) behave very differently depending on their water content. A soft clay at high water content flows like a viscous liquid; as it dries it becomes plastic (mouldable), then semi-solid (crumbly), then solid (hard and brittle). These states are separated by specific water content boundaries called Atterberg limits, first proposed by Swedish soil scientist Albert Atterberg in 1911 and later standardised for engineering use by Casagrande.
1.1 The Four Consistency States
| State | Behaviour | Water Content Boundary |
|---|---|---|
| Liquid | Flows under its own weight; no shear strength | Above LL |
| Plastic | Can be moulded without cracking; retains shape | Between PL and LL |
| Semi-solid | Crumbles when moulded; volume still decreases on drying | Between SL and PL |
| Solid | Hard; no further volume decrease on drying | Below SL |
The limits are defined for remoulded (disturbed) soil — they do not directly represent the in-situ behaviour of undisturbed natural deposits. However, the indices derived from the limits (LI, CI, PI) are powerful predictors of soil engineering properties and are used extensively in classification and geotechnical design.
2. Liquid Limit (LL or wL)
The liquid limit is the water content at which a soil transitions from the plastic to the liquid state. By Casagrande’s definition, it is the water content at which a standard groove cut in a soil pat closes over 12.5 mm when the cup is dropped 25 times from a height of 10 mm.
2.1 Casagrande Cup Method (IS 2720 Part 5)
Soil mixed with water is placed in a brass cup and a standard grooving tool cuts a trapezoidal groove through the centre. The cup is repeatedly dropped (at 2 drops/second) and the number of blows to close the groove 12.5 mm is recorded. Tests are conducted at 4–5 different water contents; a semi-log plot of water content vs number of blows (the flow curve) is drawn, and LL is read at 25 blows.
Flow index IF = (w1 − w2) / log(N2/N1)
IF = slope of the flow curve (indicates sensitivity to water content change)
2.2 Cone Penetrometer Method
A 30° cone of 148 g is released from the soil surface; LL is defined as the water content at which the cone penetrates exactly 20 mm in 5 seconds. This method is considered more reproducible than the Casagrande cup and is preferred in many modern laboratories (BS 1377).
2.3 One-Point Method (IS 2720)
LL = wN (N/25)0.121
where wN = water content at N blows (N between 20 and 30)
Used for a quick single-test estimate of LL
2.4 Typical LL Values
| Soil Type | LL (%) |
|---|---|
| Sandy silt (low plasticity) | 25–35 |
| Inorganic clay (medium plasticity) | 35–50 |
| Inorganic clay (high plasticity) | 50–80 |
| Black cotton soil (expansive clay) | 60–100+ |
| Organic clay / peat | 80–300+ |
3. Plastic Limit (PL or wP)
The plastic limit is the water content at which soil transitions from the semi-solid to the plastic state. It is the minimum water content at which a soil can be rolled into a 3 mm diameter thread without crumbling.
3.1 Thread-Rolling Method (IS 2720 Part 5)
A small ball of soil (~8 g) is rolled on a glass plate until it forms a thread of 3 mm diameter. If the thread just begins to crumble at 3 mm diameter, the water content at that point is the PL. If the thread crumbles before reaching 3 mm, the soil is too dry (water content below PL); if it doesn’t crumble, the soil is too wet. The test is repeated until consistent results are obtained.
3.2 Typical PL Values
| Soil Type | PL (%) |
|---|---|
| Non-plastic soil (sand, gravel) | NP (cannot be rolled) |
| Silt (low plasticity) | 15–25 |
| Inorganic clay | 20–35 |
| Black cotton soil | 25–40 |
Soils that cannot be rolled into a 3 mm thread at any water content are classified as non-plastic (NP). This is typical of coarse-grained soils (sands and gravels) and clean silts with little clay content.
4. Shrinkage Limit (SL or wS)
The shrinkage limit is the water content below which further drying causes no further reduction in the total volume of the soil. At the SL, all the voids are still water-filled (S = 100 %) but the volume is at its minimum — further drying only desaturates the pores without shrinking the soil skeleton.
4.1 Significance
The shrinkage limit is particularly important for expansive soils (black cotton soils, montmorillonite clays). When the water content of such soils drops below the SL during dry seasons, they shrink and crack. When rewetted, they swell. This cyclic swelling and shrinkage causes severe damage to roads, buildings, and other infrastructure in tropical and semi-arid regions of India.
4.2 Shrinkage Ratio and Volumetric Shrinkage
Shrinkage ratio SR = Ms / (Vd × ρw) = γd / γw
Volumetric shrinkage VS = (Vo − Vd) / Vd × 100 %
Shrinkage limit: SL = wo − VS/SR (where wo is initial water content)
Or: SL = (1/Gs − 1/SR) × 100 (from phase relationships)
In practice, SL is rarely measured compared to LL and PL; it appears more in classification problems and GATE theory questions than in routine site investigations.
5. Derived Indices
5.1 Plasticity Index (PI or IP)
PI = LL − PL
PI = 0 → Non-plastic soil
PI = 1–7 → Low plasticity
PI = 7–17 → Medium plasticity
PI > 17 → High plasticity
PI represents the range of water content over which the soil remains plastic — it is the most widely used indicator of the plastic behaviour of fine-grained soils. A high PI indicates high clay content and/or highly active clay minerals.
5.2 Liquidity Index (LI or IL)
LI = (w − PL) / PI = (w − PL) / (LL − PL)
LI < 0 → Soil is in semi-solid or solid state (w < PL); very stiff
LI = 0 → w = PL; stiff
0 < LI < 1 → Soil is plastic; LI = 0.5 means w is midway between PL and LL
LI = 1 → w = LL; soft, near liquid
LI > 1 → Sensitive or quick clay; very soft, potentially unstable
5.3 Consistency Index (CI or IC)
CI = (LL − w) / PI = 1 − LI
CI = 0 → w = LL; soft, near liquid
CI = 1 → w = PL; stiff
CI > 1 → w < PL; very stiff (semi-solid / solid state)
Note: LI + CI = 1 always.
5.4 Flow Index (IF)
IF = slope of flow curve = (w1 − w2) / log(N2/N1)
Higher IF → more sensitive to water content changes → weaker soil
5.5 Toughness Index (IT)
IT = PI / IF
IT < 1 → Friable (crumbly at PL)
IT = 1–3 → Normal clay
IT > 3 → Tough, highly plastic clay
6. Activity of Clays (Skempton, 1953)
A = PI / (% of clay fraction, i.e. particles < 2 μm)
| Activity (A) | Classification | Clay Mineral |
|---|---|---|
| < 0.75 | Inactive | Kaolinite (A ≈ 0.4) |
| 0.75–1.25 | Normal | Illite (A ≈ 0.9) |
| > 1.25 | Active | Montmorillonite (A ≈ 4–7) |
Activity is significant because it quantifies the swelling and shrinkage potential of a clay. Montmorillonite (smectite), the dominant mineral in black cotton soils, has very high activity and is responsible for the severe shrink-swell behaviour seen in many parts of peninsular India. Kaolinite, common in lateritic soils, is relatively inert and stable.
7. Plasticity Chart (Casagrande)
The plasticity chart plots PI on the y-axis against LL on the x-axis. It is the graphical basis of the USCS / IS 1498 classification for fine-grained soils. Two reference lines divide the chart:
| Line | Equation | Significance |
|---|---|---|
| A-line | PI = 0.73(LL − 20) | Separates clays (above A-line) from silts and organic soils (below A-line) |
| U-line | PI = 0.9(LL − 8) | Upper boundary — no natural soil plots above this line; results above it suggest testing errors |
Classification Zones on Plasticity Chart
| Symbol | Zone | Condition |
|---|---|---|
| ML | Silt of low plasticity | Below A-line, LL < 50 % |
| CL | Clay of low plasticity | Above A-line, LL < 50 %, PI > 7 |
| MH | Silt of high plasticity | Below A-line, LL ≥ 50 % |
| CH | Clay of high plasticity | Above A-line, LL ≥ 50 % |
| CL-ML | Silty clay | Above A-line, PI between 4 and 7, LL < 50 % |
| OL / OH | Organic silt or clay | Below A-line; LL(oven-dried) / LL(undried) < 0.75 |
The vertical line at LL = 50 % separates low plasticity (L) soils from high plasticity (H) soils. This is the most-tested part of the plasticity chart in GATE CE.
8. IS 2720 Test Methods Summary
| Test | IS 2720 Part | Standard Criterion |
|---|---|---|
| Liquid Limit (Casagrande cup) | Part 5 | Groove closes 12.5 mm at 25 blows, drop height 10 mm |
| Plastic Limit (thread rolling) | Part 5 | Thread just crumbles at 3 mm diameter |
| Shrinkage Limit | Part 6 | Mercury displacement method; volume at dry mass |
| Grain size (sieve) | Part 4 | IS sieves 4.75 mm to 75 μm; dry/wet sieving |
| Grain size (hydrometer) | Part 4 | Stokes’ law for particles < 75 μm |
9. Worked Examples
Example 1 — Compute All Derived Indices
Problem: A soil has LL = 52 %, PL = 28 %, and natural water content w = 38 %. Compute PI, LI, CI, and state the consistency of the soil. Also classify the soil using the plasticity chart.
Plasticity Index
Liquidity Index
Consistency Index
Or: CI = (LL − w) / PI = (52 − 38) / 24 = 14/24 = 0.58 ✓
Consistency State
LI = 0.42 → 0 < LI < 1 → soil is in the plastic state, closer to stiff (LI < 0.5 → medium stiff).
Plasticity Chart Classification
Actual PI = 24 > 23.36 → above A-line
LL = 52 % ≥ 50 % → High plasticity zone
Classification: CH — Clay of High Plasticity
Example 2 — Toughness and Flow Index
Problem: A Casagrande cup test gives the following results:
| Number of blows (N) | Water content w (%) |
|---|---|
| 15 | 46.2 |
| 22 | 43.5 |
| 31 | 41.0 |
PL = 22 %. Find: (a) LL, (b) flow index, (c) PI, (d) toughness index.
(a) Liquid Limit from Flow Curve
IF = (46.2 − 41.0) / log(31/15) = 5.2 / log(2.067) = 5.2 / 0.3153 = 16.49
At N = 25: w = 46.2 − 16.49 × log(25/15) = 46.2 − 16.49 × 0.2218 = 46.2 − 3.66 = 42.5 %
LL = 42.5 %
(b) Flow Index
(c) Plasticity Index
(d) Toughness Index
1 < IT < 3 → Normal clay toughness ✓
Example 3 — GATE-Style: Classify Soil from Atterberg Limits
Problem (GATE CE type): A fine-grained soil has LL = 38 % and PL = 24 %. The clay fraction (particles < 2 μm) is 30 %. Find: (a) PI, (b) classify on plasticity chart, (c) activity, and (d) identify the probable dominant clay mineral.
(a) PI
(b) Plasticity Chart
Actual PI = 14 > 13.14 → above A-line
LL = 38 % < 50 % → Low plasticity
PI = 14 > 7 → CL — Clay of Low Plasticity
(c) Activity
(d) Clay Mineral
Activity = 0.47 < 0.75 → Inactive clay → dominant mineral is likely Kaolinite.
10. Common Mistakes
Mistake 1: Using the Wrong Denominator in LI and CI
What happens: Students compute LI = (w − PL) / LL instead of dividing by PI = LL − PL. This gives a dimensionally inconsistent result and a wrong numerical answer.
Fix: LI = (w − PL) / (LL − PL) = (w − PL) / PI. The denominator is always the plasticity index, not LL alone.
Mistake 2: Plotting Points Below the A-line as Clay
What happens: On the plasticity chart, soils above the A-line are clays (C prefix) and soils below are silts or organic soils (M or O prefix). Students sometimes misread the chart and classify below-A-line soils as clays.
Fix: A-line equation: PI = 0.73(LL − 20). Plot the point (LL, PI). If it falls above the A-line → clay; if below → silt or organic. If PI is between 4 and 7 and the point is very close to the A-line, classify as CL-ML (borderline).
Mistake 3: Confusing LL = 50 % as a Boundary Between Inorganic and Organic Soils
What happens: The LL = 50 % vertical line on the plasticity chart separates low (L) from high (H) plasticity — it does not separate organic from inorganic soils. Organic soils are identified by the oven-drying criterion (LL after oven drying / LL before oven drying < 0.75), not by their position relative to LL = 50 %.
Fix: LL = 50 % → L vs H (low vs high plasticity). Organic identification → compare dried vs undried LL; if ratio < 0.75, classify as OL or OH.
Mistake 4: Assuming Atterberg Limits Apply to All Soils
What happens: Atterberg limit tests are performed on coarse-grained soils (sands, gravels), giving NP (non-plastic) results, and then students attempt to classify these soils on the plasticity chart — which does not apply to them.
Fix: Atterberg limits are only meaningful for fine-grained soils (silts and clays). For coarse-grained soils, the soil behaviour is characterised by grain size distribution and relative density. In USCS/IS 1498, a soil is classified as fine-grained only if more than 50 % passes the 75 μm (No. 200) sieve.
Mistake 5: Interpreting LI > 1 as an Error
What happens: When the natural water content w exceeds LL, LI computes to a value greater than 1. Students flag this as a calculation error rather than recognising it as a physically valid — and geotechnically important — result.
Fix: LI > 1 means the natural water content is above the liquid limit, which occurs in very soft, sensitive, or quick clays (e.g., Leda clay in Canada, marine clays in Kerala). These soils have very low strength and are highly compressible. LI > 1 is a warning sign for foundation design, not a calculation error.
11. Frequently Asked Questions
Q1. Why are Atterberg limits determined on remoulded soil rather than undisturbed samples?
Atterberg limits are index properties — they characterise the mineralogy and particle size of the soil itself, not the structure of a particular deposit. By remoulding the soil and mixing it with water, the test eliminates the influence of natural structure (cementation, fissures, particle orientation) and measures only the intrinsic plasticity of the soil material. This makes the limits reproducible and comparable between different soils and laboratories. The in-situ behaviour of undisturbed soil is then assessed by comparing the natural water content to these limits using LI and CI — telling you how the natural deposit compares to the standard reference states.
Q2. What does a high plasticity index tell us about a soil’s engineering behaviour?
A high PI indicates that the soil remains plastic over a wide range of water contents — meaning it is sensitive to moisture changes, will shrink and swell significantly with seasonal wetting and drying, and will be highly compressible when saturated. High-PI soils (typically CH clays and black cotton soils) are problematic for foundations, roads, and embankments: they settle significantly under load, heave when wetted, and lose substantial strength when disturbed. In foundation design, soils with PI > 20 % require careful analysis and often soil improvement (lime stabilisation, preloading, or geosynthetics) before construction.
Q3. What is the difference between the liquidity index and the consistency index — when do you use each?
Both LI and CI describe the current consistency state of a soil relative to its Atterberg limits — they are just complementary measures: CI = 1 − LI. The liquidity index is used when you want to characterise how “liquid-like” a soil is: LI near 1 means the soil is near liquid (very soft); LI near 0 means it is near its plastic limit (stiff). The consistency index is conceptually equivalent but inverted — CI near 1 is a stiff soil; CI = 0 is near liquid. In Indian geotechnical practice and IS code references, CI is more commonly used in descriptive consistency terms (very stiff, stiff, firm, soft, very soft), while LI appears more in research and comparison with sensitivity and remoulded strength. For GATE CE, know both formulas and the interpretation of boundary values.
Q4. Why does the A-line start at LL = 20 % and not at LL = 0 %?
The A-line equation PI = 0.73(LL − 20) crosses the LL axis at LL = 20 %. This is because soils with LL < 20 % are not plastically deformable in any meaningful engineering sense — they behave essentially as non-plastic silts. The A-line was derived empirically by Casagrande from a large dataset of natural soils; the intercept at LL = 20 % reflects the practical minimum plasticity required for a soil to show clay-like behaviour. Any fine-grained soil with LL < 20 % plots below the A-line by definition and is classified as ML (low-plasticity silt) regardless of its PI, since PI for such soils is typically near zero.