Developed by Swedish chemist Albert Atterberg in 1911 and later adapted for geotechnical engineering by Arthur Casagrande, the Atterberg limits quantify the consistency of fine-grained soils based on their water content.
The three key limits are:
| Limit | Symbol | Description |
|---|---|---|
| Liquid Limit | LL or $w_L$ | Water content at which soil transitions from plastic to liquid |
| Plastic Limit | PL or $w_P$ | Water content at which soil transitions from semi-solid to plastic |
| Shrinkage Limit | SL or $w_S$ | Water content below which further drying causes no volume change |
2. The Four States of Soil Consistency
As water content increases, fine-grained soil passes through four distinct states:
Solid ──► Semi-Solid ──► Plastic ──► Liquid
↑ ↑ ↑ ↑
SL PL LL
(Shrinkage (Plastic (Liquid
Limit) Limit) Limit)
| State | Behaviour | Occurs when |
|---|---|---|
| Solid | Soil behaves as a solid; no volume change on drying | $w < SL$ |
| Semi-solid | Soil behaves as a solid but volume decreases on drying | $SL < w < PL$ |
| Plastic | Soil can be deformed without cracking or volume change | $PL < w < LL$ |
| Liquid | Soil flows under its own weight | $w > LL$ |
3. Liquid Limit (LL)
3.1 Definition
The water content at which a soil has a shear strength of approximately 2.5 kPa — the threshold where it begins to flow.
3.2 Casagrande Cup Method (AS 1289.3.1.1)
The traditional method uses a brass cup with a grooved soil sample:
- Soil paste is placed in the Casagrande cup and levelled
- A groove is cut through the centre using a standard grooving tool
- The cup is lifted and dropped 10 mm repeatedly at 2 drops/second
- The water content at which the groove closes over 25 blows is the liquid limit
Procedure:
- Test at 3–4 different water contents (typically 15–35 blows)
- Plot water content vs. number of blows on a semi-log graph
- The liquid limit is the water content corresponding to 25 blows
- The flow curve (slope) defines the flow index ($I_F$)
3.3 Cone Penetrometer Method (AS 1289.3.9.1)
The preferred method in Australia and many other countries:
- A standard 80 g cone with 30° apex angle is released from the soil surface
- The cone's penetration depth into the soil sample is measured
- The liquid limit is the water content at which the cone penetrates 20 mm
Advantages over Casagrande cup:
- Less operator-dependent
- Better reproducibility
- Suitable for all fine-grained soils, including those with coarse particles up to 2.36 mm
3.4 Comparison of Methods
| Aspect | Casagrande Cup | Cone Penetrometer |
|---|---|---|
| AS standard | AS 1289.3.1.1 | AS 1289.3.9.1 |
| Equipment cost | Moderate | Higher |
| Operator sensitivity | High | Low |
| Repeatability | ±3–5% | ±1–2% |
| Fine-grained soils | Good | Excellent |
| Soils with sand | Fair | Good |
4. Plastic Limit (PL)
4.1 Definition
The water content at which a soil begins to crumble when rolled into a thread of 3 mm diameter (approximately 1/8 inch).
4.2 Test Procedure (AS 1289.3.2.1)
- A soil sample (about 20 g) is mixed with water until it is plastic enough to roll
- The soil is rolled on a glass plate or non-absorbent surface with the palm of the hand
- The thread is rolled to 3 mm diameter (approximately the diameter of a standard pencil)
- If the thread crumbles at 3 mm diameter, the water content is the plastic limit
- If the thread can be rolled thinner without crumbling, the soil is too wet — knead and re-roll
- The crumbled thread pieces are collected, weighed, dried, and reweighed
4.3 Interpretation
| Plastic Limit Range | Soil Behaviour |
|---|---|
| < 15% | Low plastic limit — usually silty soils |
| 15–30% | Moderate plastic limit — typical clayey soils |
| > 30% | High plastic limit — highly plastic clays |
5. Shrinkage Limit (SL)
5.1 Definition
The water content below which the soil volume does not decrease with further drying. At this point, the soil is fully saturated and the voids are filled with water.
5.2 Test Procedure (AS 1289.3.3.1)
- A wet soil pat is placed in a shrinkage dish
- The soil is oven-dried and the volume is measured using mercury displacement
- The shrinkage limit is calculated from the change in water content and volume
5.3 Shrinkage Ratio
$$ SR = \frac{V_d}{V_w} $$Where $V_d$ = dry volume of soil and $V_w$ = volume of water lost.
6. Derived Indices
6.1 Plasticity Index (PI)
$$ PI = LL - PL $$The range of water content over which the soil behaves plastically:
| PI | Classification | Engineering Behaviour |
|---|---|---|
| 0 | Non-plastic (NP) | Silt — no cohesion; prone to frost heave |
| 1–7 | Low plasticity | Slightly plastic; moderate cohesion |
| 7–17 | Medium plasticity | Moderately plastic; significant shrink/swell |
| 17–35 | High plasticity | Highly plastic; reactive soil |
| 35+ | Very high plasticity | Extremely reactive; problematic for foundations |
6.2 Liquidity Index (LI)
$$ LI = \frac{w - PL}{LL - PL} = \frac{w - PL}{PI} $$Describes the in-situ consistency of a soil relative to its Atterberg limits:
| LI | In-situ Consistency |
|---|---|
| < 0 | Semi-solid or solid state |
| 0–0.25 | Very stiff |
| 0.25–0.50 | Stiff |
| 0.50–0.75 | Firm |
| 0.75–1.0 | Soft |
| > 1.0 | Very soft to liquid |
6.3 Consistency Index (CI)
$$ CI = \frac{LL - w}{PI} $$| CI | Consistency |
|---|---|
| 0 | Liquid |
| 0–0.25 | Very soft |
| 0.25–0.50 | Soft |
| 0.50–0.75 | Firm |
| 0.75–1.0 | Stiff |
| > 1.0 | Very stiff to hard |
6.4 Activity Ratio
$$ A = \frac{PI}{\%\ \text{clay fraction (} < 2\ \mu\text{m)}} $$Identifies the dominant clay mineral:
| Activity | Dominant Clay Mineral |
|---|---|
| < 0.75 | Inactive (kaolinite-dominated) |
| 0.75–1.25 | Normal (illite-dominated) |
| > 1.25 | Active (montmorillonite/smectite-dominated) |
7. The Plasticity Chart (Casagrande Chart)
The Casagrande plasticity chart plots Plasticity Index (PI) against Liquid Limit (LL) and is used to classify fine-grained soils in the Unified Soil Classification System (USCS) and AS 1726.
PI │
60 │ CH (High plasticity clay)
│ ┌──────────────┐
40 │ │ CH │
│ │ │
35 │ ─────┼────── U-Line ──────
│ │ PI = 0.9(LL-8)
20 │ │ CL (Low plasticity clay)
│ CL │ ┌──────────┐
7 │ ─────┼──┼──── A-Line ────────
│ │ │ PI = 0.73(LL-20)
4 │ ML │ │ OL (Organic)
│ ┌────┘ └────┐
0 └──┴──────┴──────┴────────── LL
0 20 35 50 80 100
A-Line: $PI = 0.73(LL - 20)$ — separates clays (above) from silts (below)
U-Line: $PI = 0.9(LL - 8)$ — upper bound of natural soils
8. Typical Values for Australian Soils
| Soil Type | LL (%) | PL (%) | PI (%) | Classification |
|---|---|---|---|---|
| Sydney sand (Bondi) | — | NP | NP | SP |
| Hawkesbury sandstone residual | 25–35 | 15–20 | 5–15 | CL / ML |
| Wianamatta Group shale | 35–55 | 15–25 | 15–30 | CH / CI |
| Black soil (Darling Downs, QLD) | 60–90 | 25–40 | 35–60 | CH |
| Basaltic clay (VIC) | 50–80 | 20–35 | 30–55 | CH |
| Coastal alluvium (Brisbane) | 25–45 | 12–20 | 10–25 | CI |
| Perth sand | — | NP | NP | SP |
| Adelaide alluvial clay | 30–50 | 15–25 | 15–30 | CI / CH |
9. Engineering Significance
9.1 Foundation Design (AS 2870)
The Atterberg limits directly determine residential site classification in Australia:
| Site Class | Characteristic Surface Movement ($y_s$) | Typical PI |
|---|---|---|
| A (Sand/rock) | 0 mm | NP |
| S (Slightly reactive) | 0–20 mm | < 10% |
| M (Moderately reactive) | 20–40 mm | 10–20% |
| H1 (Highly reactive) | 40–60 mm | 20–30% |
| H2 (Highly reactive) | 60–75 mm | 30–50% |
| E (Extremely reactive) | > 75 mm | > 50% |
9.2 Earthworks and Compaction
- High PI soils (> 30%) are difficult to compact and highly susceptible to moisture changes
- Low PI soils (< 10%) compact well but may be prone to erosion
- The OMC for compaction is typically between PL and 0.9 × LL
9.3 Pavement Design
- PI > 20% — subgrade likely to be moisture-sensitive; requires stabilisation or subbase
- PI < 6% — suitable for subgrade without modification
- Materials with PI > 30% are typically excluded from pavement subbase
10. Testing Standards (AS 1289 Series)
| Standard | Title |
|---|---|
| AS 1289.3.1.1 | Determination of the liquid limit of a soil — Casagrande method |
| AS 1289.3.2.1 | Determination of the plastic limit of a soil |
| AS 1289.3.3.1 | Determination of the shrinkage limit of a soil |
| AS 1289.3.4.1 | Determination of the linear shrinkage of a soil |
| AS 1289.3.9.1 | Determination of the cone liquid limit of a soil |
11. Common Errors and Pitfalls
| Error | Effect | Mitigation |
|---|---|---|
| Insufficient remoulding | LL too low | Mix thoroughly; allow 24-hour hydration |
| Over-drying the sample | LL too low | Keep sample covered during testing |
| Rolling too fast at PL | PL too high | Roll at 80–90 strokes per minute |
| Organic matter present | LL artificially high | Test both natural and oven-dried samples |
| Air bubbles in cone test | Erratic penetration | Remove air by thorough mixing |