Atterberg Limits & Plasticity Index Simulator

Explore the boundary water contents at which a fine-grained soil — a clay or a silt — passes between its solid, semi-solid, plastic and liquid states. Adjust the liquid limit, plastic limit and natural water content to see the plasticity index, liquidity index and the soil's class on the Casagrande chart update in real time.

Parameters

Liquid limit LL

Water content above which the soil flows like a liquid

Plastic limit PL

Water content below which the soil becomes crumbly

Natural water content w

Water the soil currently holds in the field

Shrinkage limit SL

Water content below which drying no longer reduces volume

Results

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Plasticity index PI (%)

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Liquidity index LI

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Consistency index CI

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A-line PI (%)

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Plasticity-chart class

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Natural-state verdict

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Water-content axis and the four soil states — animation

On the water-content axis the solid, semi-solid, plastic and liquid states are separated by the shrinkage, plastic and liquid limits. The pulsing pointer marks the natural water content; the orange band is the plasticity index. The inset bottom-right is the plasticity chart.

Casagrande plasticity chart

Liquidity index vs natural water content

Theory & Key Formulas

$$PI=LL-PL,\qquad LI=\frac{w-PL}{PI},\qquad CI=\frac{LL-w}{PI}$$

The plasticity index PI is the width of the plastic range; the liquidity index LI locates the natural water content within it. LL: liquid limit, PL: plastic limit, w: natural water content.

$$PI_{A}=0.73\,(LL-20)$$

The Casagrande A-line. A plasticity index above this value is a clay (C), below it a silt (M). A liquid limit below 50% is low-plasticity (L), 50% or above is high-plasticity (H).

What are the Atterberg Limits?

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"Atterberg limits" is a term I've not heard before. What about the soil do they describe?

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In short, they capture in numbers the remarkable fact that a fine-grained soil like clay becomes a completely different material depending on how much water it holds. The very same clay is a hard, brittle solid when bone-dry, a stiff mouldable putty when damp, and a soupy liquid when very wet. In the early twentieth century the Swedish scientist Albert Atterberg defined the boundary water contents where the soil passes from one state to the next. Those are the liquid limit, plastic limit and shrinkage limit — the Atterberg limits.

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Boundary water contents... the sliders on the left have a liquid limit and a plastic limit. Is the gap between them the plasticity index?

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Exactly — plasticity index PI = liquid limit − plastic limit. That is the single most useful number. The plasticity index is the range of water content over which the soil stays plastic, so a large PI is a "fat" clay that swells when wet and shrinks when dry, while a small PI is a lean, low-clay silt. With the default LL = 45 and PL = 22, PI = 23. Push the liquid limit up on the left and you'll see the point on the plasticity chart march up to the right.

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A point appeared on the plasticity chart. What does that diagonal line — the A-line — separate?

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The A-line is an empirical line separating clays from silts, drawn from PI = 0.73(LL−20). A point above the A-line is a clay (C); below it, a silt or organic soil (M). Then a liquid limit below 50% is low-plasticity (L), 50% or above is high-plasticity (H). Combine them and you get four classes — CL, CH, ML and MH. That is the backbone of the Unified Soil Classification System used worldwide. Open any site-investigation report and you'll see these symbols everywhere.

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I get the classification. So where does the natural water content come in?

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That's where the liquidity index LI earns its keep. LI = (natural water content − plastic limit)/plasticity index, and it shows where the soil's current water sits in the plastic range. An LI near 0 is near the plastic limit and stiff; near 1 is near the liquid limit and soft. The alarming case in practice is LI above 1 — the natural water content exceeds the liquid limit, a sign of a "sensitive clay" that can lose much of its strength the moment it is disturbed. It is a real problem in marine clay deposits.

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I see — you look at both the limits and the current water content. There's also a consistency index?

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The consistency index CI = (liquid limit − natural water content)/plasticity index is the mirror image of the liquidity index — it tells you how far from the liquid limit the soil is, so how much margin it has. They obey LI + CI = 1. A large CI means stiff, firm ground; a small one means soft, near-liquid soil. It is handy for compaction control of fill and for deciding whether soft ground needs improvement — it turns a field "feel" into a number.

Frequently Asked Questions

The plasticity index PI is the width of the water-content range over which a soil behaves plastically: PI = liquid limit LL - plastic limit PL. For LL = 45% and PL = 22%, PI = 23%. A large PI signals a "fat", highly plastic clay that swells, shrinks and is sensitive to water; a small PI signals a lean silt or a soil with little clay. The plasticity index is one of the single most useful numbers in geotechnical engineering.

The liquidity index LI = (natural water content w - plastic limit PL) / plasticity index PI shows where the soil's current water content sits within the plastic range. An LI near 0 means the soil sits near its plastic limit and is stiff; an LI near 1 means it sits near its liquid limit and is soft. An LI above 1 means the natural water content exceeds the liquid limit - an alarming sign of a very soft, water-rich, potentially sensitive clay that can lose much of its strength when disturbed.

The A-line is the empirical boundary on the plasticity chart that separates clays from silts (or organic soils): PI = 0.73*(LL - 20). Plotting the plasticity index against the liquid limit, a point above the A-line is a clay (C) and a point below it is a silt (M). A liquid limit below 50% gives a low-plasticity soil (L) and 50% or above gives a high-plasticity soil (H), producing the CL, CH, ML and MH classes - the basis of the Unified Soil Classification System (USCS).

The Atterberg limits do two big jobs: classifying the soil and describing its current state. First, the position on the plasticity chart classifies a fine-grained soil as CL/CH/ML/MH and forms basic information for site-investigation reports and design. Second, the liquidity index compares the natural water content with the limits to tell you how stiff or soft the soil is right now. Because the plasticity index also correlates with swell-shrink potential, permeability and compressibility, it is used when selecting fill materials, treating soft ground and checking bearing capacity.

Real-World Applications

Site investigation and soil classification: Fine-grained soil sampled from a borehole is first tested for its Atterberg limits and then placed on the plasticity chart to decide whether it is CL (low-plasticity clay), CH (high-plasticity clay), ML or MH. This is a mandatory item in site-investigation reports; from the class symbol alone, a designer reads the soil's likely swell, compressibility and permeability tendencies. Together with the grain-size test, it is the most basic information for soil identification.

Selecting fill and subgrade materials: In quality control of embankment fill for roads and dykes and of subgrade soils, the plasticity index serves as an acceptance criterion. A cohesive soil with too high a plasticity index swells and softens with rainwater and shrinks and cracks on drying, so it is judged unsuitable as a subgrade and an upper limit is specified. A non-plastic sandy soil, on the other hand, is hard to compact. The plasticity index is the yardstick that sorts "usable soil" from "unusable soil".

Assessing and treating soft ground: Ground with a liquidity index near or above 1 is extremely soft — the natural water content has reached the liquid limit. Such conditions are common in marine clays and organic soils, and when the sensitivity is high the soil loses much of its strength the instant it is disturbed. Whether sand drains, preloading or ground improvement are needed is first scoped from the liquidity index and the consistency index.

Expansive soils and slope stability: The higher the plasticity index, the more the soil tends to contain swelling clay minerals such as montmorillonite, and the more it changes volume with water content. In risk assessment for differential settlement of foundations, increased earth pressure behind retaining walls and post-rainfall slope failures, the plasticity index is used to estimate swell potential and residual strength. Simple as it is, it serves as the gateway to many design decisions.

Common Misconceptions and Pitfalls

The most common pitfall is assuming the Atterberg limits represent the soil's absolute strength. Both the liquid limit and the plastic limit are "water contents" measured by standardized remoulded tests (25 blows for the liquid limit, a 3 mm thread for the plastic limit) — not the strength itself. Even at the same plasticity index, the actual strength and consolidation behaviour vary greatly with soil structure, age and stress history. The Atterberg limits exist to classify soils and capture trends in their properties. The strength and deformation properties used in design must be obtained from separate tests such as unconfined compression and consolidation tests.

Next, assuming a liquidity index below zero can be used as is. A negative liquidity index means the natural water content is below the plastic limit — a very stiff soil in the semi-solid to solid state. That is healthy ground in itself, but an overconsolidated clay or a dried surface crust can soften abruptly with only a small increase in water content. Conversely, when the plastic limit is very close to the liquid limit (plasticity index near zero), the denominator of the liquidity index is small and the calculated value swings wildly. This tool guards against the plastic limit reaching or exceeding the liquid limit, but treat values from cases with an extremely small PI with caution.

Finally, treating the plasticity-chart class as a complete design decision. The CL, CH, ML and MH classes are only a starting point that indicates the soil's broad character. Two soils both labelled CH — say Kanto loam, Ariake clay and an overseas expansive clay — can behave very differently. The plasticity chart has regions where several boundaries overlap (A-line, U-line, organic-soil tests), and a point right on the A-line can flip class within test scatter. Use the classification as the gateway to design and judge holistically, together with the geology, formation history and local case records of the actual ground.