Atterberg limits test: liquid limit, plastic limit, and PI

The Atterberg limits are the water contents at which a fine-grained soil passes from one state of consistency to the next: from solid to semisolid at the shrinkage limit, from semisolid to plastic at the plastic limit, and from plastic to liquid at the liquid limit. The Swedish chemist and agricultural scientist Albert Atterberg proposed them in 1911, and today they are the basis for classifying silts and clays.

In the lab, the liquid limit (LL) and the plastic limit (PL) are measured following ASTM D4318, which also gives the plasticity index (PI). The shrinkage limit (SL) has its own standard, ASTM D4943, which measures the volume of a dried soil pat by submerging it in water. Both standards test only the part of the soil that passes the 425 µm (No. 40) sieve. Besides classifying the soil, the limits are correlated with its compressibility, permeability, compactibility, shrink-swell behavior, and shear strength.

Atterberg limits calculator

The calculator also has a page of its own, to keep at hand: the Atterberg limits calculator.

What are the Atterberg limits?

A clay can be molded at some water contents and not at others. With little water, it behaves like a solid; with a lot, the soil and water flow together like a thick liquid. The Atterberg limits mark the water contents where that behavior changes. Each one is a water content expressed as a percentage of the mass of the oven-dry soil, and each comes from a test defined by convention, so a value only means something when it was measured the way the standard says.

Liquid limit

The liquid limit is the water content at which the soil passes from the plastic to the liquid state. By the ASTM D4318 convention, it is the water content at which a groove cut in a soil pat in the Casagrande cup closes along 13 mm (½ in.) after 25 drops of the cup. Since it is hard to hit 25 blows exactly, several trials are run at different water contents and the value at 25 blows is read from a line.

Plastic limit

The plastic limit is the water content at which the soil passes from the semisolid to the plastic state. It is the water content at which a thread of soil, rolled out by hand or with a rolling device, crumbles when it reaches a diameter of 3.2 mm (⅛ in.) and can no longer be rolled out again.

Shrinkage limit

The shrinkage limit is the water content below which further drying no longer reduces the volume of the soil. Above it, every gram of water that evaporates takes an equal volume with it; below it, the particles are already packed as tightly as drying can pack them, and air enters the pores instead. ASTM D4943 finds it by drying a pat of soil molded at a high water content and measuring its volume before and after.

Plasticity index and related indices

The plasticity index is the range of water contents over which the soil behaves plastically:

$$PI = LL - PL$$

From the limits and the soil’s natural water content, $w_n$, two more indices describe the state of the soil where it lies. The liquidity index is 0 when the soil is at its plastic limit and 1 when it is at its liquid limit; the consistency index runs the other way:

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

ASTM D4318 also notes that the plasticity index and the percentage of particles finer than 2 µm give the soil’s activity number, a measure of how active its clay minerals are.

Equipment

Liquid limit and plastic limit (ASTM D4318)

• Casagrande liquid limit device: a brass cup that, with its hanger, weighs 185 to 215 g, a cam that lifts the cup, and a hard rubber base. The height of drop is adjusted to 10 ± 0.2 mm. It can be turned by hand or by a motor at 2 ± 0.1 revolutions per second.
• Flat grooving tool, of plastic or noncorroding metal, with a tip 1.9 to 2.1 mm wide and 7.9 to 8.1 mm deep.
• Gage block for checking the 10 mm height of drop (it often comes on the handle of the grooving tool).
• Ground glass plate, at least 30 cm (12 in.) square and 1 cm (⅜ in.) thick, for mixing the soil and rolling the threads.
• Plastic limit rolling device (optional), with the paper that goes on its plates.
• A rod 3.2 mm in diameter to compare the threads against (optional, useful while learning).
• Spatula with a blade about 2 cm wide and 10 to 13 cm long.
• 425 µm (No. 40) sieve, 200 mm (8 in.) in diameter; a 2.00 mm (No. 10) sieve may also be needed. A washing pan to go with them.
• Mixing and storage dish that keeps the soil from losing water.
• Wash bottle with distilled or demineralized water.
• Water content containers with lids.
• Balance readable to 0.01 g.
• Oven at 110 ± 5 °C.

Shrinkage limit (ASTM D4943)

• Shrinkage dish, permanently identified, and a glass plate to determine its volume.
• Grease, to coat the dish and the glass plate.
• Microcrystalline wax, with no paraffin, and a pot to melt it in.
• A tube with a cap and a caliper, to cast a cylinder of wax and measure its density.
• Steel straightedge and spatula.
• Thread to hang the soil pat from.
• Balance readable to 0.01 g with a suspension apparatus and a water bath, to weigh the pat submerged.
• The Casagrande device, to bring the soil to the right consistency, and the oven at 110 ± 5 °C.

Preparing the specimen (ASTM D4318)

The same prepared soil is used for the liquid limit and the plastic limit. ASTM D4318 has two preparation procedures. The client or the project specifies which one; if nobody does, the wet preparation is used.

• Wet preparation (procedure 1, the default). Start from the soil at its natural water content, without drying it. Take enough to give 150 to 200 g of material passing the 425 µm (No. 40) sieve. If the soil has little coarse material, mix it with distilled water on the glass plate and remove the coarser particles by hand or by pressing the soil through the sieve. If it has a lot, soak it until the lumps soften and wash it through the 425 µm sieve, no more than 500 g at a time, and discard what stays on the sieve. Then dry the slurry toward the liquid limit, at room temperature or with warm air (the required way when the soil has soluble salts), by decanting clear water, or by filtering.
• Dry preparation (procedure 2). Only when it is specified. Dry the sample at no more than 60 °C, break up the lumps with a rubber-covered pestle so the particles themselves don’t break, and pass the fine material through the 425 µm sieve. Soak what is retained, wash its fines through the sieve, and add that wash water to the dry fines.

Either way, mix in distilled water until the soil reaches the consistency of the first trial: about 25 to 35 blows for Method A, or 20 to 30 blows for Method B. Cover it and let it stand for at least 16 hours (overnight), and remix it thoroughly just before testing. Drying changes the result: the liquid limit of a soil with a lot of organic matter drops sharply when it is oven-dried, so comparing the liquid limit before and after oven-drying is a qualitative check for organic matter.

Liquid limit procedure with the Casagrande cup (ASTM D4318)

ASTM D4318 gives two methods. Method A (multipoint) is the default and the more precise one; ASTM recommends it whenever the result may be disputed. Method B (one-point) takes less time, but it depends on the operator’s judgment, it is not recommended for inexperienced operators, and its correlation may not hold for organic soils or soils from a marine environment.

Before starting, check that the device is clean and not worn (the base, the cup, the cam, and the tip of the grooving tool) and adjust the height of drop to 10 mm with the gage.

Method A: multipoint

Method B: one-point

Plastic limit procedure (ASTM D4318)

Shrinkage limit procedure (ASTM D4943)

The water submersion method finds the volume of the dry pat by coating it in wax and weighing it under water. The standard’s procedure tests one pat; a teaching lab can run two or three to see how much the results scatter.

Volume of the shrinkage dish

Density of the wax

The soil pat

Calculations

Water content of each container

Every liquid and plastic limit trial gives one water content, calculated as ASTM D2216 does:

$$w = \frac{m_{cw} - m_{cd}}{m_{cd} - m_c} \times 100$$

Where:

• $w$ = water content of the trial (%)
• $m_c$ = mass of the empty container (g)
• $m_{cw}$ = mass of the container with the wet soil (g)
• $m_{cd}$ = mass of the container with the oven-dry soil (g)

Liquid limit, Method A: the flow curve

1. Plot each trial’s water content (arithmetic scale) against its number of blows (logarithmic scale).

2. Draw the best straight line through the three points. That line is the flow curve:

   $$w = C - I_F \log_{10} N$$

   Where:

   • $N$ = number of blows to close the groove
   • $I_F$ = flow index, the drop in water content over one log cycle of blows (%)
   • $C$ = the line’s water content at $N = 1$ (%)

   With two points on the line, $(N_1, w_1)$ and $(N_2, w_2)$, the flow index is:

   $$I_F = \frac{w_1 - w_2}{\log_{10} (N_2 / N_1)}$$

3. Read the water content of the line at 25 blows. That is the liquid limit; round it to the nearest whole number. The calculator fits the line by least squares and reads it at 25 blows the same way.

Liquid limit, Method B: one point

1. For each of the two water content specimens, calculate a trial liquid limit:

   $$LL_n = w_n \left( \frac{N}{25} \right)^{0.121}$$

   Where:

   • $LL_n$ = trial liquid limit (%)
   • $w_n$ = water content of the specimen (%)
   • $N$ = blows that closed the groove for that specimen

2. The liquid limit is the average of the two trial values, rounded to the nearest whole number. If they differ by more than one percentage point, the USACE laboratory manual has the test repeated.

Plastic limit

The plastic limit is the average of the water contents of the two containers, rounded to the nearest whole number.

Plasticity index

$$PI = LL - PL$$

Where:

• $PI$ = plasticity index
• $LL$ = liquid limit, as a whole number
• $PL$ = plastic limit, as a whole number

If the liquid limit or the plastic limit can’t be determined, or if the plastic limit is equal to or greater than the liquid limit, the soil is reported as nonplastic (NP). The same goes when the soil keeps sliding in the cup after several trials at higher water contents, or when the groove always closes in fewer than 25 blows: the liquid limit can’t be determined, and the plastic limit test is skipped.

Shrinkage limit

The calculations below and the symbols they use follow ASTM D4943.

1. Mass of the dry soil:

   $$m_s = m_d - m$$

   Where:

   • $m_s$ = mass of the oven-dry soil pat (g)
   • $m_d$ = mass of the dish with the oven-dry soil (g)
   • $m$ = mass of the greased dish (g)

2. Water content of the soil when it was placed in the dish:

   $$w = \frac{m_w - m_d}{m_s} \times 100$$

   Where:

   • $w$ = initial water content of the soil in the dish (%)
   • $m_w$ = mass of the dish with the wet soil (g)

3. Mass of water displaced by the wax-coated pat:

   $$m_{wsx} = m_{sxa} - m_{sxw}$$

   Where:

   • $m_{wsx}$ = mass of water displaced by the wax-coated pat (g)
   • $m_{sxa}$ = mass of the wax-coated pat in air (g)
   • $m_{sxw}$ = mass of the wax-coated pat in water (g)

4. Volume of the wax-coated pat:

   $$V_{dx} = \frac{m_{wsx}}{\rho_w}$$

   Where:

   • $V_{dx}$ = volume of the dry pat with its wax (cm³)
   • $\rho_w$ = density of water (1.000 g/cm³)

5. Density of the wax, from its cylinder:

   $$\rho_x = \frac{m_{wp}}{\pi d^2 h / 4}$$

   Where:

   • $\rho_x$ = density of the wax (g/cm³), to at least two significant digits
   • $m_{wp}$ = mass of the wax cylinder (g)
   • $d$, $h$ = average diameter and height of the wax cylinder (cm)

6. Mass and volume of the wax on the pat:

   $$m_x = m_{sxa} - m_s \qquad V_x = \frac{m_x}{\rho_x}$$

   Where:

   • $m_x$ = mass of the wax (g)
   • $V_x$ = volume of the wax (cm³)

7. Volume of the dry pat:

   $$V_d = V_{dx} - V_x$$

   Where:

   • $V_d$ = volume of the oven-dry soil pat (cm³)

8. Shrinkage limit:

   $$SL = w - \frac{(V - V_d)\,\rho_w}{m_s} \times 100$$

   Where:

   • $SL$ = shrinkage limit (%), reported to the nearest whole number
   • $V$ = volume of the wet soil pat, equal to the volume of the dish (cm³)

   In the calculator, the wet volume is $V$ and the dry volume is $V_d$.

9. Shrinkage ratio, reported to two decimal places:

   $$R = \frac{m_s}{V_d \, \rho_w}$$

   With it, the standard also gives the volumetric shrinkage from a given water content $w_1$ (%), and the linear shrinkage, both to the nearest whole number:

   $$V_s = R\,(w_1 - SL) \qquad L_s = 100 \left[ 1 - \left( \frac{100}{V_s + 100} \right)^{1/3} \right]$$

What to report

For the liquid and plastic limits (ASTM D4318):

• Sample identification (project, boring, sample, depth) and a description of the soil.
• Liquid limit, plastic limit, and plasticity index, as whole numbers; NP if the soil is nonplastic.
• The liquid limit method (A or B) and the preparation procedure (wet or dry).
• An estimate of the percentage of the sample retained on the 425 µm (No. 40) sieve, and any special selection, such as removing sand lenses.
• If you have it, the natural water content and the liquidity index.

For the shrinkage limit (ASTM D4943):

• Sample identification, date, and who ran the test, with a description of the soil and any special preparation.
• Shrinkage limit and volumetric and linear shrinkage, as whole numbers, and the shrinkage ratio to two decimal places.
• The masses of the wet and dry pat, the pat with wax in air and in water, the density of the wax, and the initial volume of the soil.

Using the results

The liquid limit and the plasticity index place a fine-grained soil on the plasticity chart, which is how the Unified Soil Classification System separates silts from clays and low plasticity from high plasticity, with the boundary at a liquid limit of 50. The USCS lesson goes through it. A point above the upper limit line, $PI = 0.9\,(LL - 8)$, has never been found in a natural soil, so it usually points to a mistake in the calculation.

Common mistakes

• A height of drop that wasn’t checked, or worn parts: a worn spot on the base, a groove worn into the cup, or a grooving tool whose tip has worn wider than 2.1 mm.
• Soil left on the base where the cup strikes it.
• Letting the soil dry out during the test. Keep the dish covered.
• Adding dry soil to a mix that came out too wet. Let it dry on the glass plate instead.
• Testing soil that was air-dried or oven-dried when the wet preparation was asked for, or that wasn’t mixed and left to stand long enough.
• Water contents measured on too little soil, or on different balances.
• In the plastic limit, a final diameter judged by eye without the 3.2 mm rod, or stopping the rolling too soon. If you are unsure whether the thread has crumbled, roll it once more.

References

• ASTM International. ASTM D4318, Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils: scope and significance. https://www.astm.org/d4318-26.html
• ASTM International. ASTM D4318-00, scope (notes on the one-point method). https://store.astm.org/d4318-00.html
• ASTM International. ASTM D4943, Standard Test Method for Shrinkage Factors of Cohesive Soils by the Water Submersion Method: scope and significance. https://www.astm.org/d4943-25.html
• NICET. Performance Examination, Soils: ASTM D4318-17e1 checklist (2020). https://www.nicet.org/nicetorg/assets/file/public/performance_examination_checklists/soils/astm_d4318-17e1.pdf
• Oklahoma Department of Transportation. Procedure Checklist, ASTM D4943 Shrinkage Factors of Cohesive Soils by the Water Submersion Method (2023). https://www.odot.org/materials/C97001_WEB_REP/EVALD_CLAB_TECHS/FNL_EVAL_CLISTS/9734242405301330_00058.pdf
• U.S. Army Corps of Engineers (1970, Change 2 1986). EM 1110-2-1906, Laboratory Soils Testing, Appendices III and IIIA. https://vulcanhammer.net/wp-content/uploads/2017/01/em-1110-2-1906.pdf
• Alberta Transportation. TLT-412, Liquid Limit, Plastic Limit, and Plasticity Index of Soils (one-point method). https://alberta.ca/system/files/trans-tlt41202.pdf
• Hossain, M. S., Islam, M. A., Badhon, F. F., & Imtiaz, T. (2021). Properties and Behavior of Soil: Online Lab Manual, chapter 5, Atterberg Limit Test. Mavs Open Press, University of Texas at Arlington. https://uta.pressbooks.pub/soilmechanics/chapter/atterberg-limit-test/
• Germaine, J. T., & Germaine, A. V. (2009). Geotechnical laboratory measurements for engineers. Wiley.