Soil Tests: Sieve Analysis, Cu and Cc, and Atterberg Limits Explained
Before designing a foundation, road or embankment, the engineer must know what kind of soil is present. Two basic laboratory tests answer most of that question. Sieve analysis tells you the particle size distribution of coarse-grained soil, and the Atterberg limits tell you how fine-grained soil behaves with changing water content. Both are done under the IS 2720 series of soil test methods and are used for soil classification as per IS 1498. This article walks through both tests with worked numbers.
Sieve Analysis (Grain Size Distribution)
An oven-dried soil sample is washed through the 75 µm sieve to remove fines, dried again, and then shaken through a stack of IS sieves. The mass retained on each sieve is weighed and converted into percent finer. Soil passing 75 µm is analysed separately by hydrometer if needed.
Worked example: 500 g sandy soil
| IS sieve | Mass retained (g) | Cumulative retained (g) | % finer |
|---|---|---|---|
| 4.75 mm | 20 | 20 | 96 |
| 2.36 mm | 45 | 65 | 87 |
| 1.18 mm | 90 | 155 | 69 |
| 600 µm | 120 | 275 | 45 |
| 300 µm | 110 | 385 | 23 |
| 150 µm | 70 | 455 | 9 |
| 75 µm | 30 | 485 | 3 |
| Pan | 15 | 500 | - |
% finer = (Total mass - Cumulative retained) / Total mass x 100 Example, 600 µm: (500 - 275) / 500 x 100 = 45 %
Plot percent finer against sieve size on a semi-log graph (size on the log axis). From the curve, read D10, D30 and D60, the sizes at which 10, 30 and 60 percent of the soil is finer. Interpolating on the log scale between sieves:
D10: between 150 µm (9 %) and 300 µm (23 %)
log D10 = log 0.150 + (10 - 9)/(23 - 9) x log(0.300/0.150)
D10 = 0.158 mm
D30: between 300 µm (23 %) and 600 µm (45 %) -> D30 = 0.374 mm
D60: between 600 µm (45 %) and 1.18 mm (69 %) -> D60 = 0.916 mm
Coefficient of uniformity Cu = D60 / D10 = 0.916 / 0.158 = 5.80
Coefficient of curvature Cc = D30² / (D10 x D60)
= 0.374² / (0.158 x 0.916) = 0.97For a sand to be well graded, Cu should be greater than 6 and Cc should lie between 1 and 3. Here Cu = 5.80 and Cc = 0.97, so both conditions fail narrowly and the soil is poorly graded sand (SP). Fines are only 3 percent, below 5 percent, so no dual symbol is needed.
Atterberg Limits
A fine-grained soil changes from solid to semi-solid to plastic to liquid as water content increases. The water contents at the boundaries are the Atterberg limits.
| Limit | Symbol | Boundary between | Test |
|---|---|---|---|
| Liquid limit | wL | Plastic and liquid states | Casagrande cup: groove closes 12 mm at 25 blows |
| Plastic limit | wP | Semi-solid and plastic states | Thread crumbles when rolled to 3 mm diameter |
| Shrinkage limit | wS | Solid and semi-solid states | Further drying causes no volume decrease |
Liquid limit by Casagrande apparatus
Soil passing the 425 µm sieve is mixed with water to a paste, placed in the brass cup, and divided by a standard grooving tool. The cup is dropped 10 mm onto the rubber base at two drops per second, and the number of blows to close the groove over 12 mm is counted. The test is repeated at different water contents and the results plotted as water content against log of blows (the flow curve).
| Trial | Number of blows | Water content (%) |
|---|---|---|
| 1 | 32 | 38.2 |
| 2 | 26 | 40.1 |
| 3 | 19 | 42.3 |
| 4 | 13 | 44.6 |
From the flow curve, water content at 25 blows: wL = 40.2 %
Flow index If = (w1 - w2) / log10(N2 / N1)
= (44.6 - 38.2) / log10(32 / 13)
= 6.4 / 0.391 = 16.4
Plastic limit from thread test: wP = 22.0 %
Plasticity index Ip = wL - wP = 40.2 - 22.0 = 18.2 %
Toughness index It = Ip / If = 18.2 / 16.4 = 1.11Classifying the Fine-Grained Soil
IS 1498 classifies fine-grained soils using the plasticity chart. The A-line separates clays (above) from silts and organic soils (below), and the liquid limit divides soils into low (below 35), intermediate (35 to 50) and high (above 50) compressibility.
A-line: Ip = 0.73 (wL - 20) At wL = 40.2: Ip(A-line) = 0.73 x 20.2 = 14.7 Actual Ip = 18.2 > 14.7 -> above A-line -> clay wL between 35 and 50 -> intermediate compressibility Classification: CI (clay of intermediate compressibility)
| Symbol | Meaning | Liquid limit range |
|---|---|---|
| CL / ML | Clay / silt of low compressibility | Less than 35 |
| CI / MI | Clay / silt of intermediate compressibility | 35 to 50 |
| CH / MH | Clay / silt of high compressibility | Greater than 50 |
High plasticity clays such as the black cotton soils of Maharashtra, Karnataka and Madhya Pradesh swell and shrink strongly with moisture changes and need special foundation treatment.
Common Mistakes
- Dry sieving clayey soil without washing; lumps of fines are retained and the soil appears coarser.
- Overloading sieves, which blocks the mesh and gives wrong retained masses.
- Reading the liquid limit from a single trial instead of drawing the flow curve.
- Rolling plastic limit threads on a wet glass plate, which keeps adding moisture.
Summary
Sieve analysis gives the grading curve, from which D10, D30 and D60 lead to Cu and Cc and the decision between well graded and poorly graded soil. Atterberg limits describe fine soils, with plasticity index equal to liquid limit minus plastic limit. Plotting wL and Ip on the plasticity chart with the A-line gives the IS 1498 classification, which is the first step in any geotechnical design.