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Sieve Analysis and the Classification of Coarse-Grained Soils
Two numbers tell whether a sand is well or poorly graded: Cu and Cc. Both are read from the grain-size distribution curve. But reading from the curve is less certain than it seems: in one of the examples here, a one-point difference at a single sieve changes the soil's class.
1. The test
A dry soil sample is passed through a stack of sieves with openings decreasing from top to bottom, and the mass retained on each sieve is weighed. The result is the mass passing each sieve as a fraction of the total. The part passing the 0.075 mm (No. 200) sieve is "fines" (silt and clay), the part retained on 4.75 mm (No. 4) is "gravel", and the part between is "sand". The behaviour of the fines is governed by plasticity (see ZEM-01), that of the coarse part by its grain-size distribution.
2. The grain-size distribution curve
The results are plotted as a curve with logarithmic grain size on the horizontal axis and percent passing on the vertical. The logarithmic axis matters: grain sizes span several orders of magnitude, and values read from the curve must be read against that axis. Sieve results for three example soils:
| Sieve opening (mm) | W | A | B |
|---|---|---|---|
| 37.5 | 100 | 100 | 100 |
| 19 | 100 | 100 | 100 |
| 9.5 | 97 | 98 | 100 |
| 4.75 | 88 | 92 | 96 |
| 2 | 60 | 75 | 88 |
| 0.85 | 36 | 52 | 80 |
| 0.425 | 22 | 30 | 72 |
| 0.25 | 14 | 18 | 60 |
| 0.15 | 9 | 9 | 40 |
| 0.075 | 3 | 4 | 8 |
Values are percent passing each sieve (%).
D10, D30 and D60 are the grain sizes than which 10%, 30% and 60% of the sample is finer. They usually fall between two sieves and are read by interpolation.
3. Cu and Cc
The coefficient of uniformity Cu measures the breadth of the distribution: a large Cu means many different grain sizes. The coefficient of curvature Cc measures the shape of the curve: a very small or very large Cc means some sizes are missing. In a well-graded soil small grains fill the voids between large ones; the soil compacts better and shows higher strength and lower permeability.
4. Classification rules
Under ASTM D2487 a coarse-grained soil is classified as follows:
- Main group: G if most of the coarse fraction is gravel, S if it is sand.
- Fines below 5%: look at grading. Cu ≥ 4 for gravel or Cu ≥ 6 for sand, and 1 ≤ Cc ≤ 3 in both cases, means well graded (W); otherwise poorly graded (P): GW, GP, SW, SP.
- Fines above 12%: look at the plasticity of the fines rather than grading: GM, GC, SM, SC.
- Between 5% and 12%: a dual symbol is used; the first half shows grading and the second the fines, e.g. SW-SM or SP-SC.
5. Three examples
Results for the three soils above (D values by logarithmic interpolation):
| Soil | Gravel / sand / fines (%) | D10 (mm) | D30 (mm) | D60 (mm) | Cu | Cc | Class |
|---|---|---|---|---|---|---|---|
| W | 12 / 85 / 3 | 0.166 | 0.632 | 2.00 | 12.04 | 1.200 | SW |
| A | 8 / 88 / 4 | 0.159 | 0.425 | 1.14 | 7.21 | 0.994 | SP |
| B | 4 / 88 / 8 | 0.078 | 0.121 | 0.25 | 3.19 | 0.745 | SP-SM / SP-SC |
- W is clearly well graded: Cu = 12 ≥ 6 and Cc = 1.20, between 1 and 3. Hand check: 0.632² / (0.166 × 2.0) = 1.20.
- A is on the edge: Cu = 7.2 is sufficient, but Cc = 0.994, six thousandths below the threshold. The soil falls into SP.
- B has 8% fines, so a dual symbol is needed. Since Cu = 3.2 < 6 the first half is P: SP-SM if the fines are silty, SP-SC if clayey.
6. Uncertainty: soils near a threshold
Soil A shows how sensitive classification can be. There are two sources of uncertainty:
- Measurement: had the percent passing the 0.425 mm sieve been measured as 29% instead of 30%, Cc = 1.056 and the soil would be SW. A one-point difference at one sieve can arise from ordinary variations in weighing and sieving time.
- Interpolation method: reading the D values of the same soil A by linear interpolation gives Cc = 0.897; logarithmic interpolation gives 0.994. Because the curve is drawn on a logarithmic axis, logarithmic interpolation is the consistent choice; linear interpolation gives Cc about 10% different.
The practical conclusion: a Cc or Cu near a threshold should not be reported as a definite class. Repeating the test, stating the interpolation method and noting the result as "borderline" is more honest. All classifications in this article are checked by tests/v580-grading.test.js.
References
- ASTM D6913 — Standard Test Methods for Particle-Size Distribution (Gradation) of Soils Using Sieve Analysis. ASTM D2487 — Standard Practice for Classification of Soils for Engineering Purposes (USCS). TS 1900-1 — Laboratory tests on soils for civil engineering, Part 1.
- Holtz, R. D., Kovacs, W. D. and Sheahan, T. C. (2011). An Introduction to Geotechnical Engineering, 2nd ed., Chapters 2–3. Pearson.
- The example gradings were constructed for teaching; the calculations are reproduced in the test.
The numbers in this article were computed with closed-form relations and are checked by the stated test.