1. Introduction

Particle-size distribution is one of the fundamental properties used in soil mechanics and geotechnical engineering. It describes the proportions of different particle sizes present in a soil sample. The distribution can be determined using sieve analysis for coarse particles and sedimentation methods, such as hydrometer analysis, for finer particles.

A particle-size distribution curve plots particle diameter on the horizontal axis and cumulative percentage finer by weight on the vertical axis. By reading the percentage finer at selected particle diameters, we can calculate the percentages of gravel, sand, silt and clay.

This article explains the method using three curves, A, B and C, and the approximate results shown in the supplied graph.

Important concept: The graph gives cumulative percentage finer. It does not directly give the percentage of each soil fraction. The percentage of a fraction is calculated by subtracting the cumulative percentages at its upper and lower boundaries.

2. Particle-size boundaries

For this example, the following particle-size boundaries are used. These correspond to the divisions shown in the supplied graph.

Soil fraction Symbol Particle diameter Boundary significance
Gravel G Greater than 4.75 mm Particles coarser than the No. 4 sieve
Sand S 0.075 to 4.75 mm Particles passing the No. 4 sieve and retained on the No. 200 sieve
Silt-size fraction M 0.002 to 0.075 mm Particles between 75 micrometres and 2 micrometres
Clay-size fraction C Smaller than 0.002 mm Particles finer than 2 micrometres

The important boundaries are 4.75 mm, 0.075 mm and 0.002 mm. The first two are associated with standard sieve sizes. The 0.002 mm boundary is generally determined using a sedimentation method rather than an ordinary sieve.

Classification note: These are particle-size fractions. In the Unified Soil Classification System (USCS), silt and clay are distinguished principally by their plasticity and engineering behaviour, not solely by particle diameter. Therefore, a particle-size calculation alone does not establish the final USCS classification.

3. Understanding the particle-size distribution curve

3.1 Horizontal axis: particle diameter

The horizontal axis represents particle diameter in millimetres and is logarithmic. Consequently, equal horizontal distances represent equal ratios of particle size, rather than equal arithmetic differences.

For example, the interval from 1 mm to 0.1 mm occupies the same logarithmic distance as the interval from 0.1 mm to 0.01 mm.

3.2 Vertical axis: percentage finer by weight

The vertical axis represents the cumulative percentage of the sample having particle diameters smaller than the selected diameter.

  • At 100%, the complete sample is finer than the corresponding diameter.
  • At 60%, 60% of the sample is finer than the corresponding diameter.
  • At 10%, only 10% of the sample is finer than the corresponding diameter.

Let P(d) represent the percentage finer at particle diameter d. The percentage coarser than that diameter is approximately 100 − P(d), assuming a normalized sample and consistent boundary conventions.

4. General formulas for calculating soil fractions

Let the following symbols represent cumulative percentage finer values read from a particle-size distribution curve:

  • P(4.75): percentage finer at 4.75 mm.
  • P(0.075): percentage finer at 0.075 mm.
  • P(0.002): percentage finer at 0.002 mm.

4.1 Percentage of gravel

Gravel percentage

G = 100 − P(4.75)

Gravel represents the material coarser than 4.75 mm. Therefore, subtract the percentage finer at 4.75 mm from 100%.

4.2 Percentage of sand

Sand percentage

S = P(4.75) − P(0.075)

Sand lies between 4.75 mm and 0.075 mm. The cumulative percentage finer at 4.75 mm includes both sand and finer particles. Removing the percentage finer than 0.075 mm leaves the sand fraction.

4.3 Percentage of silt-size material

Silt-size fraction

M = P(0.075) − P(0.002)

The percentage finer than 0.075 mm includes both silt-size and clay-size particles. Subtracting the percentage finer than 0.002 mm gives the silt-size fraction.

4.4 Percentage of clay-size material

Clay-size fraction

C = P(0.002)

The clay-size fraction is the cumulative percentage finer than 0.002 mm, according to the size convention used in this example.

4.5 Verification equation

G + S + M + C = 100%

This equation is the most useful check for calculations. If the four fractions do not total approximately 100%, recheck the graph readings, arithmetic and boundary definitions.

5. Worked example: Soil A

Read the Soil A curve at the three important particle diameters. The following are approximate readings consistent with the results reported in the supplied image.

Particle diameter Cumulative percentage finer
4.75 mm98%
0.075 mm0%
0.002 mm0%

Step 1: Calculate gravel

The percentage finer at 4.75 mm is 98%.

G = 100 − 98 = 2%

Step 2: Calculate sand

The percentage finer at 4.75 mm is 98%, while the percentage finer at 0.075 mm is approximately 0%.

S = 98 − 0 = 98%

Step 3: Calculate silt-size material

M = 0 − 0 = 0%

Step 4: Calculate clay-size material

C = 0%

Step 5: Verify the total

2 + 98 + 0 + 0 = 100%

Result for Soil A: Gravel = 2%, sand = 98%, silt-size fraction = 0%, and clay-size fraction = 0%. The sample is predominantly sand with a very small gravel fraction.

6. Worked example: Soil B

The approximate cumulative readings for Soil B, based on the supplied solution, are:

Particle diameter Cumulative percentage finer
4.75 mm99%
0.075 mm38%
0.002 mm7%

Step 1: Calculate gravel

G = 100 − 99 = 1%

Step 2: Calculate sand

Sand is the difference between the cumulative percentages finer at 4.75 mm and 0.075 mm.

S = 99 − 38 = 61%

Step 3: Calculate silt-size material

The percentage finer at 0.075 mm is 38%, of which 7% is finer than 0.002 mm.

M = 38 − 7 = 31%

Step 4: Calculate clay-size material

C = 7%

Step 5: Verify the total

1 + 61 + 31 + 7 = 100%

Result for Soil B: Gravel = 1%, sand = 61%, silt-size fraction = 31%, and clay-size fraction = 7%. Sand is the largest individual fraction, with a substantial proportion of fine particles.

7. Worked example: Soil C

The approximate cumulative readings for Soil C, based on the supplied solution, are:

Particle diameter Cumulative percentage finer
4.75 mm100%
0.075 mm69%
0.002 mm12%

Step 1: Calculate gravel

G = 100 − 100 = 0%

Step 2: Calculate sand

S = 100 − 69 = 31%

Step 3: Calculate silt-size material

M = 69 − 12 = 57%

Step 4: Calculate clay-size material

C = 12%

Step 5: Verify the total

0 + 31 + 57 + 12 = 100%

Result for Soil C: Gravel = 0%, sand = 31%, silt-size fraction = 57%, and clay-size fraction = 12%. The silt-size fraction is the largest of the four fractions.

8. Comparison of all three soils

Soil Gravel (G) Sand (S) Silt-size (M) Clay-size (C) Total
A2%98%0%0%100%
B1%61%31%7%100%
C0%31%57%12%100%

9. General calculation procedure

The same procedure can be applied to any cumulative particle-size distribution curve.

flowchart TD A["Start: Obtain particle-size distribution curve"] --> B["Read P at 4.75 mm"] B --> C["Read P at 0.075 mm"] C --> D["Read P at 0.002 mm"] D --> E["Gravel = 100 - P(4.75)"] E --> F["Sand = P(4.75) - P(0.075)"] F --> G["Silt-size = P(0.075) - P(0.002)"] G --> H["Clay-size = P(0.002)"] H --> I{"Do fractions total approximately 100%?"} I -- Yes --> J["Report the four percentages"] I -- No --> K["Check readings, boundaries and arithmetic"] K --> B

10. How to read the graph accurately

  1. Identify the curve for the soil under consideration.
  2. Locate 4.75 mm on the logarithmic horizontal axis.
  3. Move vertically until you intersect the selected soil curve.
  4. Move horizontally to the vertical axis and read the cumulative percentage finer.
  5. Repeat the process at 0.075 mm and 0.002 mm.
  6. Substitute the three readings into the formulas.
  7. Check that the four calculated fractions total approximately 100%.

If a curve lies between grid lines, estimate the reading carefully. Do not assume that the logarithmic horizontal axis has equal millimetre intervals. Where greater accuracy is required, use the original laboratory data rather than estimating values from a low-resolution image.

11. Common mistakes to avoid

  • Confusing cumulative percentage with fraction percentage: The percentage finer at 0.075 mm represents the combined silt-size and clay-size fractions, not silt alone.
  • Adding cumulative percentages: Adjacent fractions are obtained by subtraction, not addition.
  • Using incorrect boundary sizes: For this example, use 4.75 mm, 0.075 mm and 0.002 mm consistently.
  • Ignoring the total: A total different from 100% may indicate a reading or arithmetic error.
  • Confusing particle-size fractions with formal soil classes: A size-based calculation does not replace the laboratory tests needed for a complete engineering classification.

12. Soil classification: an important qualification

The original image describes Soil A as poorly graded sand (SP), Soil B as silty sand (SM), and Soil C as sandy silt (M). These descriptions should be interpreted carefully.

  • Soil A: The reported 2% gravel and 98% sand indicate a predominantly sandy, nearly clean soil. Confirming SP requires suitable gradation data, including the relevant characteristic diameters and grading coefficients.
  • Soil B: The reported 38% passing 0.075 mm indicates substantial fines. Under USCS, whether these fines are silty or clayey must be determined from their plasticity characteristics; particle size alone is insufficient.
  • Soil C: The reported 69% passing 0.075 mm indicates that more than half the sample consists of fines. Under USCS, further plasticity testing is required to establish whether the soil is classified as silt or clay.

For formal USCS classification, consult the applicable requirements of ASTM D2487. In India, IS 1498 is also an important reference for classification and identification of soils for general engineering purposes.

13. Engineering significance

Particle-size distribution helps engineers understand several important soil characteristics:

  • Permeability: Clean sands and gravels are generally more permeable than soils containing large quantities of fine particles, although density, gradation and soil structure also matter.
  • Compaction: The proportions of coarse and fine particles influence achievable dry density and moisture requirements.
  • Drainage: The distribution of particle sizes helps assess drainage behaviour and the need for filter layers.
  • Settlement and compressibility: Fine-grained soils may exhibit significant consolidation, depending on their mineralogy, plasticity, stress history and drainage conditions.
  • Foundation design: Particle-size distribution is one input to geotechnical assessment; it cannot independently establish safe bearing capacity or settlement.

14. References and further reading

  1. ASTM International, ASTM D2487, Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System).
  2. Bureau of Indian Standards, IS 1498, Classification and Identification of Soils for General Engineering Purposes.
  3. U.S. Bureau of Reclamation, Earth Manual, discussion of soil grain size, soil fractions and engineering properties. Read the reference.
  4. North Vancouver Environmental Services, Soil Classification Guide: USCS and AASHTO Reference, for a summary of particle-size boundaries. Read the guide.

15. Final summary

Remember these four equations:

Gravel = 100 − P(4.75 mm)

Sand = P(4.75 mm) − P(0.075 mm)

Silt-size fraction = P(0.075 mm) − P(0.002 mm)

Clay-size fraction = P(0.002 mm)

Final check: G + S + M + C = 100%.

Yogendra Gopal Borse

Yogendra Gopal Borse

Civil Engineer | Assistant Engineer Grade-I, Maharashtra PWD

B.Tech (Civil) from VJTI Mumbai. Experienced in bridge design, road works, estimation, project monitoring and digital engineering tools. Creator of YogiPWD – practical technical resources for civil engineers.

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