The dimensional distribution of particles composing a soil is the primary physical parameter for its identification, geotechnical classification, and prediction of hydraulic or mechanical behavior. While mechanical sieving characterizes coarse fractions (sands and gravels), hydrometer sedimentation quantifies the colloidal spectrum of silts and clays. This article details standardized testing procedures, calculations associated with Stokes' law, the construction of the particle size distribution curve, and the interpretation of uniformity and curvature coefficients in the technological control of infrastructure.
1. What is the test and what problem does it solve?
Particle size analysis is the laboratory process designed to determine the mass percentages of different dimensional fractions that constitute a soil sample. The test is methodologically divided into two complementary stages: sieving (for particles larger than 0.075 mm or 0.063 mm) and sedimentation (for fine particles smaller than these limits).
In geotechnical engineering practice, soils with continuous or discontinuous gradations exhibit completely distinct mechanical behaviors, permeability, and frost susceptibility. Particle size analysis solves the problem of geometrically characterizing the solid matrix, allowing the soil to be framed within international classification systems (AASHTO and USCS), predicting drainage behavior, and validating specifications for filters and granular foundation layers.
2. What is it for and when should it be used?
Performing particle size analysis is indispensable in the following project and construction phases:
• Preliminary and systematic classification of foundation soils, borrow pits, and fill materials for embankments and dams.
• Verification of filter criteria (Terzaghi's criteria) for drain protection in slopes and geotechnical structures.
• Control of the particle size composition of materials for granularly stabilized sub-base and base layers.
• Determination of the need for complementary plasticity and fine sedimentation tests in clayey and silty soils.
3. Reference standards
The test must strictly follow the guidelines of the technical standards adopted by the project:
• NP 84: Soils - Particle size analysis test.
• ASTM D6913 / D6913M: Standard Test Methods for Particle-Size Distribution (Gradation) of Soils Using Sieve Analysis.
• ASTM D7928: Standard Test Method for Particle-Size Distribution (Gradation) of Fine-Grained Soils Using the Sedimentation (Hydrometer) Analysis.
• EN ISO 17892-4: Geotechnical investigation and testing - Laboratory testing of soil - Part 4: Determination of particle size distribution.
• LNEC E 196: Soils - Particle size analysis.
4. Sample preparation and fractionation
Prior sample preparation requires care to preserve the integrity of mineral aggregates:
- Drying of the representative sample in air or in an oven at controlled temperature (maximum 60 °C).
- Meticulous disaggregation of clods with a rubber-coated mortar, avoiding the fracture of quartz mineral grains.
- Quartering to obtain a representative mass based on the maximum aggregate size present (e.g., 500 g to 1000 g for fine and sandy soils; larger masses for gravelly soils).
- Washing the sample through a 0.075 mm (ASTM No. 200) or 0.063 mm sieve to separate the coarse fraction from the fine fraction, collecting and drying the retained material for subsequent dry sieving.
5. Equipment and materials
The necessary equipment for complete execution includes:
• Set of standardized square mesh sieves (ASTM or ISO series: 75 mm, 37.5 mm, 19 mm, 9.5 mm, 4.75 mm, 2.0 mm, 0.85 mm, 0.425 mm, 0.25 mm, 0.106 mm and 0.075 mm / 0.063 mm), with bottom pan and lid.
• Mechanical sieve shaker with vibratory and vertical motion.
• For sedimentation: 1000 mL sedimentation cylinders, hydrometer calibrated in g/L for 20 °C, high-precision thermometer, high-speed mechanical dispersion mixer (10,000 rpm).
• Standard deflocculating agent (4% sodium hexametaphosphate) to neutralize electrostatic forces between fine particles.
• Precision balances, oven regulated at 110 °C ± 5 °C, and wash bottles.
6. Step-by-step procedure
The test is divided into two distinct operational parts:
A. Mechanical Sieving (Coarse and Medium Fraction):
- The material retained on the 0.075 mm sieve after pre-washing is dried in an oven at 110 °C and weighed (Mretaineddry).
- The set of sieves is assembled in decreasing order of opening, topped by the largest opening sieve and closed with the lid.
- The sample is placed on top of the sieve column, and the assembly is subjected to the mechanical shaker for 10 to 15 minutes.
- The mass of soil retained on each sieve is carefully weighed individually, ensuring that the sum of the partial masses does not differ from the initial total mass by more than 1%.
B. Hydrometer Sedimentation Test (Fine Fraction - Silts and Clays):
- The fraction that passed the 0.075 mm sieve is treated with 125 mL of sodium hexametaphosphate deflocculating solution and left to rest for a minimum period of 12 hours.
- The suspension is transferred to the mechanical dispersion cup, stirring for 1 minute at high speed.
- The suspension is transferred to the 1000 mL sedimentation cylinder, completing the volume with distilled water up to the calibration mark.
- The cylinder is vigorously agitated by inverted manual rotation for 1 minute and placed on a vibration-free table.
- The hydrometer is introduced, and readings are taken at standardized times (e.g., 2 min, 5 min, 15 min, 30 min, 1 h, 2 h, 4 h, 8 h, and 24 h), simultaneously recording the suspension temperature at each reading.
7. Calculations and results processing
The mathematical treatment of data follows the fundamental equations of soil mechanics:
1. Percentages retained and passed in sieving:
Initial total mass of the sample = M_total
Accumulated mass retained on sieve i = Maccumulatedi
Accumulated percentage retained = (Maccumulatedi / M_total) * 100 (%)
Percentage passing (fraction smaller than opening d) = 100 - Accumulated percentage retained (%)
2. Stokes' Law in Sedimentation:
The equivalent particle diameter (d in mm) is calculated as a function of time t and effective depth R:
d = sqrt( (30 eta L) / (980 (Gs - G_w) t) )
Where eta is the dynamic viscosity of water, Gs is the specific gravity of solids, G_w is the density of water, and L is the immersion depth of the hydrometer.
3. Characteristic Coefficients of the Particle Size Distribution Curve:
• Effective diameters d10, d30, and d60 (corresponding to 10%, 30%, and 60% of soil passing on the curve).
• Coefficient of Uniformity (Cu): Cu = d60 / d10
• Coefficient of Curvature (Cc): Cc = (d30^2) / (d10 * d60)
8. Interpretation of results
The analysis of the particle size distribution curve plotted on semi-logarithmic paper (diameters on a logarithmic scale and percentages passing on an arithmetic scale) allows for inference:
• Well-graded soils (Cu >= 4 for gravels or Cu >= 6 for sands, with Cc between 1 and 3): Exhibit a continuous distribution of particle sizes, filling voids and ensuring high compaction and mechanical stability.
• Poorly graded or uniform soils (small Cu): Particles with very similar dimensions, resulting in a high void ratio and pronounced permeability.
• Discontinuous or gap-graded soils: Absence of certain dimensional fractions, which can induce instability under water percolation (piping phenomenon).
9. Common errors and how to avoid them
Main experimental deviations in particle size analysis:
• Sieve overload: Exceeding a sieve's retention capacity prevents smaller particles from passing through the meshes. Solution: Fractionate the sample or use larger diameter sieves.
• Torn or deformed meshes: Continuous use of damaged sieves drastically alters retention. Solution: Visually inspect the condition of the meshes and calibrate periodically.
• Incomplete deflocculation in sedimentation: Aggregation of fine particles due to the absence or ineffectiveness of the chemical deflocculant. Solution: Respect the resting time with sodium hexametaphosphate.
• Thermal variations during sedimentation: Temperature changes alter the viscosity of water and the fluid density. Solution: Keep the cylinder in a thermostatic bath or rigorously record the temperature at each reading.
10. QA/QC and traceability
Within the laboratory quality system (ISO/IEC 17025):
• Metrological verification of sieves: Annual control of mesh openings by optical inspection or tests with certified reference material.
• Hydrometer calibration: Periodic verification of the density scale and meniscus.
• Document traceability: Mandatory recording of the test sheet with gross partial masses, hydrometer temperature corrections, and signature of the responsible operator.
11. Practical application in construction
In the technological control of infrastructure:
• Granulometric validation ensures that crushed materials for base and sub-base layers comply with the particle size envelopes stipulated in the Specifications.
• In the design of embankment filters in dams, the correct application of piping criteria is directly based on the d15 and d85 values obtained from the particle size distribution curve.
12. Limitations and points requiring confirmation
Particular aspects that deserve technical attention: