Grain size analysis is a typical laboratory test conducted in the soil mechanics field. The purpose of the analysis is to derive the particle size distribution of soils.
The analysis is conducted via two techniques. Sieve Grain Size Analysis is capable of determining the particles’ size ranging from 0.075 mm to 100 mm. Any categorization of grains larger than 100mm will be conducted visually whereas particles smaller than 0.075 mm can be distributed using the Hydrometer Method.
The test is carried out with the utilization of a set of sieves with different mesh sizes. Each sieve has squared shaped openings of a certain size. The sieve separates larger from smaller particles, distributing the soil sample in 2 quantities. The grains with diameters larger than the size of the openings are retained by the sieve, while smaller diameter grains pass through the sieve. The test is conducted by placing a series of sieves with progressively smaller mesh sizes on top of each other and passing the soil sample through the stacked sieve “tower”. Therefore, the soil particles are distributed as they are retained by the different sieves. A pan is also used to collect those particles that pass through the last sieve (No. 200).
The nomenclature of the sieves typically used for Grain Size Analysis of soils as well as the corresponding opening sizes are presented in Table 1. Based on the range of the particle sizes, and the Unified Soil Classification System (USCS), soils can be classified in the generic categories presented in Table 2. Further categorizations are possible upon further analysis of the Grain Size Distribution results.
Table 1: The sieves typically utilized in the Grain Size Analysis test
Table 2: Soil classification based on particle size range (USCS)
A typical Sieve Analysis test set-up is composed of:
A typical set-up of stacked sieves placed on a mechanical sieve shaker is shown in Figure 1.
Figure 1: Typical set-up of stacked sieves on mechanical shaker (Credits: Prof. Susan Burns, Georgia Tech University, Department of Civil and Environmental Engineering)
The typical testing procedure consists of the following steps:
The weight of the soil retained on each sieve is calculated by subtracting the weight of the empty sieve from the recorded weight of the sieve after the test. The total weights of particles retained are added and compared to the initial weight of the soil sample. A difference lower than 2% is required.
The percentage retained on each sieve is determined by dividing each weight retained by the initial weight of the soil sample. Subsequently, the total percentage passing from each sieve is calculated by subtracting the cumulative percentage retained in that particular sieve and the ones above it from totality.
A typical Grain Size Analysis data sheet is presented below (Table 3). Moreover, a typical grain size distribution curve of a medium sand is shown in Figure 2.
Table 3: Typical Grain Size Analysis data sheet
The uniformity coefficient (Cu) expresses the variety in particle sizes of soil and is defined as the ratio of D60 to D10 (Figure 1). The value D60 is the grain diameter at which 60% of soil particles are finer and 40% of soil particles are coarser, while D10 is the grain diameter at which 10% of particles are finer and 90% of the particles are coarser. Therefore, Cu is estimated as:
When Cu is greater than 4, the soil is classified as well graded, whereas when Cu is less than 4 the soil is classified as poorly graded/uniformly graded.
Figure 2: Grain Size Distribution curve of a medium-fine sand
The hydrometer analysis is utilized for particle sizes finer than 75 μm. These particles pass through the last sieve (No. 200) of the Sieve Analysis.
A hydrometer is a device designed to measure the relative density of a liquid which refers to the ratio of the actual density of the substance to the density of the water. The apparatus consists of a cylindrical stem and a bulb that contains a specific portion of mercury or lead at the bottom, calibrated to float upright in the liquid. The liquid is poured in a tall cylinder usually made out of glass and the hydrometer is placed inside until it is stabilized. The test is based on the principle that in a low-density liquid, the hydrometer will sink deeper until it balances.
The hydrometer contains a scale which is used to record the relative density of the liquid based on its submersion.
The hydrometer grain size analysis takes advantage of the change in the relative density of a soil-water mixture as the soil particles sink. The test relies on the fact that when the soil is poured in the liquid, the relative density of the soil-water mixture will rise. As the soil particles sink the density decreases until it reaches the initial density of the liquid. The heaviest particles (larger in diameter) will sink first.
A typical Hydrometer test set-up, shown in Figure 3, is composed of:
Figure 3: Hydrometer Test set-up by Controls Group (for more information click here)
The typical testing procedure consists of the following steps:
If the temperature throughout the hydrometer test remains constant, the Stoke’s Law can be utilized to derive the diameter of the particles.
The formula of Stoke’s Law is presented below:
D: The maximum diameter of soil particles corresponding to the percentages indicated by a single hydrometer test reading.
μ: The fluid’s viscosity
v: the terminal velocity of settlement
γs: The unit weight of soil particles
γf: The unit weight of the fluid
Because the fluid’s viscosity, the unit weight of soil particles and the unit weight of the fluid depend only on the temperature and the specific gravity of the soil particles, GS (typical value ~ GS=2.70), the first term of the equation is substituted by a constant known as Sedimentation constant K.
Therefore, Stoke’s Law is simplified as following:
The terminal velocity of the particles (v, in cm/min) is calculated by dividing the sedimentation depth L (the distance from the surface of the suspension to the center of volume of the hydrometer, in cm) by time (t, in min).
Therefore, Stoke’s Law is re-written as (D in mm):
For a given hydrometer and cylindrical container, L values vary according to the hydrometer readings:
Where R is the hydrometer reading in grams/liter.
The Stoke’s law calculates the larger possibly diameter of the particles that are in suspension.
To derive the particles’ percentage passing for each reading stage the following equation is utilized:
- α: correction factor for particle density
- W: weight of the original dry soil (typically, 50 gr)
- b: correction factor associated with temperature and 1 is added to eliminate the meniscus effect.
Finally, the cumulative particle percentage passing is plotted versus the maximum Diameter of the soil particles on a semi-logarithmic scale.
The assumptions that are made using Stoke’s Law in the hydrometer test are the following:
Geotechnical Test Method: Test Method and Discussion for the Particle Size Analysis of Soils by Hydrometer Method (2015). Geotechnical Engineering Bureau. Department of Transportation. State of New York. GTM-13, Revision 2
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