Grain Size Analysis of Soil

The grain size distribution of any soil can be determined using the grain size analysis, also called mechanical analysis. The basic method of mechanical analysis is to sieve the soil through a set of sieves of standard opening size. Sieve analysis can be used only for the mechanical analysis of gravel and sand as the smallest sieve size available is 75 nm (0.075 mm).

To determine the grain size distribution of silt and clay and hence to get the grain size distribution for the complete particle size range in soils, sedimentation analysis is carried out.

Grain size analysis of soil is done by the following methods:

1. Sieve Analysis:

(a) Sieve analysis of gravel.

(b) Sieve analysis of sand.

(c) Wet sieve analysis.

(d) Dry sieve analysis.

2. Sedimentation Analysis:

(a) Pipette method.

(b) Hydrometer method.

(c) Plummet balance method.

Sedimentation analysis will not be required if the soil contains less than 10% silt and clay (fines).

1. Sieve Analysis:

Sieve analysis is useful to determine the grain size distribution of soils that have a particle size greater than 75 µm. The basic principle of sieve analysis involves sieving the soil through a set of standard sieves and computing the cumulative % finer corresponding to each sieve size or grain size. The cumulative percentages of the different soil particles, passing through each sieve, are determined and plotted to obtain the grain size distribution curve. From the grain size distribution curve, two parameters namely, uniformity coefficient and coefficient of curvature, are determined, as these two are required for soil classification.

IS – 2720 (Part 4) – 1985 recommends the following two methods for sieve analysis:

i. Wet Sieve Analysis:

Applicable to all soils.

ii. Dry Sieve Analysis:

Applicable only to soils that do not have an appreciable amount of clay.

A graph is then plotted between grain size and cumulative % finer. If less than 10% of the soil passes the 75-µm sieve, the results of the sieve analysis are sufficient to plot the grain size distribution curve. However, if more than 10% of the soil passes the 75-µm sieve, the sieve analysis is to be supplemented with sedimentation analysis and the results are to be combined to plot the grain size distribution curve.

This is because soil classification requires the deter­mination of the uniformity coefficient (C_u) and the coefficient of curvature (C_c), which are functions of D₁₀. D₁₀ is the particle size by which 10% of the soil by weight is finer (than that particle size). If the % fines (% slit and % clay) by dry weight in the soil are less than 10%, D₁₀ will be more than 0.075 mm and then it is not necessary to conduct sedimentation analysis to determine the gradation and classify the soil.

Sieve analysis is done in two stages – Sieve analysis of gravel and that of sand using the following procedure:

i. Air-dried soil samples of quantities as given in Table 6.1 are taken for the test.

ii. The weight of the soil taken for the test is determined (W₁).

iii. The soil is sieved through a 4.75-mm sieve and is divided into two portions, one coarser (gravel) and another finer than 4.75 mm (sand and fines).

a. Sieve Analysis of Gravel:

Sieve analysis of gravel is done in the following steps:

i. The portion of the soil sample retained on the 4.75-mm IS sieve is taken and its weight is determined (W₂).

ii. IS sieves of sizes 100, 80, 63, 40, 20, and 4.75 mm and a pan are taken.

iii. The portion of the soil retained on the 4.75-mm IS sieve is sieved through each sieve, keeping the pan at the bottom and a cover plate at the top.

iv. Sieving is done with the sieve of the largest opening size, that is, 100 mm first, and the portion of soil passing through the sieve is then sieved through the sieve of the next smaller opening size.

v. While sieving through each sieve, the sieve is agitated so that the soil sample rolls in irregular motion over the sieve.

vi. While sieving, the soil is not pushed through the opening. The material before sieving may be rubbed with a rubber pestle in the mortar, taking care to see that the individual soil particles are not broken and re-sieved to make sure that only individual soil particles are retained.

vii. The weight of the soil retained on each sieve is determined and recorded.

viii. If the soil sample appears to contain more than 5% water content, the water content of the soil is determined.

ix. If the water content is less than 5%, all the computations used in the sieve analysis can be based on wet weight only.

x. If the soil contains more than 20% gravel and the fines are very cohesive, adhering to the gravel after separa­tion, the gravel is washed on a 4.75-mm IS sieve using sodium hexametaphosphate solution, if necessary.

b. Sieve Analysis of Sand:

Sieve analysis of gravel is done in the following steps:

i. The sieves used for this purpose are 2-mm, 425-µm, and 75-µm IS sieves. Typical 20-cm diameter brass sieves used.

ii. Sieve analysis of sand may be done by wet sieving for clayey soils and by dry sieving for soils that do not contain an appreciable amount of clay.

Further procedure consists of two stages:

(c) Wet sieving and

(d) Dry sieving.

(c) Stage 1 – Wet Sieving:

i. The portion of the soil passing through the 4.75-mm IS sieve is oven dried at 105°C-110°C.

ii. About 200 g of this soil is taken and is weighed accurately. This soil is placed and spread out in a large tray or bucket and covered with water.

iii. If the soil contains a significant clay fraction, a dispersing agent is added and the contents are mixed thoroughly.

iv. The dispersing agent is prepared by adding 2 g of sodium hexametaphosphate or 1 g of sodium hydroxide and 1 g of sodium carbonate to distilled water to make 1 L of solution.

v. The contents are left undisturbed for sufficient time, usually overnight in the case of clayey soil.

vi. The material is then washed through the 75-µm IS sieve.

(b) Stage 2 – Dry Sieving:

i. The material retained on the 75-µm IS sieve is carefully collected in a tray and dried in the oven.

ii. The material is then sieved through a stack of sieves, 2-mm, 425-µm, and 75-µm IS sieves, placed one below the other, either by hand or by using a mechanical sieve shaker. A typical mechanical sieve shaker with stack of sieves.

iii. Care is taken to see that the sieves are not overloaded by ensuring that the maximum quantity of soil retained on each sieve should be as given in Table 6.2.

iv. The weight of soil retained on each sieve is determined and recorded.

v. In the case of soils that do not contain the clay fraction, dry sieving can be done without soaking, dispersing (using a dispersing agent), and washing through the 75-µm IS sieve.

vi. The cumulative weight of soil retained on each sieve is calculated.

2. Sedimentation Analysis:

The soil particles finer than 75 µm cannot be sieved because sieves of finer opening size are not available and also because sieving becomes difficult and ineffective through such small openings. The theory of sedimentation of soil particles in water using Stokes’ law is used to determine the grain size distribution of soil particles finer than 75 µm.

Principle:

The principle of sedimentation analysis is to determine the particle size and cumulative %finer using Stokes’ law, which gives the terminal velocity of a freely falling spherical particle in a liquid mass. Soil particles are assumed as spherical and the liquid used is distilled water. The particle size obtained from sedimentation analysis, therefore, is the diameter of an equivalent spherical particle having the same weight as the soil particle.

Stokes’ Law:

When a small sphere settles in a liquid, its terminal velocity at any time is given by Stokes’ law as –

where r is the radius of the sphere (in m), D is the diameter of the sphere (in m), v is the terminal velocity of the falling sphere (in m/s), γ_s is the density of the sphere material (in kN/m³), γ_w is the density of water (in kN/m³; 9.81 kN/m³), µ is the dynamic viscosity of water (in poise), and g is the acceleration due to gravity (in m/s²; 9.81 m/s²). The diameter of a spherical particle falling through a liquid can be obtained from Stokes’ law as –

If H_e is the depth of the particle (in cm) from the free surface at t s, then the terminal velocity will be –

Substituting the value of v from Eq. (6.4) in Eq. (6.3), we get –

Substituting the value of γ_s from Eq. (6.6) in Eq. (6.5), we have –

Equation (6.7) is used to compute the particle size at any time t in both pipette method and hydrometer method.

(a) Pipette Method:

Pipette method is the standard method of sedimentation recommended by IS – 2720 (Part 4) – 1985.

Apparatus:

The apparatus consists of the following:

i. Pipette of 10-mL capacity.

ii. Two 500-mL measuring cylinders.

iii. Weighing bottles of 25-mm diameter and 50-mm height.

iv. Constant temperature bath.

v. Mechanical stirrer.

vi. Balance.

vii. Oven.

Procedure:

The sedimentation analysis by pipette method consists of the following stages:

i. Calibration of pipette.

ii. Pretreatment of soil.

iii. Dispersion of soil.

iv. Sedimentation.

(b) Hydrometer Method:

Hydrometer is an instrument used for determining the specific gravity of liquids.

Principle:

In hydrometer method, the hydrometer is used to determine the density of a soil suspension in a measuring cylinder from which the average particle size is computed at the sampling depth. The hydrometer gives the density of the soil suspension at the mid-height of the bulb. As the soil particles in the suspension go on settling with time, the sampling depth does not remain constant, but goes on increasing with time, unlike in pipette method.

Apparatus:

A special type of hydrometer with a long narrow stem at the top and a bulb at the bottom, as shown in Fig. 6.10(a), is used for hydrometer method. The stem has graduations from 0.995 at the top to 1.030 at the bottom. The hydrometer is calibrated using a liquid of surface tension 55 dynes/cm.

Procedure:

The procedure for sedimentation analysis in hydrometer method consists of:

(a) Calibration of hydrometer,

(b) Pretreatment of soil,

(c) Dispersion of soil, and

(d) Sedimentation

c. Plummet Balance Method of Sedimentation Analysis:

IS – 2720 (Part 4) – 1985 recommends an alternate method to pipette and hydrometer analyses, for sedimentation analysis, using a plummet balance.

Apparatus:

Figure 6.12 shows a typical plummet balance. It consists of a base with three leveling screws over which a vertical stand is fixed. The light-weight pointer beam along with the graduated arc scale is fixed through a pivot to the vertical stand. The pointer has two adjusting screws, allowing the adjustment of the zero reading. A plummet made of perspex is attached with a string and a hook hanging to the other end of the pointer. The plummet weighs 3 g in water. A plumb bob is provided on the scale arm carrier for adjusting the level of the instrument.

Principle:

The plummet balance enables direct reading of the cumulative % finer at any time, as indicated by the pointer on a graduated scale, in the shape of an arc. The depth of immersion of the plummet in the measuring cylinder contain­ing the soil suspension is used to determine the particle diameter corresponding to the cumulative % finer indicated by the pointer.

Limitations of Sedimentation Analysis:

Following are the limitations of sedimentation analysis:

1. Sedimentation analysis uses equivalent diameter of particle that has same terminal velocity and mass as the actual soil particle in the soil suspension during sedimentation. This equivalent diameter is somewhat less than the particle size given by sieve analysis.

2. Stokes’ law is applicable only for a freely falling sphere in an infinite mass of liquid. In sedimentation analysis of soils, there is interference of other soil particles as well as the walls of the measuring cylinder. The error due to particle interference is negligible if the mass of soil used in sedimentation analysis is not more than 50 g per 1000 mL of the soil suspension.

3. For particles of size less than 0.002 mm, Brownian movement takes place and their terminal velocity v, as com­puted from Stokes’ law, gives erroneous results.

4. As the soil consists of particles of different specific gravity, use of average specific gravity in the calculations becomes a source of error. However, as the range of specific gravity of different particles is usually small, the error is negligible.

Despite the above limitations, sedimentation analysis is used for the grain size analysis of fine-grained soils mainly to determine the value of D₁₀. The grain size distribution of silt and clay fractions is not very significant as their properties are more influenced by plasticity characteristics than the grain size distribution.