HYDROMETER ANALYSIS OF SOIL – WHAT, WHY & HOW?

In geotechnical engineering, hydrometer analysis is primarily used to know the grain size distribution of a fine grained soil. In this post I will share with you the following things.

• What is a hydrometer?
• Why hydrometer analysis is done?
• What is the theory behind hydrometer analysis of soil?
• How to perform hydrometer analysis of soil?

WHAT IS HYDROMETER?

Fig-1 Hydrometer

A hydrometer is an instrument which is used to measure the relative density of a liquid. Hydrometer is made of glass and primarily consists of two parts;

• A cylindrical stem with graduation marks
• A bulb at bottom weighted with mercury

The lower the density of the liquid the more the hydrometer will sink. Consider water and petrol for example. The density of petrol is lower than that of water, therefore the depth of immersion of a hydrometer will more in case of petrol than water.

WHY HYDROMETER IS USED FOR GRAIN SIZE ANALYSIS OF FINE GRAINED SOIL?

In case of fine grained soil, sieve analysis test does not give reliable test result. This because a fine grained soil consist of different sizes of particles starting from 0.075 mm to 0.0002 mm. and it is not practicable to design sieve having so smaller screen size. Also there is a chance of lost of sample during sieving. Therefore hydrometer analysis is done for grain size analysis of fine grained soils.

WHAT IS THE THEORY BEHIND HYDROMETER ANALYSIS TEST OF SOIL?

Hydrometer analysis is based on Stokes law. According to this law, the velocity at which grains settles out of suspension, all other factors being equal, is dependent upon the shape, weight and size of the grain.

In case of soil, it is assumed that the soil particles are spherical and have the same specific gravity. Therefore we can say that in a soil water suspension the coarser particles will settle more quickly than the finer ones.

If V is the terminal velocity of sinking of a spherical particle, it is given by;

V = 1/18 [(Gs-Gw)/n)]*D2

Where,

V = Terminal velocity of soil particle (cm/s)

D = Diameter of soil particle (cm)

Gs = Specific gravity of soil particle

Gw = specific gravity of water

n = viscosity of water (g-s/cm2)

HOW TO DO HYDROMETER ANALYSIS OF SOIL

EQUIPMENT

• Hydrometer
• Dispersion cup with mechanical stirrer with complete accessories
• Two glass jar of 1 litre capacity
• Deflocculating agent (sodium Hexa metaphosphate solution prepared by dissolving 33g of sodium Hexa metaphosphate and 7g of sodium carbonate in distilled water to make one litre solution)
• Stop watch
• Thermometer
• Scale

PROCEDURE

1. Take about 50g in case of clayey soil and 100g in case of sandy soil and weigh it correctly to 0.1g.
2. In case the soil contains considerable amount of organic matter or calcium compounds,             pre-treatment of the soil with Hydrogen Peroxide or Hydrochloric acid may be necessary. In case of soils containing less than 20 percent of the above substances pre-treatment shall be avoided.
3. To the soil thus treated, add 100 cc of sodium hexametaphosphate solution and warm it gently for 10 minutes and transfer the contents to the cup of the mechanical mixer using a jet of distilled water to wash all the traces of the soil.
4. Stir the soil suspension for about 15 minutes.
5. Transfer the suspension to the Hydrometer jar and make up the volume exactly to 1000 cc by adding distilled water.
6. Take another Hydrometer jar with 1000cc distilled water to store the hydrometer in between consecutive readings of the soil suspension to be recorded. Note the specific gravity readings and the temperature T0C of the water occasionally.
7. Mix the soil suspension roughly, by placing the palm of the right hand over the open end and holding the bottom of the har with the left hand turning the jar upside down and back. When the jar is upside down be sure no soil is tuck to the base of the graduated jar.
8. Immediately after shaking, place the Hydrometer jar on the table and start the stopwatch. Insert the Hydrometer into the suspension carefully and take Hydrometer readings at the total elapsed times of ¼, ½, 1 and 2 minutes.
9. After 2 minutes reading, remove the Hydrometer and transfer it to the distilled water jar and repeat step no-8. Normally a pair of the same readings should be obtained before proceeding further.
10. Take the subsequent hydrometer readings at elapsed timings of 4, 9, 16, 25, 36, 49, 60 minutes and every one hour thereafter. Each time a reading is taken remove the hydrometer from the suspension and keep it in the jar containing distilled water. Care should be taken when the Hydrometer recorded to see that the Hydrometer is at rest without any movement. As time elapses, because of the fall of the solid particles the density of the fluid suspension decreases reading, which should be checked as a guard against possible error in readings of the Hydrometer.
11. Continue recording operation of the Hydrometer readings until the hydrometer reads 1000 approximately.

CALIBRATION OF THE HYDROMETER

The hydrometer shall be calibrated to determine its true depth in terms of the hydrometer reading (see Fig-2) in the following steps:

Fig-2 Hydrometer calibration

1. Determine the volume of the hydrometer bulb, VR. This may be determined in following way:

By measuring the volume of water displaced. Fill a 1000-cc graduate with water to approximately 700 cc. Observe and record the reading of the water level. Insert the hydrometer and again observe and record the reading. The difference in these two readings equals the volume of the bulb plus the part of the stem that is submerged. The error due to inclusion of this latter quantity is so small that it may be neglected for practical purposes.

2. Determine the area, A, of the graduate in which the hydrometer is to be used by measuring the distance between two graduations. The area, A, is equal to the volume included between the graduations divided by the measured distance.
3. Measure and record the distances from the lowest calibration mark on the stem of the hydrometer to each of the other major calibration marks, R.
4. Measure and record the distance from the neck of the bulb to the lowest calibration mark. The distance, H1, corresponding to a reading, R, equals the sum of the two distances measured in steps (3) and (4).
5. Measure the distance from the neck to the tip of the bulb. Record this as h, the height of the bulb. The distance, h/2, locates the center of volume of a symmetrical bulb. If a nonsymmetrical bulb is used, the center of volume can be determined with sufficient accuracy by projecting the shape of the bulb on a sheet of paper and locating the center of gravity of this projected area.
6. Compute the true distances, HR, corresponding to each of the major calibration marks, R, from the formula:

HR = H1 + ½ [h – (VR/A)]

7. Plot the curve expressing the relation between HR and R as shown in Figure 3. The relation is essentially a straight line for hydrometers having a streamlined shape.

Fig-3 Typical hydrometer calibration chart

CALCULATIONS

If the temperature during the experiment is constant, then the the following formula can be used to calculate the diameter of the soil particles

D2 = K HR/t

Where

T = time in minutes

D = diameter of soil particle in mm

K = 30n/(G-gw)

The percentage finer N may be obtained from

N% = G*V/((G-1)*W) * (r – rw)*100

Where

V = Volume of soil suspension (1000 cc)

W = weight of dry soil taken for the test

r = Hydrometer reading in distilled water

rw = Hydrometer readings in soil suspension

G = Specific gravity of soil particles

Since V = 1000 cc, the above equation may be conveniently represented as follows:

N% = K1 (Rh1 – 1000) * 100

Where

K1 = G/(G-1) * (100/W)

Rh1 = Hydrometer reading = Rh + Cm – Cd ± Ct

Where,

Rh = actually observed hydrometer reading (upper meniscus)

Cm = the meniscus correction (i.e. 0.5)

Ct = Correction for temperature (positive if the test temperature is more than the temperature at which the hydrometer is calibrated and vice versa) (see table-1)

Cd = Correction for dispersing agent. This is determined as mentioned below

The addition of a dispersing agent to the soil suspension results in an increase in density of the liquid and necessitates a correction to the observed hydrometer reading. The correction factor, Cd, is determined by adding to a 1000-ml graduate partially filled with distilled or demineralized water the amount of dispersing agent to be used for the particular test, adding additional distilled water to the 1000-ml mark, then inserting a hydrometer and observing the reading. The correction factor, Cd is equal to the difference between this reading and the hydrometer reading in pure distilled or demineralized water.

Table-1 Temperature Correction (Ct) for Hydrometer Analysis
Temp in 0C	Ct	Temp in 0C	Ct
20.0	Nil	27	0.00150
20.5	0.00009	27.5	0.00163
21	0.00017	28	0.00178
21.5	0.00027	28.5	0.00191
22	0.00037	29	0.00206
22.5	0.00049	29.5	0.00219
23	0.00058	30	0.00232
23.5	0.00068	30.5	0.00247
24	0.00081	31	0.00262
24.5	0.00092	31.5	0.00278
25	0.00102	32	0.00291
25.5	0.00116	32.5	0.00320
26	0.00127	33	0.00350
26.5	0.00139	33.5	0.00380