Object: To determine the particle size distribution of fine-grained soil by Hydrometer Analysis.

Standard:

ASTM D7928

Apparatus:

• Hydrometer (152H model preferable)
• Quantity (about 2.5L per test) of distilled water.
• A sedimentation cylinder (1000mL cylinder) is also termed a hydrometer jar.
• Graduated 1000 mL cylinder for control jar.
• Soil-dispersion device (malt mixer or air-jet dispersion).
• Dispersion agent (NaPO₃ or Na₂ SiO₃)
• Thermometer
• Stopwatch
• A balance readable to 0.1g

Theory:

Hydrometer analysis is a widely used method of obtaining an estimate of the distribution of soil particle sizes from the No. 200 (0.075 mm) sieve to around

1. mm. It covers the quantitative determination of the particle size distribution in soil from coarse sand size to clay size using sedimentation. The test is normally not required if less than 10% of the material passes the 75m test sieve. The hydrometer analysis is based on Stokes’ Law, which gives the relationship between the velocity of fall of spheres in a fluid, the diameter of the sphere, the specific weights of the sphere and the fluid, and the fluid viscosity. In equation form this relationship is

Where,

𝑣 =

𝛾𝑠 − 𝛾𝑤 18𝐷² ᶯ

v = velocity of fall of the spheres (cm/s)

= unit weight of water

_s = unit weight of soil particle

 = absolute, or dynamic, viscosity of the fluid (g /(cm * s))

D = diameter of the sphere (cm)

𝑫 = √

𝟏𝟖𝒗

𝜸𝒔 − 𝜸𝒘

For a soil particle of size ‘D’ falling through a distance h, in time t

𝒉

𝒗 =

𝒕

Procedure:

𝑫 = √

𝟏𝟖𝒉

∗

𝜸𝒔 − 𝜸𝒘𝒕

• 1. Prepare the control jar by adding 125 ml of 4% sodium metaphosphate (NaPO₃) solution and sufficient distilled water to produce 1000 ml. (This solution can be made by mixing 40g of dry chemical with enough water to make 1000 ml). Put the hydrometer into the control cylinder and record zero and meniscus correction; then record the temperature by putting the thermometer in it.
  2. Weigh out exactly 50g of soil passing the No. 200 sieve. Mix the soil with 125 ml of 4% sodium metaphosphate (NaPO₃) solution. Allow the soil mixture to stand for about 12 hours.
  3. At the end of the soaking period, transfer the mixture to a dispersion (or malt mixer) cup and add tap water until the cup is about two-thirds full. Mix for 1 minute. After mixing, carefully transfer all the contents of the dispersion cup to the sedimentation cylinder. Rinse any soil in the dispersion cup by using a plastic squeeze bottle or adding stabilized water and pour this into the sedimentation cylinder. Now add distilled water to fill the cylinder to the 1000 ml mark.
  4. Cap the sedimentation cylinder with a No. 12 rubber stopper and carefully agitate for about 1 min. Agitation is defined as turning the cylinder upside down and back 60 turns for 1 minute. An upside-down and back movement is 2 turns.
  5. Put the sedimentation cylinder beside the control cylinder and start the stopwatch immediately. This is cumulative time t = 0. Insert the hydrometer into the sedimentation cylinder.
  6. Take hydrometer readings at cumulative times t = 0.25 min., 0.5 min., 1 min. and 2 min. Always read the upper level of the meniscus. Remove and place the hydrometer in the control jar.
  7. Continue taking hydrometer and temperature readings at approximate elapsed times of 8, 15, 30, and 60 min. and then 2, 4, 8, 24 and 48 hr. For each reading, insert the hydrometer into the sedimentation cylinder about 30 sec before the reading is due. After the reading is taken, remove the hydrometer and put it back into the control cylinder.
     

Corrections:

The following corrections are applied in Hydrometer observations:

Temperature correction (𝑪𝒕):

If the temperature of the soil suspension is more than the calibrated temperature of the hydrometer (i.e. 20C), the correction shall be positive and if the mixture temperature is less than the calibrated temperature of the hydrometer, it shall be negative.

Meniscus correction (𝑪𝒎):

The difference between the upper level of the meniscus and the water level of the control cylinder is called meniscus correction. This correction is always positive and is constant for the hydrometer.

Dispersing agent correction (𝑪𝒅):

The addition of a dispersing agent in the soil increases the density of the suspension. Hence the dispersing agent correction is always negative.

The corrected hydrometer reading therefore is given by

𝑅 = 𝑅ℎ + 𝐶𝑚 ± 𝐶𝑡 − 𝐶𝑑

Where 𝑅ℎ= hydrometer reading, observed at the top of the meniscus.

Temperature corrections (for Hydrometer calibrated at 20C)

Viscosity () of water at different temperatures (values given in milli-poise)

Specific Gravity of water at different temperatures

22

20

18

16

H_e (cm)

14

12

10

8

6

4

2

0

-5-2.502.557.5 10 12.5 1517.52022.5 25 27.5 30

R_h

Observations and calculations:

1. Percentage of soil passing 75m sieve =
2. Mass of the dry soil (passing 75m sieve)W_d =
3. Meniscus correction (C_m) =
4. Specific gravity G_s of soil (passing 75m sieve) =

𝑀1 = √

30

980(𝐺𝑠 − 1)

𝑀2 =

𝐺𝑠

𝑤𝑑(𝐺𝑠 − 1)

𝑥100

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