The University of Toledo
Soil Mechanics Laboratory
1
Grain Size Distribution – Hydrometer Analysis
Introduction
The hydrometer analysis, also called sedimentation method, is used to determine the grain
size distribution for the fraction of soil that is smaller than the No. 10 (2.00 mm) sieve. Fine soil
particles are dispersed by soaking the soil sample in a dispersing agent and by rapid stirring to
neutralize the charges between the soil particles. The test uses a Type 152H hydrometer
calibrated to give the mass of solids with specific gravity equal to 2.65 in suspension and the
settling velocity of the dispersed soil particles. The soil grain diameter D (mm) is computed by
application of Stokes’ Law, a theoretical equation for the terminal settling velocity of spheres in
a fluid, according to the following equations.
v =
D =
where
2 G s - G1 æ D ö
ç ÷
h
9
è2ø
2
(1)
30 h v
980(G s - G1 )
(2)
v = settling velocity of the fluid, water plus dispersing agent
Gs = specific gravity of the soil solids
G1 = specific gravity of the water and dispersing agent solution
h = absolute viscosity of the suspending fluid which depends on the temperature
Since the soil particles are particles are not spheres, the hydrometer analysis gives the diameters
of spheres that would be settling at the same velocity as the soil particles. This approximation to
the particle size distribution is useful for such engineering purposes as estimating the percentage
of fine grained particles and the percentage of clay sized particles.
Apparatus
1. Balance capable of measuring to 0.1 g
2. Evaporating dish
3. Mechanical mixer and mixing cup to assist in dispersing the soil
4. Type 152H hydrometer which reads grams of soil per 1000 ml. of slurry
5. 2 - 1000 ml. cylinders, 1 - 1000 ml. glass sedimentation cylinder
6. Rubber stopper
7. Thermometer
1
ASTM D 422 – 1963 (Reapproved 1998)
Hydrometer Analysis – 1
Procedure
A. Preparation (at least 24 hours before test)
1) Prepare a solution of sodium hexametaphosphate mixed at the rate 40 g of sodium
hexametaphosphate per liter of solution.
2) Weigh out a sample of 50.0 g of oven-dried soil (Ws). Hydrometer sample should be
finer than the No. 10 sieve. The mass of oven-dried soil must be divided by the percent
passing the No. 10 sieve if the sample includes sizes larger than the No. 10 sieve. Place
the soil in an evaporating dish and cover with 125 ml of the sodium hexametaphosphate
solution. Allow soaking for at least 16 hours.
3) Prepare one cylinder with 125 ml of solution and enough water to bring the solution to
1000 ml. This is the control solution used to get the zero correction. Prepare another
cylinder with 1000 ml of water to provide a supply of room temperature water.
B. Laboratory
1) Practice placing the hydrometer in the control solution so that the hydrometer will not
move up and down after releasing it. This is done by lowering the hydrometer water
level to about zero on the hydrometer stem, which corresponds to zero grams of solids
per 1000 ml of solution. Practice taking readings of the top of the meniscus formed on
the stem of the hydrometer. The reading in the control solution is the zero
correction, Cz. When taking readings in the soil-water suspension, estimate the
hydrometer reading before placing the hydrometer in the suspension. The reading will
be less than 50 initially and will decrease as soil settles out of solution.
2) Transfer the soil-water slurry to the dispersion cup making sure that all soil is washed
from the dish. If necessary, add enough water to the slurry so that the cup is more than
half full. Stir with the mechanical mixer for a period of 1 minute.
3) Immediately after dispersion, transfer the soil slurry into the glass sedimentation
cylinder making sure that all soil is washed from the mixer and the dispersion cup. Add
enough water to fill the cylinder to the 1000-ml mark.
4) Use a stopper or the palm of the hand to cover the end of the cylinder. Turn the cylinder
upside down and back for 1 minute at a rate of 30 times per minute to agitate the
mixture. Place the cylinder in a convenient place on the counter where it will not be
disturbed. Start timing immediately.
5) Obtain the hydrometer readings using the top of the meniscus on the hydrometer.
Obtain 2 readings within the first 2 minutes recording the actual times of the readings.
Recommended times for additional readings are: 2, 5, 15, 30, 60, 250, and 1440 minutes.
Record the actual time of readings, if readings are taken at other times.
6) After the 2-minute reading, remove the hydrometer from the soil suspension after each
reading. Place the hydrometer in the control solution with a spinning motion.
7) Obtain the temperature of the slurry (or the control solution) after each reading.
Hydrometer Analysis – 2
Calculations
For Type 152H hydrometers, the velocity v is equal to L/T, and Equation 2 is written as
D = K L /T
where
(3)
K = a constant depending on the specific gravity of the solids and the temperature of
the fluid (mm x (min/cm)1/2), given in the Table 1;
L = effective depth in cm. of the hydrometer which is the distance from the surface of
the suspension to the center of the hydrometer bulb (cm);
T = elapsed time (min).
For Type 152H hydrometers, the effective depth can be given as
L = 16.3 – 0.164 R
(4)
where R is the reading on the hydrometer in grams of solids per liter of suspension. The
effective depth is the distance that the soil has settled that can then be used to calculate velocity.
The equation for the percentage of the soil remaining in suspension is
P = (Rc a / M s) x 100%
(5)
Rc = Actual hydrometer reading - zero correction, Cz + temperature correction, CT (6)
where the zero correction is obtained as described in laboratory step (1) above and CT, given in
the Table 1, is a factor that accounts for variation in the density of the soil-water suspension for
different temperatures.
a = correction factor required when the specific gravity of the soil grains is not equal
to 2.65 and given by the following equation
1.65 Gs
2.65 (Gs - 1)
M s = oven dry mass in g of the soil sample dispersed in preparation step (2).
a=
Results
Complete the Table 2 on the next page using Equations 3 though 7 and temperature
dependent constants provided in Table 1. The grain size distribution is plotted on Figure 1, since
the particle diameter and percent of soil in suspension, equivalent to the percent finer, are
computed.
Hydrometer Analysis – 3
(7)
Table 1 – Temperature Dependent Fluid Constants
K (ASTM Type 152H Hydrometer)
Temperature
o
C
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
CT
-0.90
-0.70
-0.50
-0.30
0.00
+0.20
+0.40
+0.70
+1.00
+1.30
+1.65
+2.00
+2.50
+3.05
+4.80
2.60
0.0146
0.0144
0.0142
0.0140
0.0139
0.0137
0.0135
0.0134
0.0132
0.0131
0.0129
0.0128
0.0126
0.0125
0.0124
Specific Gravity of Soil, Gs
2.65
2.70
0.0144
0.0141
0.0142
0.0140
0.0140
0.0138
0.0138
0.0136
0.0137
0.0134
0.0135
0.0133
0.0133
0.0131
0.0132
0.0130
0.0130
0.0128
0.0129
0.0127
0.0127
0.0125
0.0126
0.0124
0.0124
0.0123
0.0123
0.0121
0.0122
0.0120
2.75
0.0139
0.0138
0.0136
0.0134
0.0133
0.0131
0.0129
0.0128
0.0126
0.0125
0.0124
0.0122
0.0121
0.0120
0.0118
Table 2 – Calculation Sheet for Hydrometer Analysis
Hydrometer Analysis
Group __________
Soil Description
Oven Dry Soil Mass, M s
Specific Gravity, Gs
Zero Correction, Cz
Specific Gravity Correction, a
Elapsed Hydrometer
Time
Reading
Temp.
L
min
R
(oC)
(K) (cm)
D
(mm)
2
5
15
30
60
Hydrometer Analysis – 4
CT
Date _________
Corrected
Reading,
Rc
Percent
Finer,
P
100%
Percent Finer
80%
60%
40%
20%
0%
1.000
0.100
0.010
0.001
Particle Diameter, mm
Figure 1 – Grain Size Distribution of Fine-Grained Soil
Conclusions
Is the grain size distribution curve representative of the type of soil tested in the laboratory?
How would it affect the results if the test were conducted when the temperature was 5o C
higher?
What is the percent finer than the # 200 sieve (0.075 mm) and the percent finer than
0.002mm (clay particles)?
What correction would be required if the soil was first sieved and it was determined that the
hydrometer sample included only 60% of the total soil sample, i. e. the other 40% was
larger in diameter than any of the grain diameters measured?
Hydrometer Analysis – 5
1000-ml Cylinders
Hydrometer
Thermometer
And Timer
Rubber
Stopper
Picture 1 – !000-ml Cylinders and Hydrometer
Mixer
and
Mixing Cup
Evaporating Dish
Picture 2 – Mixer and Mixing Cup
Hydrometer Analysis – 6