Page 157 - Geotechnical Engineering Soil and Foundation Principles and Practice

Particle Size and Gradation
152 Geotechnical Engineering

and sizes smaller than about 0.001 mm settle more slowly. In 1827 an English
botanist, Robert Brown, noticed that pollen grains suspended in water jiggled
about when observed in a microscope, a movement that now is called Brownian
motion. This grabbed the attention of an employee of the Swiss patent office, who
wrote a brief paper attributing it to random molecular bombardment. The
employee’s name was Albert Einstein, who later became famous for another
matter. Particles smaller than about 0.001 mm tend to remain in suspension and
are referred to as colloidal size particles.

According to eq. (7.3) the rate of settling depends on the specific gravity
of the
particles, which varies depending on the mineral. Because sedimentation is a bulk
test, an average specific gravity is used in the calculations for particle size.
A method for measuring average specific gravity is described later in this chapter.
However, the assumption that all grain densities are average means that particles
of dense minerals will be reported as larger than their true dimensions because
they settle faster.

Sedimentation rate is influenced by the fluid viscosity, , which in turn depends on
temperature. A standardized temperature of 208C (688F) is used for laboratory
analyses. Other temperatures may be used with appropriate correction factors
based on viscosity tables.

An obvious limitation of Stokes’ Law is that it applies only to spherical particles,
whereas silt grains are angular and clay particles flat. Particle sizes determined
from sedimentation rates often are reported in terms of ‘‘equivalent particle
diameters.’’

7.4.5 Simplifying Stokes’ Law
In eq. (7.3), a particle radius in cm equals the diameter 0.05D in mm. The settling
velocity in cm/s equals 600L/T, where L is the settling distance in mm and T is
time in minutes. Substituting values for the acceleration of gravity and the
viscosity gives
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
D ¼ K L=10T ð7:4Þ
where D and L are in mm and T is in minutes. K depends on the specific gravity of
the soil and temperature of the solution; with a representative soil specific gravity
of 2.70, and a standardized temperature of 208C, K ¼ 0.01344. Other values for
this coefficient for different specific gravities and temperatures are given in ASTM
Designation D-422.

Example 7.3
A soil suspension is prepared containing 50 g/l. After 60 minutes the hydrometer reads
22 g/l. The temperature is controlled at 208C. (a) What particle diameter is being measured,
and (b) what is the percent of particles finer than that diameter?

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