Page 156 - Geotechnical Engineering Soil and Foundation Principles and Practice

Particle Size and Gradation
Particle Size and Gradation 151

Hydrometer reading, g/l Depth, mm Table 7.2
Depth to hydrometer
5 155
center of volume
10 147
15 138
20 130
25 122
30 114
35 106
40 97
45 89
50 81

Note: Adapted from ASTM Designation D-422.

Temperature also must be controlled and measured to enable correction for
changes in the fluid viscosity.

7.4.4 Stokes’ Law of Sedimentation
In 1851 a British mathematician, G. G. Stokes, solved for the settlement
velocity of spherical particles in a suspension by equating their buoyant weight
to viscous drag on the outer surfaces. Surface area increases in proportion to
the radius while weight increases as the radius cubed, so the larger the particle,
the faster it will settle. The classic derivation for Stokes’ formula in the cgs
system is
R ¼ 6 r v ð7:1Þ
2
where R is the resisting force in g cm/s , r is the particle radius in cm, is the fluid
1 1
viscosity in poise or g-cm s , and v is the settlement rate in cm/s. Equating to
the buoyant weight of a spherical soil grain gives
4 3
6 r v ¼ r ð

w Þg ð7:2Þ
3
where
and
w are respectively the density of the soil grain and that of water, and
g is the acceleration of gravity. Solving for velocity v gives
2ð

w Þgr 2
v ¼ ð7:3Þ
9
Thus, the settlement rate v depends on the square of the particle radius r.

Experiments have confirmed the validity of the formula for particles between
0.001 and 0.10 mm in size, that is, for silt and most clay particles. Sand sizes are
influenced by mass displacement considerations that slow their rates of sinking,

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