Page 158 - Geotechnical Engineering Soil and Foundation Principles and Practice

Particle Size and Gradation
Particle Size and Gradation 153

Answer: (a) The effective depth of the hydrometer is obtained by interpolation of data in
Table 7.2, which gives L ¼ 127 mm. From eq. (7.4),
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
D ¼ 0:01344 127=10 60 ¼ 0:0062 mm ¼ 6:2 mm:

(b) P ¼ 100 22/50 ¼ 44%.

7.4.6 Interpolating the Percent 2 mm Clay from
Hydrometer Analyses

The sedimentation time for a hydrometer analysis to measure 2 mm clay is
approximately 8 hours, which is inconvenient with an 8-hour working day.
However, as this part of the accumulation curve often is approximately linear
on a semilogarithmic plot, the percent 2 mm clay can be estimated from a
proportionality of the respective logarithms. As an approximation,

P 002 ¼ 0:4P 001 þ 0:6P 005 ð7:5Þ

7.5 USES OF PARTICLE SIZE DATA

7.5.1 Median Grain Size
As previously mentioned, the size that defines 50 percent of the soil as being
finer and 50 percent coarser is the median grain size, designated as D 50 , and is
read from the intersection of the particle size distribution curve with the 50
percent line, as shown in Fig. 7.3. The median approximates but is not the same
as a mean or average particle size, which would be very difficult to determine
because it would involve measuring many individual particles and calculating an
average.

7.5.2 Effective Size and Uniformity Coefficient
A measurement that often is made for sand is the effective size, D 10 , or the size
whereby 10 percent of the particles are finer, and was shown by an engineer,
Allen Hazen, to correlate with the permeability of filter sands. Hazen defined the
uniformity coefficient, C u , as the ratio D 60 /D 10 . The uniformity coefficient can
be as low as 1.5 to 2 for washed sands that are nearly all one size. For engineer-
ing uses a soil is said to be ‘‘well graded’’ if it contains a wide range of particle
sizes. A well-graded sand-gravel mixture may have a uniformity coefficient of
200–300.

Example 7.4
The sand in Fig. 7.2 has approximate values of D 10 ¼ 0.12 mm and D 60 ¼ 0.20 mm, from
which C u ¼ 1.7. For engineering purposes this soil would be described as ‘‘poorly graded.’’
Because D 10 is off the chart for fine-grained soils, another measure for degree of
uniformity suggested by a geologist, Trask, is the ‘‘sorting coefficient,’’ S o , which

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