Void Ratio of Sand
Name: Armin S.
What is the maximum and minimum void ratio of ottawa
sand (silica sand)?
Ottawa sand, so called because it is mined in Ottawa, Illinois, is used in
many experimental situations because the individual sand particles are very
uniform in size and very spherically shaped. Consequently, the behavior of
this material may be modeled as a group of uniformly sized spheres and
It is assumed that the spheres are all in contact with one another. This
condition is referred to as "close packing". In the least efficient close
packing form, simple cubic packing (SCP), it can be shown that solids fill
52% of the total volume of a sample. In the most efficient close packing
arrangement, cubic close packing (CCP), solids fill 74% of the total sample
Void ratio (e) is defined as the ratio of the volume of voids to the volume
of solids. So, in the SCP case, e = 0.48/0.52 = 0.92. In the CCP case, e =
0.26/0.74 = 0.35. Realistically, however, these are theoretical extremes
that may be difficult to achieve in actual samples. The concept of "random
close packing" suggests that spheres will naturally gravitate towards a
density of about 64%, or a void ratio of 0.56. This may be a more realistic
value for uncompacted Ottawa sand.
It should be noted that these ideas may not be applied to real world soils
because they typically consist of a wide range of particle sizes and shapes.
Observation indicates that if the cumulative grain size distribution of a
soil is raised to the 0.45 power, soils whose distributions plot as a
straight line will yield the highest actual densities.
Dr. Andy Johnson, P.E.
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