Page 194 - Geotechnical Engineering Soil and Foundation Principles and Practice

Soil Density and Unit Weight
Soil Density and Unit Weight 189

For comparison, the unit weight of Portland cement concrete, which contains
3
3
3
water, is approximately 2.4 Mg/m , 150 lb/ft , or 23.6 kN/m . Heavier concretes
used for radiological containment vessels or to contain gas pressures in deep oil
wells require denser aggregates.
A theoretical lower bound with all particles touching can be obtained by assuming
uniform spheres packed in a cubic arrangement (Fig. 9.5).

The void ratio of the cubic arrangement can be obtained from the volume of a
sphere and the volume of the enclosed cube. If V ¼ 1, V s ¼ 0.5236, and
e¼ 0:928

Multiplying V s times the mineral unit weight gives the dry unit weight, which with
quartz spheres is

d ¼ 2:65 0:5236 ¼ 1:39 Mg=m 3

d ¼ 1:39 62:4 ¼ 86:6lb=ft 3

d ¼ 13:6kN=m 3

Coincidentally silt soils that have a lower unit weight than about 90 lb/ft 3
3
3
(1.44 Mg/m ; 14.1 kN/m ) generally are collapsible.
A rhombic arrangement is obtained by sliding one layer of spheres over interstices
between the next lower layer of spheres, and is the densest packing arrangement
for uniform spheres. This also is the pattern of a tetrahedral arrangement around
the void, as each sphere is supported by and in contact with three spheres in the
next lower layer. This arrangement gives a volume of solids V s ¼ 0.75, and a void
ratio of
e¼ 0:34
The corresponding dry density is

3 3 3

d ¼ 2:65 0:75 ¼ 1:99 Mg=m ,ð124 lb=ft Þ,19:5kN=m
This is a high unit weight for a soil and will be decreased if there are voids where
particles are not in contact. The density will be even higher as spaces are filled
with progressively smaller particles, approaching that of Portland cement
concrete.

Figure 9.5
Packing
arrangements for
uniform spheres.
Similar
arrangements
occur in crystals.

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