Page 188 - Geotechnical Engineering Soil and Foundation Principles and Practice

Soil Density and Unit Weight
Soil Density and Unit Weight 183

Figure 9.3
A block diagram simplifies calculations of moisture content and density relationships by filling in
the blanks according to the formula shown at the top. The dashed line indicates variability of
water and air contents as the total volume of voids, V v , remains constant.

Newton’s formula f ¼ ma. On Earth the acceleration usually is denoted by g and
2
2
nominally is 9.81 m/s or 32.2 ft/s . Gravitational acceleration varies with altitude
and location relative to mountain ranges and ocean basins, but the amount of the
variation on Earth does not significantly influence the determination of unit
weights. In dealing with weights on Earth, unit weight is the term preferred in
engineering.

9.2.3 A Benchmark for Unit Weight
The solid portion of soil shown in Fig. 9.3 is the base for calculating the dry unit
weight. The moisture content may change but the dry unit weight remains the
same (unless it is expansive clay). Including water gives a wet unit weight, which
varies between limits that are fixed by the dry unit weight and by the unit weight
when the soil is saturated with water.

The wet unit weight and moisture content are measured and then converted to dry
unit weight, which reflects only the degree of packing of a soil.

Example 9.1
A cylindrical sample of undisturbed soil 3 in. (76.2 mm) in diameter and 6 in. (152.4 mm)
long weighs 3.04 lb (1.38 kg mass) and 2.57 lb (1.166 kg mass) after oven-drying. What are
(a) its wet and dry unit weights and (b) its densities?
3
3
Answer: (a) The volume of the cylindrical sample is 42.4 in. , or 0.0245 ft . The wet unit
3
3
weight is 3.04 7 0.0245 ¼ 124 lb/ft . The dry unit weight is 2.57 7 0.0245 ¼ 105 lb/ft .
3
3
3
(b) The volume is 695 cm . The wet density is 1.99 g/cm and the dry density is 1.68 g/cm .
3
In SI these values are expressed as Mg/m , also called ‘‘bulk densities,’’ the bulk density of
water being 1.00.
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