Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 73

The mass of fluid in a material, M f , can also be written as

M f = w f G s ρ w V s (2.98)

Equating Eqs. 2.97 and 2.98 gives rise to a basic volume-
mass relationship for a material where the pore fluid has a
density other than that of pure water,

w f G s ρ w =

Seρ f

(2.99)

or

w f G s ρ w
ρ f

Se = (2.100)

Figure 2.48 Standard and modified American Association of
State Highway and Transportation Organization (AASHTO) com-
paction curves.

The density of the pore fluid appears in the basic volume-
mass relationship. If the pore fluid is pure water, the density
of the pore fluid is 1.0 and can be omitted from the equation.
If the pore fluid has a density different from that of water,
the density of water and the alternate pore fluid must be
retained in all calculations.
Bulk density is defined as the ratio of total mass of the
materials involved to the total volume and can be written in
one of several forms. The mass of each component of the
multiphase system can be written in terms of the respective
volumes multiplied by the density of each phase:

an understanding of the changes in the soil properties as the
compaction water content varies from optimum conditions.
The objective of the compaction process in the field is
generally to increase density, decrease soil compressibility,
increase soil shearing strength, and reduce water perme-
ability. Typical compaction curves are shown in Fig. 2.48
illustrating the relationship between compaction effort and
the density of the soil. The line corresponding to a degree of
saturation of 100% is called the “zero air voids” curve. The
compaction curves show that different states of density are
attained when the soil is compacted with the same apparent
energy input but different water contents. The water con-
tent at the peak of the compaction curve is called optimum
water content and represents the water content at which dry
density is a maximum for a given compaction energy.
Since the pioneering work of Proctor in 1933, many
researchers have attempted to qualitatively explain the
fundamental mechanisms involved in the densification
process. The desire has been to understand the shape of the
compaction curve, particularly on the dry side of optimum
water content. The compaction curve has been explained in
terms of a capillarity and lubrication theory (Proctor, 1933),
a viscous water theory (Hogentogler, 1936), a pore pressure
theory (Hilf, 1956), a physicochemical interaction theory
(Lambe, 1960b), and an effective stress theory (Olson,
1963). More recently, Barden and Sides (1970) undertook
an experimental study of the relationship between the
engineering performance of compacted, unsaturated clay
and microscopic observations of clay structure. Lee and
Suedkamp (1972) also conducted research on the shape of
the compaction curve for different soils.
Various theories have been proposed to assist in
understanding the compaction process in soils. In general,
these theories have utilized little information related to the
unsaturated soil mechanics principles. Modeling of the soil
compaction curve within the context of unsaturated soil
mechanics has been undertaken by Kurucuk et al. (2007).
The

V s ρ s + V f ρ f

ρ = (2.101)

V s ( 1 + e)

The volume of the pore fluid must be converted to the pore
fluid in the mass, giving rise to the following equations for
density of the overall mass:

G s + SeG f

ρ = ρ w (2.102)

1 + e

ρ s /ρ w + Seρ f + ρ w

ρ = ρ w (2.103)

1 + e

The unit-weight equations for a three-phase system are
equal to the density equations multiplied by acceleration
due to gravity, g .

2.5 SOIL COMPACTION

Compaction is the mechanical process used to increase the
density of a soil through the elimination of air (i.e., densifi-
cation). Soil compaction is widely used in geotechnical engi-
neering practice for the construction of roads, dams, land-
fills, airfields, foundations, hydraulic barriers, and ground
improvement. A laboratory compaction curve determined
using a standard test procedure is used as a guide for con-
trol of the construction process in the field. The objective of
laboratory testing is to determine the optimum water content
that will produce the maximum density. Also of interest is

research provides insight into the role of various