Environmental Engineering Reference
In-Depth Information
unsaturated soil variables that appear to affect the shape
of the compaction curve. It appears that the fundamental
theories of unsaturated soil mechanics (Fredlund and
Rahardjo, 1993a) can assist in understanding the compaction
process and explain the inverted parabolic shape of the
compaction curve.
The prediction of the soil compaction curve has been
studied for static loading conditions (Kurucuk et al., 2007,
2008). Theoretically based estimations of the compaction
curve have been compared to data found in the literature
and found to compare favorably. Only the theoretical aspects
associated with compaction are discussed in this topic. The
application of compaction in geotechnical engineering prac-
tice can be found in many other textbooks.
The main unsaturated soil mechanics theories utilized
in formulating a theoretical framework for the compaction
process are the undrained pore pressure generation theory
described by Hilf (1948) and the volume change theory for
unsaturated soils described by Fredlund and Morgenstern
(1976). The theory of pore pressure generation under
undrained conditions is further discussed in Chapter 15.
The
was also assumed that the change in pore-air pressure was
equal to the change in pore-water pressure, and therefore,
changes in matric suction were insignificant. Experimental
results show that during compaction suction changes can be
large.
Following compaction the soil is unloaded. Unloading the
soil forces matric suction from the wetting SWCC toward
the drying SWCC (Tarantino and De Col, 2008; Tarantino
and Tombolato, 2005). Hilf's (1948) assumption of suction
remaining constant during compaction appears to be reason-
able based on later laboratory tests performed by Kurucuk
et al. (2007).
2.5.2 Computation of Volume Change and Dry Density
The volume change relationship for
K
0
loading of an unsat-
urated soil can be written in terms of two independent stress
variables as proposed by Fredlund and Morgenstern (1976):
V
v
V
o
m
1
(σ
y
−
m
2
(u
a
−
ε
v
=
=
u
a
)
+
u
w
)
(2.105)
where:
theory
related
to
volume
change
is
discussed
in
Chapters 13 and 14.
ε
v
=
volumetric strain,
V
v
=
overall volume change of soil element,
2.5.1 Pore Pressure Development During Static
Compaction
The compaction process is assumed to involve the undrained
loading of the soil with respect to the air and water phases.
Hilf (1948) developed a relationship between changes in
pore-air pressure and the applied total stress. Other assump-
tions made by Hilf (1948) were that loading conditions
could be simulated as one-dimensional (
K
0
) compression,
and Boyle's law and Henry's law were applicable. The
derived equation became known as the Hilf (1948) equation
and can be written as
V
o
=
initial total volume of soil element,
m
1
=
compressibility
of
soil
structure
with
respect to net applied stress (
σ
y
−
u
a
),
m
2
=
compressibility
of
soil
structure
with
respect to matric suction (
u
a
−
u
w
),
(σ
y
−
u
a
)
=
change in net applied stress, and
(u
a
−
u
w
)
=
change in matric suction.
Deformation during undrained loading of the soil mass is
assumed to be due primarily to compression of the pore-
air phase and air going into solution. The volume change
constitutive relationship along with Hilf's (1948) equation
provides the basic physical relationship for formulating a
compaction model for unsaturated soils. The challenge is to
determine the appropriate soil parameters for the prediction
of the compaction curve.
⎡
⎣
⎤
⎦
1
1
hS
o
n
o
u
a
=
σ
y
(2.104)
−
S
o
+
1
+
¯
u
a
m
v
u
ao
+
where:
2.5.3 Compaction Model Assumptions
Initially the assumption was made that the compressibility
coefficients of the soil remained constant during the com-
paction process. However, this assumption did not produce
the required parabolic shape for the compaction curve, par-
ticularly on the dry side of optimum water content (Kurucuk
et al., 2007). The results showed that volume change during
compaction was primarily controlled by the compressibil-
ity of the soil with respect to the total stress state variable
for the soil structure (i.e.,
m
1
). There appeared to be some
influence due to changes in matric suction, but its influence
was relatively small. Superior results were obtained when
the volumetric compressibility of the soil was assumed to
u
a
=
change in pore-air pressure,
S
o
=
initial degree of saturation,
h
=
coefficient of solubility (i.e., 0.02 by volume),
n
o
=
initial porosity,
u
ao
=
¯
initial absolute air pressure, and
σ
y
=
change in applied vertical stress.
The coefficient of volume change,
m
v
, was used to repre-
sent the volume change property of the soil. Overall volume
change was assumed to be equal to the amount of air dissolv-
ing in the water and the compression of free air. The liquid
and solid phases were considered to be incompressible. It
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