Environmental Engineering Reference
In-Depth Information
pore-air pressure will be controlled by the compressibility
of the air and the compressibility of the soil structure.
The following sections illustrate how the compressibil-
ity of an air-water mixture can be used to calculate pore-
air and pore-water pressures induced as a result of total
stress loading. The induced pore-air and pore-water pres-
sures constitute the initial boundary conditions when solv-
ing the PDEs associated with the pore-air and pore-water
pressure dissipations. The initial pore-air and pore-water
pressures are assumed to be uncoupled from any other pro-
cess. The pore-air and pore-water pressures are subsequently
solved as processes that take place with respect to time.
The dissipation of the pore-air and pore-water pressures
can be solved in either a coupled or uncoupled manner.
A decision can be made regarding whether the dissipation
of pore pressures should be solved in a coupled or uncou-
pled manner. Often it is easier to use an uncoupled solution
and the results are satisfactory for geotechnical engineering
practice.
mass with respect to a pressure change per unit volume at a
constant temperature:
1
V
dV
du
C
=−
(15.1)
where:
C
=
compressibility,
V
=
total volume of the element under consideration,
dV
/
du
=
volume change with respect to a pressure change,
and
du
=
pressure change.
The term
dV
/
du
in the above equation has a negative sign
because the volume decreases as the pressure increases. A
negative sign is used in order to render a positive compress-
ibility value.
In an unsaturated soil, the pore fluid consists of water,
free air, and air dissolved in water. The individual com-
pressibility of air and water is required in formulating the
compressibility of the air-water mixture.
15.3.1 Compressibility of Pore Fluids
Pore-air and pore-water are not allowed to flow out of an
unsaturated soil during undrained compression. Volume
change occurs as a result of the compression of the air and, to
a lesser extent, the water. The compression of soil solids can
be assumed to be negligible for the stress range commonly
encountered in engineering practice. The pore fluid volume
change is related to changes in the pore-air and pore-water
pressures. The pore-air and pore-water pressures increase
as an unsaturated soil is compressed. The pore pressure
increase is commonly referred to as an excess pore pressure.
The volume change of a phase is related to a pressure
change through its compressibility. Figure 15.5 defines the
compressibility of a material at a point on the volume-
pressure curve during undrained compression. Isothermal
compressibility is defined as the volume change of a fixed
15.3.1.1 Air Compressibility
The isothermal compressibility of air can be expressed as
C
a
=
−
1
V
a
dV
a
du
a
(15.2)
where:
C
a
=
isothermal compressibility of air,
V
a
=
volume of air,
dV
a
/
du
a
=
air volume change with respect to an air pres-
sure change, and
u
a
=
air pressure.
The volume-pressure relationship for air during isother-
mal, undrained compression can be expressed using Boyle's
law:
u
a
0
V
a
0
u
a
V
a
=
(15.3)
where:
u
a
0
=
initial absolute air pressure (i.e.,
u
a
0
=
u
a
0
+
u
atm
),
u
a
0
=
initial gauge air pressure,
u
atm
=
atmospheric pressure (i.e., 101.3 kPa),
V
a
0
=
initial volume of air, and
u
a
=
absolute air pressure (i.e.,
u
a
=
u
a
+
u
atm
).
Differentiating the volume of air,
V
a
, with respect to abso-
lute air pressure
u
a
gives
dV
a
d u
a
=−
u
a
0
V
a
0
1
u
a
Figure 15.5
Definition of variables associated with isothermal
compressibility.
(15.4)
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