Environmental Engineering Reference
In-Depth Information
2.4.7.1 Volume-Mass Relationships (Pore Fluid Other
Than Water)
Figure 2.47 shows the volume and mass designations for
a multiphase material that is comprised of a solid, a fluid,
and a gas. The fluid could be water, an acid (e.g., liquor),
or some other liquid whose density may vary from that of
pure water. The gas is assumed to be air and conditions are
assumed to remain isothermal. The mass variables can be
written as the respective volumes multiplied by the density
of the corresponding phase. The subscript
f
is used to refer
to a fluid phase where the fluid has a density that differs
from that of water (i.e., an alternate fluid).
The term “specific gravity” is used for the components
of the multiphase system. The attached subscript designates
the material to which reference is being made. The specific
gravity of the solids is defined as
The calculation of void ratio is likewise unaffected by the
nature of the pore fluid:
V
v
V
s
e
=
(2.94)
where:
V
s
=
volume of solids.
Gravimetric water content is defined as the ratio of the
mass of water to the mass of solids when the pore fluid is
water:
M
w
M
s
w
=
(2.95)
where:
M
w
=
mass of water and
ρ
s
ρ
w
G
s
=
(2.91)
M
s
=
mass of solids.
where:
ρ
s
The gravimetric fluid content when the fluid is other than
water can be defined as the ratio of the mass of alternate
fluid to the mass of solids:
=
density of solids or particles and
density of water at 4
◦
C.
ρ
w
=
M
f
M
s
The specific gravity of a liquid other than water is;
G
f
.
given as
w
f
=
(2.96)
ρ
f
ρ
w
G
f
=
(2.92)
where:
where:
ρ
f
M
f
=
mass of the alternate fluid.
=
density of the fluid other than water.
2.4.7.2 Basic Volume-Mass Relationship When Pore
Fluid Is Not Water
A basic volume-mass relationship can be derived by com-
paring volume and mass representations for the amount of
fluid in a material. The mass of fluid,
M
f
, in a material can
be written as the volume of fluid multiplied by the density
of the fluid:
The definition for the degree of saturation is not influenced
by the fluid in the pores:
V
f
V
v
S
=
(2.93)
where:
V
f
=
volume of fluid and
M
f
=
Seρ
f
V
s
(2.97)
V
v
=
volume of voids.
Volumes
Masses
M
a
= 0
V
a
=
e
(1-
S
)
V
s
Air
e
=
V
v
/
V
s
M
f
=
w
f
G
s
r
w
V
s
M
f
=
w
f
M
s
V
f
=
SeV
s
=
SV
v
Water
Solid
M
s
=
G
s
r
w
V
s
V
s
Figure 2.47
Three-phase soil model relating mass and volume portions.
Search WWH ::
Custom Search