Environmental Engineering Reference
In-Depth Information
The Gibbs free-energy equation is of particular interest
when solving problems related to “actual evaporation” from
the ground surface. The Gibbs equation can be viewed as the
water retention curve for air above the soil and as such defines
the evaporative potential at the ground surface. Evaporation
from the soil surface is “shut off” when the relative humid-
ity (i.e., water vapor pressure) in the soil at ground surface
becomes equal to the relative humidity in the air above the
ground surface. In this way, the Gibbs free-energy equation
defines the ground surface boundary condition for vapor flow.
50
45
40
35
30
25
20
15
10
5.2.5 Volume-Mass Constitutive Relationships
The relationship between the volume-mass properties of a
soil and stress state provides a conceptual framework for
visualizing the SWCC. Two volume-mass constitutive rela-
tions are required in order to relate all volume-mass soil
properties to the stress state (Fredlund and Morgenstern,
1976). The most common volume-mass properties used in
geotechnical engineering are void ratio
e,
gravimetric water
content
w,
and degree of saturation
S
.
The volume-mass constitutive relationships make use of
saturated soil conditions as a reference for the development
of unsaturated soil models. Overall volume change has histor-
ically been defined in terms of void ratio change,
de,
which is
then related to effective stress in a saturated soil. Critical state
models have used changes in specific volume,
d
(1
5
0
10
6
10
6
10
100,000
×
Total suction, kPa
Figure 5.15
Theoretical soil suctions corresponding to relative
humidities in extremely high total-suction range.
100
10
1
e
)
,
as the
deformation state variable. Figure 5.17 shows the reference
compression curve relationship for a saturated soil under
K
0
loading (plotted to the base-10 logarithm scale) and isotropic
loading conditions (plotted to a natural logarithm scale).
Loading along the virgin compression line, as well as the
unloading and reloading lines, is approximated as straight
lines on the semilogarithm plot. Isotropic loading conditions
act as a reference for elastoplastic models and provide a sep-
aration from the application of deviator stresses (or shear
stresses). The
K
0
loading conditions are also used because
the equipment is commonly available in soil mechanics labo-
ratories. The equation representing the reference deformation-
stress state line for a saturated soil under
K
0
loading conditions
can be written as follows:
+
0.1
0.01
0.001
10
6
10
6
100,000
10
×
Total suction, kPa
Figure 5.16
Theoretical soil suctions versus relative humidity in
extremely high total-suction range plotted on a log-log scale.
The maximum soil suction value (i.e., total suction) is con-
trolled by free-energy consideration of the water vapor in air
immediately adjacent to the air-water interface. This means
that high total-suction values are related to the free energy
associated with water in the soil. A total-suction value of
10
6
kPa is an easy value to remember, and this value is
often assumed as the soil suction value representing zero
relative humidity.
The maximum total suction is related to minimum relative
humidity conditions. When a soil is dried in an oven, it
is assumed that all water is driven from the soil. A water
content of zero is assumed equal to a relative humidity close
to zero percent. This is not necessarily true because the
environment inside the drying oven may not be zero relative
humidity. However, the differences are generally considered
insignificant.
p
−
u
w
e
=
e
o
−
C
c
log
(5.11)
p
o
−
u
w
where:
e
o
=
initial or reference void ratio at
p
o
−
u
w
,
u
w
=
pore-water pressure,
p
o
=
initial or reference total stress (i.e., vertical stress for
K
0
loading),
p
=
total stress state under consideration, and
C
c
=
compressive index (i.e., slope of the virgin compres-
sion branch).
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