Environmental Engineering Reference
In-Depth Information
30
10,000
36%
28% Optimum
20%
20%
16.5% Optimum
8%
25
1,000
20
100
15
10
10
Clay
5
Silt
1
0
0
1
2
3
4
5
6
7
0
5
10
15
20
25
Negative temperature,
°
C
Negative temperature,
°
C
Figure 10.8
Relationship between soil suction and temperature
below 0
◦
C for coarse-grained soil (after Jame, 1972).
Figure 10.6
Unfrozen water content versus temperature below
0
◦
C for silt and clay with various initial water contents (after Yong,
1965).
coarse-grained soil, as shown in Fig. 10.8. The Clapeyron
equation has been used in the development of theories
for ice segregation and frost heave models (Harlan, 1973;
Taylor and Luthin, 1978; Nixon, 1991, 1992).
35
Clay containing montmorillonite
Clay
Loam
Sandy Loam
Quartz Sand
30
25
10.3.5 Soil-Freezing Characteristic Curve
Williams (1964) presented data that showed a relationship
between SWCCS measured at room temperature and a
soil-freezing curve for the same material (i.e., temperature
below freezing and unfrozen water content). The Clapeyron
equation provides the freezing temperature for the unfrozen
water content. Koopmans and Miller (1966) noted a simi-
larity between the soil drying and wetting curves and the
freezing and thawing curves, as shown in Fig. 10.9. It was
noted that the freezing/thawing curve exhibited hysteresis
just as the wetting/drying curve exhibits hysteresis.
The Clapeyron equation allows a relationship to be devel-
oped between soil suction and the temperature below freez-
ing when the SWCC is known for a particular soil. The
SFCC is therefore inherently linked to the SWCC.
The temperature range over which water becomes frozen
is defined by the SFCC. The temperature at which water
in the soil starts to freeze is designated by the variable
T
ef
(i.e., generally 0
◦
C), and the temperature at which freezing
is complete is designated as
T
ep
. The latent heat of freezing
is applied over the temperature range between
T
ef
and
T
ep
.
Figure 10.10 shows a typical SFCC for silica flour tested
by Jame (1972). The slope of the SFCC is defined by
the variable
m
i
2
. The slope of the SFCC is defined by the
change in unfrozen volumetric water content with respect
to a change in temperature below freezing.
20
15
10
5
0
0
2
4
6
8
10
Negative temperature,
°
C
Figure 10.7
Unfrozen water content versus temperature below
0
◦
C for several nonsaline soils (after Nersesova and Tsytovich,
1965).
similar in character to the relationship of temperature below
freezing and water content. Consequently, there is a relation-
ship between water content, soil suction, and temperature
which is related to the SWCC for the soil.
10.3.4 Clapeyron Equation
The Clapeyron equation relates a change in pressure between
two phases of a substance (e.g., liquid-solid) to the change in
temperature of the system. The Clapeyron equation has been
of limited value for the solution of practical engineering
problems but has been used in the estimation of the amount
of unfrozen water in a freezing soil as a function of the
temperature below freezing (i.e., 0
◦
C).
Various forms of the Clapeyron equation have been
presented in the research literature. Jame (1972) plotted
soil
10.3.6 Coefficient of Permeability for Freezing Zone
The soil-freezing curve can be used in conjunction with the
saturated coefficient of permeability for a soil to estimate
the water coefficient of permeability versus soil suction rela-
tionship for a freezing soil (Newman, 1995). Figure 10.11
suction
versus
temperature
below
freezing
for
a
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