Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 51

mixture is increased for two reasons: (i) the density of salt
is greater than the density of water and (ii) the addition of
salt causes a decrease in overall volume. This phenomenon
is possible because of the dipolar nature of water and the
slight changes in molecular arrangement and bonding that
occur when salts are added to water.
McCutcheon et al. (1993) proposed an empirical equation
for the density of water when salts are added in varying
concentrations. The density of water when temperature and
salt concentration, s , are varied can be written as

The results show that (i) the relative effect of a tempera-
ture change from 40 to 10 ◦ Celsius is comparable to a salt
concentration change from zero to 10 g/kg and (ii) water
density changes are relatively small until the salt concentra-
tion exceeds 10 g/kg.

2.3.2.3 Thermal Properties of Water
Water can exist in three phases in a soil; namely, liquid
phase, solid phase and vapor phase. Each phase has its own
thermal properties of specific heat capacity and thermal con-
ductivity. Typical values of specific heat capacity for water
are 4.19 kJ/kg K for the liquid phase, 2.11 kJ/kg K for the
solid phase (i.e., ice), and 1.97 kJ/kg K for the vapor phase.
The specific heat of water, C w , is a function of temperature
and typical values are presented in Table 2.4. The thermal
conductivity of water, λ w , also depends on temperature and
typical values are presented in Table 2.4.
The change from the liquid phase to the solid phase occurs
at 0 ◦ C in the absence of soil particles. The phase change
from the liquid to the vapor phase occurs at 100 ◦ Cata
pressure state of 1 atm. The latent heat of melting is 334
kJ/kg when there is a phase change from a solid to a liquid.
The latent heat of evaporation is 2270 kJ/kg when there
is a phase change from liquid to the vapor phase. Water
also has a thermal expansion coefficient of 0.042 when the
temperature range is between 4 and 100 ◦ C.

Bs 1 . 5 Cs 2

ρ ws = ρ w + As + + (2.13)

where:

density of water containing salts, kg/m 3 ,

ρ ws =

=

s salt concentration, g/kg,

10 − 5 T 2 A = 0 . 824493 − 0 . 0040899 T + 7 . 6438 ×

10 − 7 T 3 10 − 9 T 4 − 8 . 2467 × + 5 . 3675 ×

10 − 4 T B =− 0 . 005724 + 1 . 0227 × − 1 . 6546 ×

10 − 6 T 2 ,

C = 0 . 00048314, and

temperature, ◦ C.

T =

Figure 2.32 shows a graph of water density versus temper-
ature for salt concentrations varying from zero to 100 g/kg.

1090

1080

1070

100 g/kg

1060

1050

75 g/kg

1040

1030

50 g/kg

1020

1010

25 g/kg

1000

10 g/kg

5 g/kg

990

980

0 10 20 30 40 50 60

Temperature ( ° C)

Figure 2.32 Density versus temperature for water with various concentrations of salt.