Environmetal Soil Properties and Behaviour

Environmetal Soil Properties and Behaviour


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soil.
For the conditions of no-volume change and little-to-no change in pore 
geometry (rigid porous block), the linear relationship between x and \u221at, 
square root of time, shown in Figure 3.23, confirms the use of a similarity 
solution technique for Equation (3.30). 
Using the Boltzmann transform \u3bb \u3bb \u3b8= =( ) x
t
, Equation (3.30) can be 
reduced to an ordinary differential equation:
 
\u3bb \u3b8
\u3bb \u3bb
\u3b8
\u3bb2
d
d
d
d
D
d
d
=
\uf8eb
\uf8ed\uf8ec
\uf8f6
\uf8f8\uf8f7 (3.31)
Subject to the usual boundary conditions:
 t = 0, 0 < x < \u221e (thus, \u3bb = \u221e), \u3b8 = \u3b8i
 t > 0. x = 0 (thus, \u3bb = 0), \u3b8 = \u3b8o,
the amount of water entering per unit area, (qt)o, at the plane of x = 0 can be 
obtained using the Boltzmann transform as follows:
 
( ) ( )q t d xdt o
i
sar
i
sat
= =\u222b \u222b12 \u3bb \u3b8 \u3b8 \u3b8
\u3b8
\u3b8
\u3b8
\u3b8
 (3.32)
3.5.1.2 Vapour Transfer
In partly saturated soils, the mechanism for moisture transfer will depend 
on whether the soil is dry, relatively dry, or relatively wet. For dry (anhy-
drous) soils, vapour transfer is greater than liquid water transfer, espe-
cially if large temperature gradients exist. Vapour movement can also 
occur under isothermal conditions. This happens when there is a moisture 
content gradient. Movement in the vapour phase is by convective (bulk) 
flow of the soil air, or by diffusion of water molecules, in the direction 
of decreasing vapour pressure. A vapour-pressure gradient can be devel-
oped by such factors as temperature, salt concentration, or differential suc-
tion within the soil. Of these factors, the temperature gradient is by far the 
122 Environmental Soil Properties and Behaviour
most important. Differences in salt concentration result in a reduction in 
the vapour pressure of the porewater in proportion to the salt concentra-
tion. This causes a vapour pressure gradient, which in turn will result in 
vapour transfer.
Diffusion of water vapour is generally modelled as a Fickian diffusion 
process, and under isothermal conditions, this is given as qv = \u2013 Dv \u2202c\u3b8v/\u2202x, 
where qv is the vapour flux, Dv is the vapour diffusion coefficient, x is the 
spatial coordinate, and c\u3b8v is the concentration of vapour in the gaseous 
phase. Considering the state of vapour to obey the equation of state of an 
ideal gas, the concentration of vapour will be given as a function of pressure 
and temperature. For nonisothermal condition, a temperature factor needs 
to be added to the Fickian diffusion equation (Nakano and Miyazaki, 1979).
Under isothermal conditions, in the absence of a gravitational term and con-
vective flow currents and assuming that linear superposition could be applied 
to water transfer, we can combine this Fickian process with the relationship 
given in Equation (3.30) to obtain the combined water transfer (water move-
ment and vapour transfer) relationship for partly saturated clays as follows:
 
\u2202
\u2202 =
\u2202
\u2202 +
\u2202
\u2202
\uf8eb
\uf8ed\uf8ec
\uf8f6
\uf8f8\uf8f7
\u3b8 \u3b8
\u3b8 \u3b8t x
D D
xv l
( ) (3.33)
where D\u3b8v = Dv \u2202c\u3b8v/\u2202\u3b8, and D\u3b8l is equal to D(\u3b8) in Equation (3.30) and the total 
water diffusivity coefficient D\u3b8 is defined by D\u3b8 = D\u3b8v+D\u3b8l. Since the water 
content at the surface will change with time, the initial and boundary condi-
tions are given as follows:
\u3b8 = \u3b8i = const. at x > 0, t = 0, and \u3b8 = f(t). at x = 0, t > 0
Figure  3.24 shows the total water diffusivity coefficient D\u3b8 calculated for 
a sample of Kunigel bentonite\u2013sand mixture (bentonite mixed with 30% 
sand), based on Equation (3.33). The calculated values are for changes of 
volumetric water content with time in unsteady infiltration experiments 
conducted at 25°C, reported by Chijimatsu et al. (2000). The total water dif-
fusivity coefficient (D\u3b8 = D\u3b8v+D\u3b8l ), which is larger at low water contents close 
to air-dried condition and at high water contents near the fully saturated 
condition, is due to (a) the larger D\u3b8v value, which reflects the predominant 
vapour flow in the unsaturated region, and (b) the larger D\u3b8l value, reflective 
of the predominant liquid water flow in the near-saturated region of the soil. 
The results shown in the figure indicate that vapour flow occurs up to a volu-
metric water content \u3b8 of about 0.25 (i.e., about 25%), which is attributable to 
the presence of macropores developed because of the sand component in the 
bentonite\u2013sand mixture. The influence of temperature on the production of 
vapour flow will be discussed in Chapter 4.
The general relationship for the isothermal vapour diffusivity D\u3b8v has 
been given as 
123Soil\u2013Water Systems
 D\u3b8v = \u3b1\u3c9Datm \u3b3g\u3c1v/\u3c1LRT \u2202\u3c8w/\u2202\u3b8, 
where \u3c8w is the soil\u2013water potential, \u3b1 denotes tortuosity, \u3c9 is the volumet-
ric air content, Datm is the molecular diffusion coefficient, \u3b3 is the mass flow 
factor, g is gravitational acceleration, \u3c1v represents the density of vapour, 
\u3c1L is the density of liquid, and R is the universal gas constant (Yong et al., 
2010). The dependence of the soil\u2013water potential \u3c8 on temperature T has 
been previously given by Philip and deVries (1957) as \u2202\u3c8w/\u2202T = \u3c8w/\u3c3 \u2202\u3c3/\u2202T. In 
general, the molecular diffusion coefficient at temperature T is given as fol-
lows: Datm = D0 p0/p (T/T0)n, where D0 is the molecular diffusion coefficient at 
a reference condition, p is the air pressure, p0 is the reference pressure, T0 is 
the reference temperature, and n is a constant that is 2.3 for vapour (Rollins 
et al., 1954).
3.6 Chemical Reactions in Porewater
The surface functional groups associated with the various soil fractions, 
discussed in Chapter 2, and the ions and other dissolved solutes such as 
0 0.1 0.2 0.3 0.4
Volumetric Water Content, \u3b8
10\u201311
10\u201310
10\u20139
10\u20138
10\u20137
W
at
er
 D
iff
us
ivi
ty
, D
\u3b8, 
m
2 /s
Measured values
Calculated function
\u3c1d = 1.6 Mg/m3
FIguRE 3.24
The total water diffusivity coefficient D\u3b8 calculated for a sample of Kunigel bentonite\u2013sand 
mixture (bentonite mixed with 30% sand) at a dry density of 1.6 Mg/m3. The calculated val-
ues use the results of changes of volumetric water content with time in unsteady infiltration 
experiments at 25oC reported by Chijimatsu et al. (2000).
124 Environmental Soil Properties and Behaviour
naturally occurring salts in the porewater of a soil will react chemically when 
brought together as a wet soil mass (soil\u2013water system). The chemistry of the 
porewater is linked to the chemistry of the reactive surfaces of the soil sol-
ids. Interactions between the solutes in porewater and soil particles involve 
many different sets of chemical reactions, including biologically mediated 
chemical reactions. The pH of the soil\u2013water system and the various other 
dissolved solutes in the pore water influence the various interaction mecha-
nisms such as acid-base reactions, speciation, complexation, precipitation, 
and fixation.
3.6.1 Acids, bases, and pH
The porewater in a wet soil, without dissolved solutes, is a solvent that can 
be either a protophillic or a protogenic solvent. This means to say that it can 
function as an acid or as a base. Through self-ionization, it can produce a 
conjugate base OH\u2212 and a conjugate acid H3O+.
 2H2O (solvent)\u21d4 H3O+ (acid) + OH\u2014 (base)
In the standard Arrhenius definition of an acid, this is defined as an aque-
ous substance which dissociates to produce H+ ions, and a base as an aque-
ous substance which dissociates to produce OH\u2212 ions. In other words, acids 
are substances that produce hydrogen ions, H+, in solution, and bases are 
substances that produce hydroxide ions, OH\u2212, in solution. The pH scale, 
which was developed by Sörenson in 1909 in his studies of the Arrhenius 
theory of electrolytic dissociation as a means to identify the degree of acidity, 
determines the pH of a solution to be the negative logarithm to the base ten 
of the molar hydrogen ion concentration. This concept of acids and bases, 
first