Environmental Engineering Reference
In-Depth Information
10
−
3
=10
−
4
m/s
k
s
k
s
k
s
k
w
=
n
(
u
a
-
u
w
)
w
g
⎡
⎣
⎤
⎦
10
−
4
1
+
a
ρ
a
= 0.001,
n
=2
a
= 0.001,
n
=3
a
=0.1,
n
=2
a
=0.1,
n
=3
10
−
5
10
−
6
10
−
7
1
10
100
1000
10,000
Matric suction head [(
u
a
-
u
w
) /
ρ
w
g
], m
10
100
1000
10,000
100,000
Matric suction (
u
a
-
u
w
), kPa
Figure 7.11
Gardner's (1958a) equation for water coefficient of permeability as function of
matric suction.
in the permeability function. There are also an infinite
number of scanning curves passing from the wetting to the
drying curve and vice versa. Coefficient-of-permeability
models have been proposed for unsaturated soils that
include scanning paths between the wetting and drying
curves (Watson and Sardana, 1987); however, geotechnical
engineers generally decide whether it is a drying or wetting
process that is being modeled and then select the appropriate
permeability function.
The permeability function for an unsaturated soil is not
routinely measured in the laboratory. Rather, the saturated
coefficient of permeability and the SWCC are measured (or
estimated) and combined through use of an estimation pro-
cedure that yields a permeability function. The drying (or
desorption) branch of the SWCC is most often measured
in the laboratory, and consequently, the permeability func-
tion is first computed for the drying curve. The permeability
function for the wetting curve is then estimated based on
measured or estimated hysteresis loops associated with the
SWCCs (Pham et al., 2003b).
Anisotropic soil conditions add another variation to the
permeability function, as shown in Fig. 7.14. The primary
change in the permeability function is related to the differ-
ence between the saturated major and minor coefficients of
permeability (Freeze and Cherry, 1979). The air-entry value
observed on the SWCC corresponds to the point where
both the major and minor coefficients of permeability
start to decrease. Consequently, the mathematical form for
the permeability function is similar for both the drying
and wetting branches. The water storage function is also
obtained from the SWCC and will also have hysteretic
behavior.
7.3.8 Water Vapor Flow
The movement of water in the form of water vapor is partic-
ularly important when considering the loss of water from a
soil through evaporation. Diffusion of water vapor is driven
by a gradient in water vapor pressure. Vapor flow can also
be driven as air flow in the form of vapor advection. Vapor
diffusion follows Fick's law and is further discussed in the
chapter on air flow. Vapor advection is governed by the flow
of air and is a function of vapor content in the air. Water
vapor behaves as a gas and in fact can be considered as one
component of air.
Understanding the mechanisms related to water vapor
flow is important for the development of a soil-atmospheric
model as well as other applications. As a soil desaturates
there is a point at which water vapor flow becomes more
significant than liquid water flow. The challenge is to know
when the predominant component of moisture flow changes
from liquid to vapor flow and how each component of flow
can be quantified. The water mass flux by liquid flow is
traditionally described using Darcy's law. The mass flux by
water vapor and advection within bulk air can be described
using a modified form of Fick's law (Philip and de Vries,
1957; Dakshanamurthy and Fredlund, 1981) as follows:
D
v
∗
∂u
air
D
v
∂C
v
ρ
v
ρ
a
D
a
∂C
a
ρ
v
ρ
a
D
a
∗
∂
u
a
∂y
(7.21)
¯
v
∂y
−
q
y
=−
∂y
−
∂y
=−
Search WWH ::
Custom Search