Theory of Water Flow through Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 327

CHAPTER 7

Theory of Water Flow through Unsaturated Soils

7.1 INTRODUCTION pore-water pressures (Fig. 7.1). The glass beads were

initially saturated and then subjected to a series of
applied negative water pressures (or matric suctions). The
coefficient of permeability of the glass beads was measured
starting at saturated conditions. The results showed that
the coefficient of permeability of the glass beads started
to decrease when the matric suction was 3 kPa. A further
increase in suction caused the coefficient of permeability to
drop by several orders of magnitude.
It was also noted that the permeability function was dif-
ferent when the beads were in a drying mode than when the
beads were in a wetting mode. In other words, the permeabil-
ity function was hysteretic in the sense that it was dependent
upon whether the soil was undergoing a drying mode or a
wetting mode. The water content of the glass beads was
also measured during the drying and wetting processes, as
shown in Fig. 7.2. The hysteresis in the water content versus
matric suction relationship was related to the hysteresis in
the water permeability function.
The results from the Mualem (1976b) experiment showed
that a decrease in the coefficient of permeability com-
menced at the air-entry value of the soil. The relationship
between the permeability function and the SWCC would
subsequently become the basis for a variety of estimation
procedures proposed for the estimation of the permeability
function. The SWCC along with the saturated coefficient
of permeability became the basis for estimating the water
permeability function.

The rate of flow of water through a porous medium is
regulated by the hydraulic conductivity or coefficient of per-
meability of the soil. The coefficient of permeability is the
primary soil property required when analyzing steady-state
and transient (or unsteady-state) flow of an incompressible
fluid through a porous medium. The water storage prop-
erties must also be defined when analyzing transient flow
problems.
The coefficient of permeability is generally assumed to be
a constant when analyzing flow through saturated soil. How-
ever, the coefficient of permeability for an unsaturated soil
can vary widely depending on the stress state (or degree of
saturation) of the soil. The coefficient of permeability of an
unsaturated soil takes on the form of a mathematical func-
tion. Any change in the stress state of a soil can affect the
coefficient of permeability, but it is changes in soil suction
beyond the air-entry value that have the greatest effect on
the coefficient of permeability.
The coefficient of permeability generally changes by sev-
eral orders of magnitude as a soil desaturates. Water can only
flow through that portion of a porous medium that consists
of water. As the amount of water in a soil decreases (i.e.,
a decrease in the degree of saturation), the coefficient of
permeability decreases because there is less cross-sectional
area through which water can flow. However, there is not a
one-to-one relationship between the amount of water in the
soil and the coefficient of permeability. The coefficient of
permeability decreases at a much faster rate than the degree
of saturation. A reduction in the amount of water in the soil
also increases the tortuosity of the flow path. As a conse-
quence, an arithmetic decrease in the volume of water in
the soil generally results in a logarithmic decrease in the
coefficient of permeability. A dry soil has a much lower
coefficient of permeability than a wet soil.
Mualem (1976b) performed a laboratory experiment that
assists in understanding the coefficient of permeability of
unsaturated materials. The experiment involved flowing
water through glass beads subjected to varying negative

7.2 THEORY OF FLOW OF WATER

Several concepts have been used to explain the flow of water
through an unsaturated soil. For example, it has been sug-
gested that a water content gradient, a matric suction gradient,
or a hydraulic head gradient could form the driving poten-
tial for water flow through a porous media. Geotechnical
engineers have historically described water flow through a
saturated soil in terms of hydraulic head gradient. It is impor-
tant to also use hydraulic head gradient for water flow through