Ground Surface Moisture Flux Boundary Conditions - Unsaturated Soil Mechanics in Engineering Practice - page 283

The primary variable that must be computed during the
solution of the PDE is the hydraulic head. In order to solve
the saturated-unsaturated water flow equation (Eq. 6.5), it
is necessary to have information on two soil properties,
namely, the coefficient of permeability k w (or hydraulic con-
ductivity) of the soil and the water storage coefficient m 2
for the soil. Both the coefficient of permeability and water
storage coefficient soil properties are nonlinear functions of
soil suction (Fredlund et al., 1994b).
The pore-water pressure term of soil suction is one compo-
nent of hydraulic head and as a result the partial differential
equation being solved is nonlinear. The nonlinearity requires
that the soil properties first be estimated (i.e., hydraulic con-
ductivity and water storage are usually set to saturated soil
parameters), while the hydraulic heads are computed. Then
the soil properties must be adjusted in consideration of the
newly computed hydraulic heads. A new set of hydraulic
heads are then computed. This process is repeated until
the nonlinear partial differential equation for seepage has
converged (i.e., the hydraulic heads used in estimating the
soil properties match the computed hydraulic heads within
a specified level of accuracy).
Convergence means that reasonably accurate soil prop-
erties (i.e., coefficients of permeability and water storage)
were used when computing the hydraulic heads. The iter-
ative process may need to be repeated many times when
the soil properties are highly nonlinear. It is also possible
that the nonlinear partial differential equation may not con-
verge. It is also possible for the partial differential equation
to appear to have converged but the convergence may be to
the wrong values of hydraulic head. The solving of highly
nonlinear partial differential equations has become an area
of extensive research in mathematics and computing science
and much can be learned from research in these disciplines.
The permeability and water storage functions are actually
more complex than shown in Fig. 6.10 since both func-
tions exhibit hysteresis. In other words, one set of relation-
ships correspond to conditions when the soil is drying and
another set of conditions apply when the soil is wetting, as
shown in Fig. 6.11 (Pham et al., 2003b). While hysteresis
is known to exist in all soils, its effect is often not taken
into account in the design of cover systems. This is just
one of many approximations that are made in the design of
covers systems.
The material(s) used for a cover system may change
considerably with time because of environmental influences.
Cracking resulting from settlement and volume change is
quite certain to occur. Furthermore, the growth of vegeta-
tion creates a network of root holes, fissures, and cracks.
Freezing and thawing cycles tend to produce a nugget-
type structure particularly in fine-grained soils. The end
result is a change in the near-ground-surface soil properties
with time.
There may also be microbial contamination and other
bio-intrusions that affect the soil structure. Changes in the

Clay silt

Sand

Log suction, kPa

10 6

(a) Soil-water characteristic curves

k a Sand

k b

Clay silt

Log suction, kPa

(b) Permeability functions

Figure 6.10 Typical SWCCs and permeability functions for two
soil types.

soil structure tend to significantly change the SWCC for
the materials involved. Figure 6.12 illustrates the type of
changes that might occur in a measured SWCC on a soil that
contains clay-size particles. It is possible that the SWCC will
take on a bimodal character and the saturated hydraulic con-
ductivity may increase by one or more orders of magnitude
as a result of freeze-thaw cycles or drying-wetting cycles.
Consequently, numerical modeling simulations based on the
properties of originally intact materials can be considerably
different from the properties of soils that develop near the
ground surface over time.
There are challenges associated with solving the nonlin-
ear partial differential equations defining the flow of water
through the unsaturated soil. There are also challenges asso-
ciated with determining the net moisture flux that should
be applied at the ground surface. Much of this chapter is
devoted to describing how the ground surface moisture flux
can be quantified for engineering purposes.

6.3.3 Water Balance at Ground Surface
Methodologies for the computation of net moisture flux con-
ditions at the ground surface were not part of historical soil
mechanics. The calculation of ground surface moisture flux
based on climatic data has become an important part of
unsaturated soil mechanics. The calculation of net moisture
flux involves a number of assumptions and approximations.
Some inherent difficulties are mentioned in the following
sections along with suggested engineering protocols for their
solution. Other factors such as freezing and thawing are
often not adequately taken into account and are not discussed
in detail in this chapter.
The ground surface forms a flux boundary which inter-
acts with atmospheric weather. Water is either entering the