Ground Surface Moisture Flux Boundary Conditions - Unsaturated Soil Mechanics in Engineering Practice - page 291

Runoff must be computed in an interactive manner with
actual evaporation.
Runoff water is removed from the ground surface if a
drainage system exists. For runoff to occur, net moisture flux
NF should not produce pore-water pressures at ground sur-
face. The following set of equations can be used to represent
runoff conditions (Gitirana et al., 2005):

5.0

Precipitation
Infiltration
Runoff

4.0

3.0

2.0

1.0

⎧
⎨

0.0

P cos α 2 − AE if P cos α 2 − AE > 0 and u ws < 0

EF 0 u ws NF = − if P cos α 2 − AE > 0 and u ws 0 − 1.0

⎩

0.0 0.2 0.4 0.6 0.8 1.0

P cos α 2 − AE if P cos α 2 − AE ≤ 0

Time, days

(6.18)

Figure 6.21 Illustration of the ability to simulate infiltration and
runoff conditions.

where:

u ws = pore-water pressure at the ground surface and

atmosphere to transport water vapor away from the ground
surface. PE is lower when the sky is cloudy due to a reduc-
tion in net radiation reaching the soil surface. PE is higher
in the summer and at locations nearer to the equator. PE is
also higher on windy days because the evaporated moisture
is quickly removed from the soil surface, allowing further
evaporation to take place.
The PE can either be measured using an evaporation pan
or calculated based on climatic factors. Weather stations
commonly record precipitation events, net radiation, temper-
ature, wind velocity, relative humidity, and possibly some
other variables. The above-mentioned weather information
can be used to calculate PE.
The PE also depends on a number of surface factors (e.g.,
free water surface, pan of water, soil type, and vegetation).
Average annual potential evaporation can be compared to the
average annual precipitation P, and the ratio of precipitation
to potential evaporation, P/ PE, is called the aridity index.
Evaporation from the ground surface can be quantified
through consideration of the physical processes involved.
Numerous studies have been conducted since the 1920s in
an attempt to predict potential evaporation from the ground
surface. It is, however, the AE and transpiration that are
of primary interest in geotechnical engineering. The factors
controlling PE need to be understood before attempting to
calculate AE. PE is the amount of water removed by the
atmosphere through evaporation if water is freely available
at the ground surface.
There are three terms commonly used when discussing
upward moisture movement from a soil surface or vegetated
surface: (i) PE , (ii) AE, and (iii) PT. The terms AE and PT
are required for quantification of the water balance at the
ground surface. Figure 6.22 illustrates the components of
evaporation from the ground surface. The AE is less than
the PE mainly because of the affinity that soil has for water
(i.e., soil suction in the soil at ground surface).
In general, about 80% of the energy required for evapora-
tion comes from the sun in the form of “net radiation,” while
wind (in the form of a “mixing term”) and the vapor deficit
of the air form a second important component contributing

EF = a large number relative to the saturated coeffi-

cient of permeability (e.g., 1000 times the satu-
rated coefficient of permeability). The EF variable
acts as a “review” boundary condition that trig-
gers the change between a moisture flux boundary
condition and a zero pore-water pressure boundary
condition.

Runoff R may take place when the value of P cos α 2 −
AE is larger than the saturated hydraulic conductivity. The
amount of runoff corresponds to the difference between
the water available (P cos α 2 − AE ) and the amount of

infiltration.
The area flux boundary condition [i.e., NF −

u ws ) ] becomes mathematically equivalent to a hydraulic
head boundary condition at the ground surface (i.e., u ws =

= EF ( 0

0)
if the multiplier EF tends to infinity (Gitirana et al., 2005).
This approach tends to avoid numerical oscillation pro-
blems associated with switching boundary conditions that
produce an instantaneous change in the value at a node. An
instantaneous change in boundary conditions does not rep-
resent real-world conditions. Instantaneous changes in node
values tend to cause extreme mesh refinements (Gitirana
et al., 2005;). Equation 6.18 imposes a realistic and stable
boundary condition.
The above-mentioned approach to the simulation of a
rainfall event allows both the infiltration and the runoff com-
ponents to be accurately simulated. Figure 6.21 illustrates an
accurate simulation of infiltration and runoff at the ground
surface boundary (Gitirana et al., 2006).

6.3.8 Potential Evaporative Flux
The word “evaporation” generally refers to moisture move-
ment from a water surface or a soil surface, while the word
“transpiration” refers to upward moisture movement through
vegetation on the ground surface. The PE is the amount of
water that can evaporate if ample water is available at the
ground surface. The PE takes into consideration the thermal
energy available for evaporation and the ability of the lower