Ground Surface Moisture Flux Boundary Conditions - Unsaturated Soil Mechanics in Engineering Practice - page 320

6.3.21.2 Root Distribution
The zone over which plant transpiration is assumed to
extract water is dependent upon the depth of the roots
and the distribution of the roots. Two functions for root
zone distribution appear to be sufficient for geotechnical
engineering applications. The root shape zones are classified
as a triangular root zone or a rectangular root zone. Both
functions extract the same volume of water from the soil,
but the water is extracted differently with respect to depth.
The triangular root distribution shape function describes a
decreasing root uptake of water with depth, as illustrated in
Fig. 6.52a. The rectangular root distribution shape function
describes a constant root uptake of water with depth, as
illustrated in Fig. 6.52b. The potential root uptake at a point
under consideration can be defined as follows:

PT = potential transpiration rate per unit time, m/day,

R T = total thickness of the root zone in length units

m, and

R n = depth to the given point in length units, m.

The PRU variable must be integrated over the root zone
when a transpiration boundary is specified. The PRU is
applied as a potential transpiration sink.

6.3.21.3 Plant Limiting Factor, PLF
A lack of available water reduces the ability of a plant to
transpire water. The PLF is a function of the suction in the
soil in the root zone. When soil suction is low, the PLF is
1.0, and when the wilting point of the plant is reached, the
PLF is reduced to zero. Figure 6.53 shows a typical plot of
PLF versus soil suction.
The root transpiration sink S root is calculated by modifying
the potential transpiration sink by a reducing term based on
the suction in the soil, as shown in the following equation:

1

R n
R T

RSF PT
R T

PRU = − (6.79)

where:

S root = (PRU)(PLF) (6.80)

potential root uptake rate per unit time, m 3 /day, PRU =

RSF = root distribution shape factor (i.e., triangular or

rectangular),

The actual transpiration sink is maintained at the poten-
tial transpiration values when soil suction is low. Once a
specified limiting value is exceeded, the actual transpira-
tion flux decreases exponentially (i.e., straight line on a
semilog plot) until the wilting point is reached. Transpiration
will be zero at soil suctions above the wilting point. Tratch
et al. (1995) suggested defaults for the limiting value and
the wilting point to be 100 and 1500 kPa, respectively. The
transpiration sink term is part of the moisture flow partial
differential equation (i.e., Eq. 6.53). A negative value indi-
cates that water is being pulled from the system.

Potential transpiration (PT)
(surface flux)

Triangular potential

root uptake

6.3.22 Net Evaporative Flux at Ground Surface
Each of the components that influence the moisture flux at
the ground surface has been described. Each of the moisture
flux components can be plotted for the year and then the
net infiltration curve can be computed (Fig. 6.54). The net
infiltration component becomes the ground surface moisture
flux boundary condition. It is possible to proceed with the
calculation of infiltration of water into the soil once the net
moisture flux at the ground surface boundary is known.
The above-mentioned calculations for net moisture flux
are not independent of modeling soil infiltration. The AE
is dependent upon knowing the total suction at ground
surface. Actual evaporation is computed as part of the
infiltration model. There is a “coupling effect” between the
infiltration model and the calculation of AE. Stated another
way, the calculations combine the climatic ground surface
moisture flux conditions with the solution of the nonlinear
partial differential equation of unsaturated soil seepage. The
combination of the unsaturated soil moisture flow model
and the climatic boundary conditions is called the soil-
atmospheric model.

(distributed flux)

Root depth

(a) Triangular potential root uptake region

Potential transpiration (PT)
(surface flux)

Rectangular potential

root uptake

(distributed flux)

Root depth

(b) Rectangular potential root uptake region

Figure 6.52 Common shapes for root uptake areas.