Chapter 5
Soil Moisture and Strength Models
5.0 Introduction
Calculating changes in the volumetric moisture content profile as a function of time is the
critical step in determining the state of the ground. This is in part due to the highly
nonlinear nature of the parameters associated with soil moisture.
5.1 Soil Moisture
5.1.1 Governing Equations
The flow of water (ν) through a porous media is governed by Darcy's Law, which states
that
∂h
v=K
(5.1)
∂z
where K (m/s) is the hydraulic conductivity, z (m) is the depth, positive downward from
the surface, and h (m) the total head equals the elevation head, or depth, (z) minus the
pressure head (ψ), i.e., h = z cos ϕ - Ψ = z cos ϕ - Pf / ρw g , Pf (Pa) is pressure, ρw (kg/m3)
is the density of water, ϕ is the surface slope, and g (m2/s) is gravity. If the soil is
unsaturated, ψ < 0 and h > zcosϕ. For saturated soils ψ ≥ 0, requiring that h ≤ zecosϕ.
Also governing the flow of moisture through a soil is the conservation of mass, which
states that the time rate of change of the moisture content in a given volume equals the
net gain/loss of fluid in the volume, i.e.,
∂θw
∂v ρ ∂θi
=- - i
+ sources - losses
(5.2)
∂z ρw ∂t
∂t
where θw (cm3/cm3) is the volumetric moisture content, θi (cm3/cm3) is the volumetric ice
content, ρi (kg/m3) is the density of ice, and t (sec) is time. Equation (5.2) assumes that
changes with respect to time in the soil porosity and water density are negligible
compared to changes in the soil moisture and total head. Further discussion on the change
in ice content is found in Chapter 6. The source and loss terms in this equation account
for occurrences such as runoff and plant root uptake. The latter is for future development.
Equation (5.2) is subject to the following flow boundary conditions at the surface and at
the bottom of the soil column:
qtop = - E + Cr + P + ( hpond + hi,melt + hs,melt ) / ∆t
@z=0
(5.3)
qbot = K sin(slope)
@ z = zbot
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