This program calculates the rate of heave for a given set of initial and boundary conditions. The strategy is the same as
presented by Black and Miller (1985). It is assumed that the heaving process can be approximated with a time step called
the lensing cycle and that any fluctuations during this lensing cycle average out to values that represent the true behavior
during the lensing cycle.
Scaling factors
λ: = 1.0 ⋅ 106
ζ: = 1.0 ⋅ 102
fw: = 1
Thermal conductivities
Khw: = 0.52
Khi: = 2.32
λ
Khg: = 3.42
ζ
fw
Soil water properties
Khw
Wsat: = 0.42
Khi
Wd: = 0.02
Khg
Kwsat: = 1.0 ⋅ 108
Wsat
Wd
Brooks and Corey functions
settings (heave, penetration): =
Kwsat
α
φb: = 11.196
β
α: = 0.36
φb
β: = 2.6
heave
penetration
Boundary conditions
gradθunfrozen
prec
heave: = 10
resol
penetration: = 100
MaxLayers
gradθunfrozen: = 10
Numeric settings
prec: = 0.1
resol: = 0.01
MaxLayers: = 100000
The function RIGIDICE takes the contents of settings and returns a 1-dimensional array containing (heave pressure,
temperature gradient in frozen soil, heat fluxes into the fringe and out of the upper boundary zone, the water flux into
the fringe and the lens spacing and thickness and iterations)
(ui gradθf qhin qhout qwin spacing thickness iters): = RIGIDICE (settings [heave, penetration])
gradθf = 70.255
ui = 76.06
spacing = 0.118
thickness = 4.251
qhin = 15.504
qhout = 199.533
iters = 2
Figure 3. MathCad program to run RIGIDICE.
6