servative predictor of stage, however, because the
less than about 0.08. A cover formed of juxtaposed
maximum stage for a static jam typically occurs
pieces is typically not much thicker than the min-
in the equilibrium reach of the profile.
imum dimension of the individual pieces.
ICETHK is a useful engineering tool because
The second process is termed "shoving thick-
many flood studies and hydraulic design projects
ening." Downstream acting forces become great
require the calculation of ice-affected stages. Before
enough to cause the accumulation to collapse or
the development of ICETHK, the calculation of
"shove" and thicken, until strong enough to resist
ice-affected backwater profiles using HEC-2 was
failure and downstream motion.
painstaking, requiring many iterations. The basic
In cases of high water-current velocity, ice
theory underlying ICETHK is well established.
thickness may actually be reduced by erosion. For
The model has two strong points. First, ICETHK
this situation, the amount of thinning is calculat-
is used in conjunction with HEC-2, the most com-
ed. ICETHK asks the user for the thickness of the
monly used backwater model in the United States.
pre-breakup ice cover (ITHICK). If the calculated
River geometry data in the HEC-2 format are
thickness by juxtaposition or shoving is less than
widely available. Second, ICETHK is designed
ITHICK, the final thickness defaults to ITHICK.
to help the user understand ice jam processes, and
A similar convention prevents the ice cover from
is relatively easy to use.
thinning to a value less than the initial ice cover
thickness.
EQUILIBRIUM ICE JAM THEORY
Juxtaposition
AND ICETHK
ICETHK uses two methods to calculate ice
cover thickness by juxtaposition. The first method
Definition of an equilibrium ice jam
uses a stability criterion developed by Michel
Figure 1 depicts an equilibrium ice jam, show-
(1978):
ing a central equilibrium reach of uniform flow
and constant ice thickness. The transition zones
at the head and toe of the jam are characterized
h h
ρ
V
2 1 - i (1 - e) 1
F=
≤
by nonuniform flow and variable ice thickness.
(1)
ρ
y y
gH
ICETHK treats each reach between adjacent
cross sections as individual equilibrium reaches.
where F = Froude number of the river
Because the ice is considered stationary, its
V = average velocity upstream of leading
momentum is not considered. Equilibrium ice
edge at which underturning and sub-
jam theory assumes that the downstream forces
mergence occur
on the ice cover are resisted by the accumulation's
h = thickness of ice accumulation's lead-
internal strength and bank shear. The down-
ing edge
stream forces are the water drag on the ice accu-
H = upstream flow depth
mulation's underside and the downslope compo-
nent of the ice accumulation's weight. The ice
y = depth of flow under the ice cover lead-
accumulation's ability to transfer these down-
ing edge = HSi h
stream forces to the banks depends on its inter-
Si = Specific gravity of ice (assumed to be
nal strength and thickness, and the model's gov-
0.916)
erning equations determine the minimum ice
ρ, ρi = densities of water and ice, respectively
thickness at which this force balance can occur.
e = porosity of accumulation.
Ice thickness calculation
ICETHK calculates ice thickness by three pro-
Juxtaposition typically occurs in situations
cesses: juxtaposition, thickening by shoving, and
where ice accumulation thickness is small relative
thinning by erosion.
to under-ice depth. As an upper bound, ICETHK
Juxtaposition, as the name implies, describes a
first checks to determine whether a juxtaposition
cover formed of ice pieces pushed edge to edge,
solution is possible by assuming an ice accumu-
in conditions of relatively low slope and low
lation thickness that is one-third the under-ice
water-current velocity. Field observations have
depth, i.e.,
shown that an ice cover of juxtaposed pieces will
h 1
remain stable when the surface velocity is less
=
y 3.
(2)
than 2.3 ft/s and the channel Froude number is
2
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