tb
ρi
η
ts
ρi
L
ni
yi
H
ρ, nc
υ
nb
Figure 2. Definition sketch for ice block stability.
ki = 2.21 - 0.11Ti
(5)
Ice cover formed by undercover deposition
Undercover deposition of ice occurs when in-
where Ti is the temperature of the ice (C) and ki
coming frazil or solid ice floes are unstable at the
has units J/m s C. Andres reported that the criti-
upstream end of an ice cover (e.g., juxtaposition
cal dimensionless stability number separating jux-
criterion is exceeded). Once the floes underturn,
taposition and shoving on the Peace River in north-
they can be transported beneath the ice cover and
ern Alberta is about 0.0003, with shoving more
into the open water beyond, or they may deposit
often observed at lower values and juxtaposition
beneath the ice, depending on the river hydrau-
most often observed at higher values. He noted
lics and the ice properties (Fig. 3). Predictions of
that river slope and crushing strength of the ice
where and how much under-ice deposition will
(again, related to temperature) contributed to the
occur have been made using three approaches:
uncertainty in determining the critical dimension-
critical velocity; Froude-number-based block sta-
less stability number. Although not widely tested
bility criteria similar to those discussed above, but
at this time, this method holds promise for deter-
for submerged ice floes; and, more recently, ap-
mining juxtaposition potential for ice cover for-
plication of bed-load transport theory. Ice jam
mation and freezeup jams.
thickening by deposition of ice is not specified in
HEC-RAS assumes single-layer juxtaposition of
either HEC-RAS or ICETHK, although ICETHK
floes if the ice-jam force balance (see section on
does allow thinning of an ice cover by erosion
shoving and internal collapse below) shows that
when the critical velocity is exceeded.
the thickness of the parent ice cover making up
The critical deposition velocity approach as-
the floes exceeds that necessary to balance forces
sumes that frazil deposits (or hanging dams) ac-
in the downstream direction. The ICETHK option
cumulate from upstream to downstream, begin-
of the USACE step-backwater computer program
ning with the most upstream location where the
HEC-2 (USACE 1990) uses the criteria developed
average cross-sectional flow velocity is less than
by Ashton (1974) and Michel (1978) to determine
some critical deposition velocity. Frazil will de-
when juxtaposition may occur. However, it is rec-
posit at that location until the critical velocity has
ommended here that eq 2 be applied to variables
been reached. Any additional frazil will be trans-
derived from ICETHK and other numerical mod-
ported downstream to some point where the ve-
els for the determination of juxtaposition poten-
locity is less than the critical velocity, where the
tial because of its good agreement with the results
process begins again. According to Beltaos (1995),
of the fairly complex model presented by
this critical velocity method is used in the numeri-
McGilvary and Coutermarsh (1992). Application
cal model ICESIM to estimate the location and
of eq 2 will require some knowledge or estima-
thickness of frazil deposition.
tion of the following ice properties: tb, ρ, ρi , and
Observations reported by Michel and Drouin
H, of which two, ρ and ρi, are well known (1000
(1981) indicate that critical velocity can vary over
kg/m3 and 916 kg/m3, respectively).
the course of a winter. They reported that the value
4
Previous Page
