Ci = 96 Pa. Assuming a value of = 1.3, Calkins
The 95% confidence interval is (0.029, 0.105), which
can be interpreted to mean that one can be 95%
(1983) calculated Ci = 168 Pa and 254 Pa for
confident that the Manning's n values for breakup
breakup jams on the Ottauquechee River and First
jams will lie between 0.029 and 0.105, based on
Branch White River (Vermont), respectively. He
the data shown in Figure 8a.
concluded that cohesion in breakup jams is insig-
Using these data, they simulated equilibrium
nificant compared to water slope, river width, and
ice thickness using eq 19 for a rectangular chan-
bankfull depth. Ashton (1986) reported that labo-
nel width of 100 m with nb of 0.030, discharge 100
ratory results suggest that Ci = 100 Pa to 500 Pa.
jam section porosity of 50%. The results showed
Coefficient of internal strength or
friction () and angle of internal friction (φ)
that ice thickness is relatively insensitive to
changes in roughness (i.e., large differences in
The coefficient of internal strength of the ice
cover, or , is sometimes called the friction coeffi-
roughness resulted in relatively small differences
in ice thickness). Stage was found to be more than
cient. This coefficient is a lumped variable repre-
twice as sensitive to roughness than ice thickness
senting the effects of a number of unknown or dif-
for the channel geometry tested. However, less un-
ficult-to-determine factors, including lateral stress
certainty was associated with stage or thickness
within the ice cover, ice on bank friction, angle of
than with roughness. The opposite was reported
internal resistance, porosity, and possibly cohe-
sion. Michel (1984) suggests that = 1.3 and φ =
by Healy et al. (1997), who evaluated the non-equi-
librium breakup jam that occurred in 1986 on
30 should be used when modeling breakup jams,
the Thames River (New Brunswick) using the Ca-
but a variety of values have been determined
nadian model ICEJAM (Flato and Gerard 1986).
(Table 2). Based on observations of a number of
jams, Beltaos (1981) hypothesized is important
They found that thickness was more sensitive to
in modeling thicker jams, but less important for
changes in roughness than stage in this situation:
a change in composite roughness from 0.040 to
thinner jams. In an evaluation of 11 case studies
0.080 caused 65% change in thickness and 25%
of breakup jams, Beltaos (1982) reports a range of
0.8 < < 1.3, with an average of 1.2. Two other
change in stage.
jams, for which = 0.6 and = 3.5, were presented
but not included; the lower value was based on
Cohesion (Ci)
highly uncertain post-jam observations and the
Fish and Zaretsky (1997) state that "Ice cohe-
upper on a thin jam for which ice on bank friction
sion is the principal strength parameter of ice."
may have been highly influential. Beltaos (1983,
This is immediately obvious to the observer of
1978) calculated = 1.6 for a 1981 breakup jam on
freezeup jam formation and progression, in which
the Thames River, New Brunswick, and 0.9 to 2.2
the apparent cohesive strength of the frazil floes
for breakup jams on the Smoky and Wapiti Riv-
plays a large part in ice cover accumulation. In
ers, Alberta. He used a value of = 1.2 in model-
addition, because freezeup jams most often occur
at very low air temperatures, freezing at the wa-
ing the 1992 and 1996 Credit River (Ontario)
ter surface level within the accumulation can lead
breakup jams (Beltaos 1999).
to rapid and large increases in strength. Tuthill et
al. (1998) suggest that cohesion can range up to
about 960 Pa to 1200 Pa in freezeup jams.
Table 2. Values of the coefficient of internal
Yet cohesion is often neglected, particularly for
strength () calculated by various researchers.
breakup jams. This is partly because no actual mea-
surements have been made. In both ICETHK and
Range of
Mean value
Reference
HEC-RAS, Ci is assumed to be 0 for breakup ice
jams formed from unconsolidated rubble. How-
0.92.2
Beltaos (1978)
ever, some researchers have considered cohesion
1.0
Andres (1980)
in breakup jams. Beltaos (1978) used a value of 96
0.81.3
1.2
Beltaos (1982)
Pa for cohesion when modeling the 1976 breakup
1.6
Beltaos (1983)
1.6, 2.0
Rivard et al. (1984)
jams on the Smoky and Wapiti Rivers (Alberta).
1.06
Prowse (1986)
Following his method, Andres and Doyle (1984)
0.82.7
1.6
Andres and Doyle (1984)
also accounted for cohesion in their analysis of
1.2
Beltaos et al. (1996)
breakup jams on the Athabasca River (Alberta) in
1.17
Tuthill and White (1997)
1977, 1978, and 1979, assuming the same value of
1.5
Korbaylo and Shumilak (1999)
13
Previous Page
