ing with thin ice sheets, we did not temper the ice,
a reasonable speed of ice shoving during a typical
because the maximum flexural strength of thin ice
ice breakup.
sheets is usually less than 87.5 kPa (12.5 psi).
Data acquisition
We measured or noted the following variables
Measurement of model ice properties
The ice sheet was characterized by measuring
during each test: ice thickness, flexural strength
the characteristic length and the flexural strength.
of ice, carriage speed, horizontal force, vertical
These properties were measured in situ using stan-
force, topography of riprap before and after each
dard testing procedures, as described below.
test, and an assessment of damage. In some tests,
The characteristic length was measured by plac-
we measured the topography of the ice pile and
ing a known dead weight P on a floating ice sheet
its maximum height. In Table 1, we have given the
and measuring the resulting elastic deflection δ (So-
values of parameters or variables that were either
dhi et al. 1982). The characteristic length L was then
set or measured during each test. We measured
calculated as
and recorded the horizontal and the vertical forc-
es along with the carriage speed using a data-ac-
L = [P/(8ρwgδ)]1/2
quisition system, which we programmed to scan
at 150 samples/second per channel. We used anti-
where ρwg is the specific weight of water.
aliasing, 45-Hz low-pass filters to remove high-
We measured the flexural strength by cutting
frequency noise at the analog input stage. We pro-
cantilever beams and breaking them in the upward
grammed the data acquisition system to acquire
or downward direction. The dimensions of the
the data when the carriage was in motion, i.e., start
beam were proportional to the ice thickness. The
and stop triggers were set on the carriage move-
length of beams was about five to six times the ice
ment. We also saved pre- and post-trigger data for
thickness, and the width was about two times the
a period of 10 seconds.
ice thickness. We measured the maximum force F
To profile the rock surface, we placed a frame
containing a 102- 102-mm (4-in. 4-in.) grid made
(applied at their tips) required to break the beams,
and also the dimensions of broken beams. The flex-
of strings (Fig. 12) on top of the fixed aluminum
ural strength σf was then calculated as
sides of the model bank, which provided a fixed
reference for each set of measurements. With a
σf = 6Fλ/(wh2)
ruler, we measured the perpendicular distances
from the rock surface to the strings at each grid
where λ = the beam length
point (Fig. 13). The width of the grid frame was
w = the width
the same as that of the box (1.32 m or 52 in.) and
h = the ice thickness.
its length was 1.52 m (60 in.). With this grid, we
measured the riprap surface profiles at 168 grid
points, which enabled us to get a reasonably good
Carriage speed
On rivers, water velocities during spring break-
profile. We profiled the rocks before and after each
up can exceed 5 m/s (16.40 ft/s) in extreme events
(Wuebben 1995). The ice action would most likely
be a combination of ice shoving and shearing along
a river bank at high velocity (≈ 1 m/s or 3.28 ft/s).
In a reservoir situation where there could be pure-
ly normal ice shoving action on a bank, the ice
would be driven by wind or thermal expansion at
speeds of less than 1 m/s (3.28 ft/s).
We used the main carriage to push the model
through an ice sheet at a constant speed of 40 cm/
s (1.31 ft/s) for all tests but the first two. We con-
ducted the first two tests at speeds of 80 cm/s (2.62
ft/s) and 20 cm/s (0.66 ft/s) for shakedown pur-
poses. We found little effect of speed on the meas-
ured forces if the ice failure took place in bending.
A speed of 40 cm/s (1.34 ft/s) in model tests scales
to full-scale speed of 1.13 m/s (3.71 ft/s), which is
Figure 12. Placement of grid over the model riprap bank.
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