times during a test. As discussed later, the forces
associated with buckling represent the maximum
force that a model ice sheet could impart on the
model riprap. Buckling events represent large-
scale failure of the model ice sheet, and this did
not cause large-scale failure of riprap in our tests.
However, the model ice sheet caused small-scale
damage by removing individual stones one at a
time.
Measured horizontal and vertical forces
The forces on the model during open water test
runs (without any ice) were much smaller than
Figure 22. Typical plot of the vertical com-
those measured during tests with model ice. Fig-
ponent of the force acting on the riprap.
ure 21 shows typical time-history plots of the hor-
izontal force, which were obtained by summing
the load measured by two load cells (Fig. 8). This
cal force, which generally increased with time be-
cause the force was largely a measure of the weight
of accumulated ice on the model. During a few
tests, one of the forward two load cells for mea-
surement of the vertical force stopped functioning.
Because of symmetry in the longitudinal direction,
the measured force from the other forward load
cell was multiplied by two and added to the mea-
sured value from the third load cell to get the total
vertical load. After the defective load cell was re-
placed with a new load cell, the outputs of three
load cells were added to obtain the total vertical
load.
Figure 21. Typical plot of the horizontal com-
Plot of maximum horizontal force
ponent of the force acting on the riprap.
In Appendix C, we have given the plots of hor-
izontal and vertical forces from all ice tests. In Ta-
plot shows a slight increase in the force, caused
ble 1, we have also tabulated the maximum hori-
by the edge of the ice sheet first coming in contact
zontal force in each test. These maximum force
with the model, at about 7 seconds after the start.
values were in the range of 1.8 and 17.8 kN (405
For the next 10 seconds, the ice rode up and over
4000 lb).
the model bank, as indicated by the relatively con-
During the model tests, we observed crushing,
stant horizontal force. This force was the result of
bending and buckling failures of the ice sheet dur-
the friction force between the ice sheet and the
ing its interaction with a model riprap bank. Crush-
riprap. For the next 30 seconds, the horizontal force
ing of ice occurred in localized areas where the ice
gradually increased until it reached a peak value
came in contact with the stones during ice ride-up.
at about the 50-second mark. Figure 21 has sever-
An intact sheet predominantly broke up into piec-
al cycles of increasing force followed by sudden
es by bending failure that took place in longitudi-
reductions in force during the remaining duration
nal as well as transverse directions. These ice piec-
of the test. Each reduction in force was due to buck-
es either rode over or piled on top of the riprap
ling failure of the ice sheet during the interaction.
surface. Ride-up occurred for low values of the
In this study, buckling failure limits the force that
bank slope, whereas a pileup formed for high val-
could be imparted to the model riprap by the mod-
ues of the bank slope. At times, the ice sheet plowed
el ice sheet.
through the piled up material, gouged the riprap
To obtain the total vertical load acting on the
at the bottom, and brought out stones with it. This
model riprap, we summed the output of three load
took place as long as the ice sheet was capable of
cells placed between the two frames (Fig. 8). Fig-
exerting sufficient force, which was limited by the
ure 22 shows a typical time-history plot of verti-
buckling failure of ice. Therefore, the maximum
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