18
16
Pile Up Event
Ride Up Event
14
12
1
10
2:
e
op
Sl
8
6
1:1
lope
S
4
2
0
2
4
6
8
10
12
Estimated Buckling Force (kN)
Figure 23. Plot of maximum force recorded during each test vs. bρwgL2,
where b is the width of ice sheet, ρwg is the specific weight of water, and L is
the characteristic length of floating ice sheet.
force that we could expect to measure during a
An ice pileup most often caused failure of the
test is the force required to buckle an ice sheet.
riprap when the advancing ice sheet was forced
The buckling force of a semi-infinite beam of float-
to go between the riprap and the piled up ice. In
ing ice is between bρwgL2 and 2bρwgL2, corre-
general, we defined the riprap to have failed if
sponding to the frictionless and hinged boundary
enough rock material was displaced to expose un-
conditions (Hetenyi 1946), respectively, where b is
derlying areas of the riprap-protected bank. For
the width of the beam, ρwg is the specific weight
example, the ice piled up significantly in test 4, as
of water, and L is the characteristic length of float-
shown in Figure 24. During that test, the ice
ing ice sheet. Figure 23 shows the plot of maxi-
gouged away enough riprap to expose large areas
mum measured force vs. bρwgL2 for all tests. Most
of the bank, as shown in Figure 25. In test 5, an ice
of the data fall between the lines having a slope of
pileup formed below the water line, as can be seen
1 and 2, indicating that the boundary condition
by the damage to riprap shown in Figure 26. Fig-
on the edge of the ice sheet was something be-
ures 27a and b show the contour plots of the rock
tween that of frictionless and hinged.
surface, which were generated from the rock pro-
Though buckling failure limits the horizontal
file data taken before and after test 5. Such con-
force in model tests, the forces in full-scale situa-
tour plots help to visualize the total displacement
tions will be limited by the amount of environ-
of the riprap during a test. The contour plots
mental forces (wind and water stresses or thermal
expansion) acting on an ice sheet, by the momen-
tum of moving ice floes, or by the forces required
to fail an ice sheet in bending, crushing, or buck-
ling. During initial stages of ice shoving, the bend-
ing failure of ice will limit the force that an ice sheet
can exert on the riprap, because this failure mode
requires the least force per unit width of the ice
sheet. If the ice sheet forms an ice pileup, the ice
sheet may be possibly confined to fail in crushing
or buckling. It is also possible for the zone of fail-
ure to progress offshore, creating a rubble field.
Observed failure of riprap
An ice pileup consisted of the ice sheet break-
Figure 24. Ice pileup after test 4.
ing into small pieces and piling one on top another.
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