a)
b)
c)
Upstream
Transition
Thickness Reach
Downstream
Transition
Intact
Sheet Ice
d)
Figure 12. Idealization of ice jam evolution with time.
The first analysis was done by the Canadian R.J. Kennedy (1958), who was inter-
ested in the forces exerted on a boom by a pulpwood jam. To determine those forces,
he developed the following relation
dF
+ τiB - 2k0λF = 0
B
(1)
dx
where
B =
width of the holding area
τi =
shear stress on the underside due to water flow
k0 =
coefficient of lateral thrust
λ =
coefficient of friction of the pulpwood against the shore boundary
F =
force per unit width acting in the downstream direction (x-direction).
If there exists a force f1 exerted by the water impinging on the upstream end of the
accumulation, then eq 1 can be integrated to obtain the force at any location x (mea-
sured from the upstream end of the accumulation), i.e.
Bτi
Bτi
-2λk0x
F=
+ f1 -
exp B .
(2)
2λk0
2λk0
12
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