Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 154

Fig. 5.9 The dependence of
coefficient C 1 on b/ ʻ

C

0.4

0.2

0

0.4

b/

where the coef cients A and B for an in nite plate are equal to 0.38 and 2.3, respectively,

while for a semi-in nite plate they are 0.16 and 2.3.

First-order approximation is obtained from the

first term of the series solution shown
by Eq. ( 5.27 ): the ice can bear mass M < ah 2 , where a = a(

σ t , ʻ ) is the model parameter,

5kgcm − 2 . The radius of in

a and, consequently, this is the

safe distance between loads if the ice thickness is close to the critical level.
Interest in the dynamical loads originates from practical problems, in particular the
problems on loads (cargo, vehicle) motion along an ice route. The possibility of dangerous
resonance phenomena has been expressed in the topic by Zubov (1942). The conclusion
that there is a certain speed, the excess of which can lead to the fracture of ice cover, was
formulated in Bregman and Proskuryakov (1943) on the basis of the data analysis of the
ice cover oscillations in Lake Ladoga.
When the speed of a motor vehicle is below the critical value, disturbances are
propagated along the ice cover at a speed of the vehicle and they disappear behind
practically with the same velocity. But when the speed becomes close to the critical level,
i.e. the speed of the shallow water wave

uence of a point load is 2 ʻ

*

g p in the water body, due to resonance in
bending of the ice the bearing capacity becomes in practice less than half of that for static
loads. When the speed is much more, the resonance disappears but then the high speed
must be kept the whole way across the lake.
In deep water, the de

c ¼

ections are always smaller than in shallow depths (the effect of
shallow water for surface waves in fluids). At subcritical speeds, maximal bending

moments occur under load. In the case of supercritical speeds, the moment peak is located
in front of the load. Motion of a load on an ice cover is accompanied by only bending
vibration, or just gravity vibration or both types of vibration, depending on the speed.