Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 155

If the flexural wave in the plate accompanies the gravitational wave in the water, the

sequence is called

flexural-gravitational wave.

Example 5.3. Assume that there is a large number of people on lake ice, evenly spaced at
distances of d, and denote ice thickness by h and mass of one person by M. First, to prevent
ice from sinking, the buoyancy conditions requires that Þ hd 2 . Second, to M q w q i ð

r t h 2 . Take d

nMg . 0 : 41 þ 2 : 3 d

p
k

prevent ice from breaking, we must have 1 m and

*

d p k . For h = 0.1 m, the buoyancy criterion gives M

≤ ʻ *

9 kg, and, since 10 m and

≤

consequently n 20 kg. The buoyancy condition is

more limiting. For h = 1 m, the buoyancy criterion gives M

* 100, the strength criterion gives M

90 kg while the strength
criterion gives M ≤ 660 kg. The buoyancy condition is more limiting factor.

≤

5.4 Ice Forces

5.4.1 Ice Load Problems

Forces due to ice have been investigated for a long time in ice engineering because of
practical applications. The maximum loading takes place when the ice fails at a structure,
then depending on the failure mode. In lake ice environment the ice loading cases are
concerned with harbour structures and piers, ships, coastal constructions, and the natural
coastline itself (Fig. 5.10 ). The failure of ice is not necessarily ever achieved due to short
fetches, and therefore the forces are generally lower than in marine environment. On the
other hand the strength of freshwater ice is higher than the strength of sea ice, and in non-
fetch-limited situations loads can be higher in lakes.
Two examples of ice loading situations are given

rst.

was
experienced on the shore of Lake Vesijärvi, Lahti, Finland (Fig. 5.10 ). The lake ice
thickness was about 10 cm. Residents in new, high buildings located about 40 cm from
the shoreline were alarmed by vibrations of the buildings. Recording of these vibrations
were started in three buildings on January 8th. The frequencies of the

Example 5.4 ' Ice quakes ' . In the beginning of January 2009, a rare ' ice quake '

oors were then

2 10 Hz, around the lowest expected natural frequency of the houses in the so-called

pendel vibration mode (Makkonen et al. 2010). All the houses, which felt the vibrations,
have been supported by using vertical concrete piles on stiff moraine. The building site
itself has been

-

filling resting on original quite soft 15 m
thick clay/silt layer above the moraine. The in-lake building site is probably the main
reason why the vibrations due to cracking of the lake ice can be transported into the
buildings via the soil. When the melting of ice began in spring, vibrations started again
after a 2 months quiet period. The highest measured velocities were 1.2 mm s − 1 ,
exceeding the comfort limit of people, but at that level no structural damages are expected
and indeed they were not observed.

filled in the lake with a 6 m thick