Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 157

distribution, k 1 takes into account incomplete contact between the ice edge and structure
while k 2 is responsible for the structure cross- section form,

k 1 1 = 2 ; k 2 1 . In case of non-

vertical structures, inclination of the loaded surface has also in uence. The indentation

factor depends on the aspect ratio D/h , and I ≈ 1 for narrow structures and I ≈ 2.5 for wide

structures.
On the basis of the Korzhavin (1962) model, further simpli

cations can be derived.

The force on a pier-type structure can be estimated by

F ¼ K r c Dh ð 5 : 32 Þ

where K is a scaling coef cient

K depends on the mechanical properties of ice and the geometry of the pier structure
(Ashton 1986). For a narrow structure the ratio

cient, and σ c is the compressive strength. The coef

ʴ

= D/h is an important parameter, K = 2.5

for 1. For wide structures and wedge-shaped piers, K = 1 can be

taken. For inclined structures K < 1 depending on the slope angle of the structure and ice-
structure friction.

ʴ = 1 and K 1 for ʴ ≫

→

Example 5.6. For a 1-m pier, the maximum force is 10 MN for thin ice (10 cm) and for
thick ice (1 m) it would be 25 MN.
When ice has frozen to structures, changes in water level elevation cause vertical forces.
The largest forces result when the change in the elevation is fast, since the ice then behaves
in elastic manner. Kerr (1975) examined vertical loads on a cylindrical pile. The load
increases with the thickness of ice and with ratio b/h. When the ice thickness is 0.5 m, the
load magnitude per water level change is 5 × 10 5 Ncm − 1 . According to Gamayunov (1960)
the ice fails in bending at the cylinder surface with an effective moment M ¼ h 2 r f = 6

.
If the ice cover is frozen to vertical walls, uplifting and downdragging forces also result
from vertical movement of the water level (Ashton 1986). Based on the theory of beam on
semi-in nite elastic foundation, the load is

P
b ¼

q w k Dn

ð 5 : 33 Þ

where ʔʾ is the change in water level elevation and ʻ is the characteristic length of ice

plate on water foundation (Eq. 5.26 ).

5.5 Drift Ice in Large Lakes

5.5.1 Drift Ice Material

The horizontal structure of ice cover in large lakes is well revealed by optical satellite
images (Fig. 5.11 ). The ice sheet is occasionally broken into floes by wind forcing, water

level variations and thermal cracking, and the floes may be forced to move. This field of