Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 143

ned as the maximum stress a test specimen can support, and it
depends on the mode of deformation and the mode of failure. In brittle failure the spec-
imen breaks but in ductile failure the strain increases in the specimen with no increase in
the stress. Usually the former deals with fast loading cases when the response is elastic,
while the latter concerns long-term viscous or plastic

The strength is de

flow. The general equation of motion
of a continuum is the Cauchy equation (Hunter 1976):

X

q D u F ð l Þ

Dt ¼ rr þ

ð 5 : 11 Þ

l

where Dt ¼ o t þ u r is the material time derivative consisting of the local change and

advection, and F (l)

is are the external forces. In a static situation, the left hand side is zero.
In the next section the mechanical properties of lake ice are brie

'

y presented. The
discussion is limited to the general level, without details of experimental techniques,
which are well covered in engineering literature (e.g., Michel 1978; Ashton 1986). The
goal is to provide the essential information of the mechanical properties of lake ice and
their variability. The information is based on laboratory experiments with ice samples,
in situ

field tests, rheological models, and semi-empirical equations for the ice properties.
In the recent decades there has been more work done on the mechanical properties of sea
ice that also can be utilized for lake ice applications (e.g., Mellor 1986; Sanderson 1988;
Palmer and Croasdale 2012).
Lake ice sheet is considered as a polycrystalline continuum, and the relatively large
variability of its mechanical properties comes from large crystal size, high homologous
temperature, and impurities. In addition, test arrangements and the sizes of ice specimens
have caused arti cial variability. Isotropy is normally assumed, although columnar ice,

which is a common ice type in lakes, has strong anisotropy between vertical and hori-
zontal in the crystal structure (see Sect. 3.2 ). Granular ice is isotropic. Lake ice lies on
water foundation, where the water pressure at the ice bottom is

gh, which is balanced by
the weight of ice. For small vertical displacements (ice is neither submerged nor raised out
of water), the response of the foundation is proportional to the displacement. This
behaviour is analogous to elasticity, and therefore the theory of plate on elastic foundation
can be utilized for the mechanics of

ˁ

field tests have the great advantage
that ice can be loaded in natural conditions with the bottom at the melting point.

floating ice. In situ

5.2 Ice Cover as a Plate on Water Foundation

5.2.1 Elastic Lake Ice Cover

In short-term loading, ice shows elastic behaviour (Michel 1978; Ashton 1986). Short
term refers here to the time scales of the order 100 s or less. In very short time scale
(seconds) ice is perfectly elastic - brittle material, where it cracks once the strength limit