Geoscience Reference
In-Depth Information
has been reached. Longer-term response is elastic-plastic, where the ice yields after having
reached the strength level.
The elastic parameters of lake ice depend on the temperature, gas content, size and
shape of crystals, and impurities. Based on experimental data, the standard references for
isotropic lake ice are Young
= 0.33 (Ashton
1986). The bulk modulus and shear modulus are then K = 0.98 E and
G = 0.38 E. Assumption for isotropy is widely used, and experimental data show that the
variations in Young
'
s modulus E = 9.0 GPa and Poisson
'
s ratio
ʼ
s ratio are within 0.5 GPa and 0.015 or 5 %
from the standard values. The elastic model is valid up to the strength of the ice.
The strength is the fundamental quantity to evaluate ice loads, bearing capacity of ice,
and the stability of ice cover. In the elastic regime, the brittle strength of ice is of the order
of 1
'
s modulus and Poisson
'
-
10 MPa, depending on the mode of loading (Table
5.1
).
Table 5.1
Elastic modulus and strength of freshwater ice
Modulus (GPa)
Strength (MPa)
Strain at breakage
1.1 × 10
−
3
Compression
9.0
10
0.17 × 10
−
3
Tension
9.0
1.5
0.29 × 10
−
3
Shear
3.4
1.0
10
−
3
. The
flexural strength of
lake ice is 1.5 MPa (e.g., Weeks 1998). Flexural strength can be measured in situ and
therefore it is a good reference for the strength of
The maximum strain at failure is strength/modulus
*
floating ice.
The brittle compressive strength of lake ice is about 10 MPa at the temperature of
-
10 °C (Ashton 1986). This holds for all congelation ice, snow ice and frazil ice. Ductile
strength is less than the brittle strength and decreases with strain-rate, reaching 1 MPa at
the strain-rate of 10
−
7
s
−
1
10
−
3
(3 h)
−
1
. Strength increases with decreasing temperature,
and the brittle compressive strength is 20 MPa at temperatures of about
*
30 °C. In various
tests, at a fixed temperature and strain-rate, the strength has varied by a factor of two. For
compressive strength borehole tests have been made with a cylindrical pressure meter.
Michel (1978b) has presented a semi-empirical model for the uniaxial compressive
brittle strength of lake ice:
-
r
c
½Pa
¼9
:
4
10
4
ð
d½m
1
=
2
þ
3 T½
C
j
0
:
78
Þ
j
ð
5
:
12
Þ
where d is grain size and the units of the quantities are given in brackets. The compressive
strength ranges then within about 1
10 MPa. Multi-axial tests have indicated higher
-
strength values.
Tensile strength depends primarily on the grain size and less on the temperature
(Ashton 1986). Also it is not sensitive to the strain-rate. The level of brittle tensile strength
has been 1
2 MPa in experimental data. Shear is a special case of multi-axial loading
-
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