Properties of Ice
II
Salinity vs. Temperature of
Maximum Density
Salt depresses the
freezing point.
Tm = temp of max density
Tf = freezing temperature
Tf = -0.055Sw
-1.33
For salinity > 24.7,
Tm = Tf
24.7
Seawater Freezing
• Issues
– For water salinity greater than 24.7 o/oo, tm = tf.
– Surface cooling results in a density increase,
and vertical mixing continues until the water
reaches tf.
– Unlike freshwater lakes, density gradients in
the upper ocean usually limit the depth to which
the water must be cooled before freezing begins
(generally 10-40 m)
Sea Ice Density
• Seawater is more dense (heavier) than freshwater
– density depends on temperature and salinity, but for
seawater of 35 o/oo at 0° C, the density is 1.028 g/cm3
– Sea ice can be more dense than fresh ice because it
contains brine. Densities can be as high as 0.95 g/cm
• They can also be very low for ice containing much air
• Net Result - Sea Ice also floats
Sea Ice Formation
• Frazil ice formation
– As in rivers, turbulence caused by wind, waves
allows slight supercooling, and frazil crystal
growth - soupy mixture (grease ice)
– Frazil crystals eventually consolidate into a
more solid ice cover - pancakes, nilas
• Columnar ice growth
– Freezing directly to the bottom of an ice sheet
(grows downward)
• Snow ice - water saturated snow
Brine Rejection
Freezing process rejects salt
– Brine and solid salt are entrapped in pockets
between platelets within crystals or crystals of
pure ice
– Newly formed sea ice has salinity of about 7 –
10 o/oo from seawater having salinity of 32o/oo
– As ice ages, brine continues to drain from the
ice, continually freshening the ice
Platelet Substructure
Growth Direction
For Columnar Sea Ice
Horizontal thin section
Dendritic Structure
Dendrites are pure ice. Brine is trapped in pockets as dendrites freeze together.
Brine Drainage Process
Gravity drainage
Interconnected brine
pockets become channels
Denser brine will migrate
to the bottom of the ice
sheet
Typical Salinity Profiles
a-d are first-year ice
Multi-year ice
Typical Crystal Structure
Sea Ice Properties
First-year Sea Ice
Formation
Sea Ice Crystal Structure
Vertical Section
Columnar Crystals
Horizontal Section
Sea Ice Crystal Structure
Vertical Section
Frazil Ice
Horizontal Section
Frazil Ice
Important Ice Properties
• Temperature, salinity, density
– Large influence on ice strength
• Brine volume and porosity = f(T, S)
– Also influence remote sensing properties
• Crystal structure
– Less important but significant effect on strength
Thermal Ice Growth
for freshwater and sea ice
h = F1/2
• h - ice thickness (cm)
•  - coefficient - average lake 1.7 - 2.4
• F - accumulated freezing degree days after
the onset of freezing
• Freezing degree days - mean daily air temperature
below freezing (i.e. -10°C = 10 freezing degree days)
Mechanical Properties
• Elastic Modulus (E) - relationship between stress and strain
• Characteristic Length (Lc) - measure of the extent of the zone
of deformation when subjected to a vertical load
Lc=[(Eh3/12(1-2)]1/4
h - ice thickness
 - specific weight of water (wg)
 - Poisson’s ratio ( usually taken as 0.3 for ice)
• E depends upon ice temperature, crystal structure, and
loading rate (and brine volume of sea ice)
Mechanical Property Values
• Elastic Modulus: Depends on testing conditions
– 0.4 to 9.8 GPa (55-1,350 kpsi)
– Sea ice : E = 5.31 - 0.436Vb1/2 (GPa)
• Characteristic Length:
– Lake ice - Lc≈ 20h for cold ice; 15h warm ice
– First year sea ice - Lc ≈15h for cold ice, 10h warm
ice
Ice Strength
• Strength: maximum stress ice can support
just before failure
– depends on mode of failure
• Bending or flexural failure
– Failure results from ride-up on a sloping
surface
• Crushing or compressive failure
– Failure from in-plane loads (normal to floe
thickness such as an ice sheet pushing against
vertical column)
Bending Failure
©E. Hill, Anchorage Daily News
Crushing Failure
Yukon River Bridge
Compressive Strength
• Freshwater ice - affected by loading (strain)
rate, crystal size and orientation, porosity and
temperature
• Sea ice - affected by strain rate, crystal size
and orientation, temperature and total porosity
• Compressive strength usually measured in a
laboratory setting
Strength Dependence
Brittle
Strain rate
dependence
Ductile
Compressive
Strength
Columnar, vert.
C-axis
Snow ice
Effect of crystal
type and orientation
Frazil ice
Columnar, horz. C-axis
Flexural Strength
• Usually measured with beam tests
Flexural strength:
f = 6PL/Bh2
P - failure load, L - deflection
B- beam width, h - ice thickness
Test to obtain
Elastic Modulus
Characteristic length
test
Flexural Strength of Sea Ice
f = 1.76e-5.88√vb
Strongly dependent on brine volume
which is a function of temperature and salinity
Loads on Ice Sheets
• The load an ice sheet can support
– depends on duration of load
– proportional to the square of the thickness
P = Ah2
– P in mega-Newtons, h in meters  A=1
– P in tons, h in inches  A=0.07
• For practical applications (inches): h = 4P1/2
(P in tons)
Summary
• Crushing failure puts higher loads on structures
– c = 3 to 10 x f
• Strength = f(temperature, crystal orientation, load
rate and porosity)
• Strength ranges:
– c = 2-10 Mpa
– f= 0.1-3.0 Mpa
• Generally, freshwater ice is stronger than sea ice