Thermal cracks in floating ice sheets

When the air temperature drops below the water temperature under a floating ice sheet, thermal cracks often occur. To acquire quantitative information on these cracks from an analytic point of view, the ice has been represented as a homogeneous elastic floating plate. The effect of thermal contraction then becomes equivalent to a lateral surface load. After the problem has been formulated in general terms, three special conditions which lend themselves to analytic treatment are considered: the wide ice sheet under conditions of plane strain, the narrow ice sheet under plane stress conditions and the axisymmetric ice sheet. The first two lead to simple solutions that illustrate general effects, the third is of more practical significance. Typical stress distributions prior to cracking are shown and for particular numerical values, some of which are applicable to arctic sea ice; typical crack spacing is related to the temperature difference between the upper and lower surface. Finally, the assumptions on which the analysis rests are examined critically with regard to establishing the validity of the results and to indicate ways in which improvements in the analytic treatment can be made.