comparing gravity and thermal forces in glacial motion

In the previous posting it has been suggested that the levels of compression potentially developed by restraining the expansion of glacial ice during the warm-up period can be immense. Just how large can be seen by considering a situation where glacial ice having a typical coefficient of thermal expansion alfa = 90x10-6m/m/oC, and modulus of elasticity E=10x10+6 kN/m2 is subjected to an averaged, through-thickness, seasonal temperature increase of say T=10oC. If fully restrained from expansion this situation will generate a compressive force in the ice of 9000t kN for every metre width of glacier. It would not require a great thickness, t, of ice to be subjected to such a temperature increase for the stresses to reach the levels required to cause both elastic-visco-plastic shear flow in the ice and/or overcome the shear resistance offered by an even rough bed friction.

In contrast, a glacier having a slope of say, 5o, and ice with a specific weight of 9 kN/m3, will be generating forces of a little under 0.8t kN for every 1m of glacier length and every 1m width. Even over a very long section of glacier these accumulated gravity forces will be orders of magnitude less than those arising from the thermal expansion. The stored energy from the thermal expansion will likewise be orders of magnitude greater than that from the effects of gravity. The relatively low magnitudes of the gravitational forces are such that it is almost inconceivable they will be entirely responsible for both the recorded motions and the erosive powers of glaciers.