Section 75. Elastic Properties 



Veinberg, who carefully collected and systematized the determinations of mechanical proper- 

 ties of ice which had been carried out by many investigators, and who himself had made quite a few 

 such determinations, presents very little data on the elastic limit, namely: 0.5 (according to 

 Fabian), 0.44 (according to Matsuyama), 0. 57 (according to Veinberg for neve ice), and 0. 9 

 (according to Veinberg for granular ice of the Hinterice glacier) . All amounts are given in kg/cm2. 



As we shall see, the limit of elasticity of even fresh ice is so small that as Veinberg says, 

 "the elastic stage in the conduct of ice under the action of forces can seem to present only a theoret- 

 ical interest, even though the elastic constants of ice are used in solving such problems as construc- 

 tion of ice crossings, airplane landings on ice, etc. Such a conclusion, however, would be pre- 

 mature, inasmuch as it is extremely difficult to foresee which aspects of a study of ice would be 

 important in the future. " Now, in determining the thickness of a layer of glacier ice, echo sounding 

 is used which requires a knowledge of the rate of propagation of elastic waves. The latter can be 

 determined either by experimentation or by computations according to density and the elastic con- 

 stants of ice. 



The elastic constants of fresh ice, determined by various methods and by various investi- 

 gators, differ greatly from each other. Thus, the modulus of elasticity, that is, the magnitude, 

 which is the reverse of the coefficient of linear expansion of the rod when it is distended, according 

 to Veinberg's resume', fluctuates from 6, 000 to 180, 000 kg/cm , and the shearing modulus, i. e. , 

 the amount of force which rotates parallel surfaces of a body by an angle equal to one radian (57. 3°) 

 and fluctuates within the limits of 2, 000 to 34, 200 kg/cm^. 



Veinberg considers that determinations of elastic constants based on the frequency of the 

 oscillations of the ice beams, or on the rate of propagation of explosive waves, are the most depend- 

 able. According to these determinations, the modulus of elasticity fluctuates within the limits of 

 49, 000 to 96, 000 kg/cm^ and the shearing modulus fluctuates within the limits of 25, 000 to 34, 000 

 kg/cm^. The most likely value for Poisson's modulus, i. e. , the ratio of the relative lateral con- 

 traction to the relative longitudinal elongation when longitudinal expanding forces are applied, is 

 considered by Veinberg to be 0. 36. 



As has been pointed out already, a knowledge of the elastic constants of ice is necessary to 

 determine the thickness of glacier ice cover (by the propagation velocity of explosive waves) . This 

 method was first applied by Moths in the Alps and later by Wegener from 1929 to 1931 in Greenland. 

 Thus, assuming the velocity of the fastest waves of the acoustic type to be 3,720 m/sec, the 

 Wegener expedition in 1931 obtained for Greenland ice a thickness of 2500 to 2700 m above the level 

 of the basic continental rocks buried under the ice. 



In 1932-1933, the same method for measuring the thickness of continental ice was adopted by 

 Ermoliaev on the northern island of Novaia Zemlya at which time the following results were 

 obtained: 



Thickness of ice cover up to 600 m, 



Velocity of longitudinal waves up to 4000 m/sec, 



Velocity of transverse waves up to 1, 850 m/sec. 



LITERATURE: 25, 62, 77, 113, 114, 152. 



185 



