

Figure 66. Ice deflection under a concentrated load. 



We should remember that the curve deflection of an elastic plate on an elastic foundation is 

 horizontal under the load, but its branches, extending into infinity are wave-like. The latter con- 

 tradicts the properties of ice under a static load and the appearance of the curves obtained during 

 observations. Actually, any displacement of ice disappears within time due to the effect of isostatic 

 forces. On the other hand, when ice deflections are in conformity with the logarithmic curve, a 

 sharp break of the ice under the weight itself is obtained. This fact arouses doubt as to the legality 

 of the assumptions made. Nevertheless, I personally allow that on the lower surface of the ice, 

 cracks might even form under the weight of the load, which is not permissible for an elastic plate, 

 but for ice, keeping in mind its properties, is not catastrophic. Actually, the cracks which are 

 formed are filled with water which freezes immediately on contact with the cold internal layers of 

 the ice. But, of course, the main conclusion in favor of the suppositions made is the fact that the 

 observed curves resemble logarithmic ones. They are all convex upwards whereas the elastic 

 plate bends with the convex surface downward a short distance from the load. 



In addition to the material which has been given, I present certain results of investigations 

 sent to me by G. lu. Vereshchagin which were conducted on the ice of Lake Baikal by the Baikal 

 Station of the Academy of Sciences in 1941 and 1942. These investigations, in particular, consisted 

 in determining the magnitudes of deflections under loads of various forms and magnitude up to 

 loads that broke through the ice, which, understandably, is of greatest practical interest. The 

 magnitudes of deflections were measured at 4 points on the same radius, beginning from the 

 periphery of the load itself. The following was observed: 



1. With a gradually increasing load, the magnitudes of the deflections first increase slowly 

 and evenly, and then discontinuously with a simultaneous appearance of cracks especially near the 

 load, and finally very rapidly just before the load breaks through the ice. 



2. The magnitude of the deflections computed for a unit of distance, decreased in a direction 

 away from the load toward the periphery. 



3. When the load was first applied, a certain swelling of the ice was observed at some dis- 

 tance from the loads. This swelling gradually decreased with further increase in the load. 



4. After the load was increased to a certain amount, the appearance of radial and concentric 

 cracks was observed along the upper surface of the ice. The concentric cracks approximately 

 duplicated the outlines of the load; they were circular under cylindrical loads. The cracks close 

 to the load went all the way through before the'load broke through. 



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