36 THE ROYAL SOCIETY OF CANADA 



perature of the ice that we are likely to have in the Northern States. 

 This is equivalent to an expansion of about 4 ft. per mile." 



Mr. Sawyer's experience with this problem is so large that his 

 conclusions should be of the greatest value and consequently we give 

 them as follows: — 



"The problem of the amount of force applied to dams by reason 

 of ice expansion is not solved. There are many experiments and 

 observations yet to be made, and in the end we cannot lay down a 

 'hard and fast rule' for the intensity of the ice pressure. As in all 

 engineering problems the engineer will have to take into considera- 

 tion the local conditions. 



"For the purpose of aiding in the study of the problem, I give 

 a few of the conditions which may be found at different places. 



"A dam may be built at the upper end of a valley, the opposite 

 shore of the lake or pond consisting of soft mud or silt, in which 

 case it would be expected that the ice thrust would force up the mud 

 into ridges, rather than act to over-turn the dam. If, however, the 

 opposite shore is formed of ledge or of a very hard soil, precautions 

 must be taken to meet the thrust on the dam. 



"The width of the shore above the dam will have a great influence 

 on the amount of thrust exerted. If the distance between the dam 

 and the opposite shore is comparatively short, we may reasonably 

 expect that the thrust will be a great deal more than it would be if 

 the distance between the dam and the opposite shore is considerable. 

 The ice, in the latter case, will act more like a long column; that is, 

 it will have a greater tendency to buckle than in the first case, the 

 movement of the ice, however, if such occurs, will be greater, the longer 

 the sheet. 



"If a dam is situated in a narrow valley, even a short distance 

 below the reservoir, we would expect that the shore at the upper end 

 of the valley would receive the greater part of the ice thrust, but if 

 these shores would happen to be of a soft or yielding nature, some of 

 the thrust might be passed on to the dam. If the dam is situated 

 below a reservoir, the elevation of which is being constantly changed, 

 as in a mill pond from which water is being drawn for manufacturing 

 purposes, the ice will be broken at the dam and on the shores, and the 

 liability of the occurrence of a dangerous thrust will be reduced. 

 Slanting up-stream faces of dams do not add an element of safety 

 against ice thrusts, unless the water level is constantly varying, — 

 that is, the tendency to slip on the slanting surface is more than offset 

 by the greater adhesion to the surface by reason of the large area of 

 ice in contact. We will admit, however, that a vertical up-stream 

 face will leave the dam open to receive blows from floating ice which 

 would not be dangerous to the dam with a slanting up-stream face." 



