836 POXJNDER [sect. 7 



agrees with this equation but points out that measurements on natural fresh 

 ice do not give dp since such ice always contains air bubbles and other flaws 

 which also act as stress concentrators. He prefers to use an equation of the form 



(7 = ao(l-|8,), (5) 



where ctq is the "basic" strength of sea-ice obtained by supposing all the brine 

 (and air) pockets filled with ice but with minute stress concentrators present. 



The next step is to relate ^e to the relative brine volume v of the ice, where v 

 is the fraction of the total volume occupied by liquid. The salinity S obtained 

 from a melted ice sample does not give v directly since at any temperature 

 below — 8.2°C some of the salt will be in the solid form. From the phase diagram 

 of sea-ice it is possible to calculate ;^ as a function of salinity and temperature. 

 The calculation of ^e from v requires a model of the size, shape and distribution 

 of the brine cells. Assur considers several models and concludes that the most 

 likely equation is 



o- = aoil — a-y/v). (6) 



The constant a depends on the model chosen and can be determined empirically. 



As sea-water is cooled the various salts are precipitated from solution 

 starting at various temperatures. Figures for these temperatures for the 

 hydrates of sodium sulphate and sodium chloride have already been given ; 

 these are the important ones in practice. The deposition of solid salts reduces 

 V but also has a second and more important effect ; the salt reinforces the ice 

 surrounding the reduced brine pockets and thus gives the much higher strengths 

 at lower temperatures. This is particularly true below — 23°C since sodium 

 chloride is the major constituent. 



The theory just outlined has had considerable success in quantitative pre- 

 dictions of ice strength and has also been used to derive equations for thermal 

 and electrical conductivities. Additional experimental work^ on phase relations 

 in sea-ice and on its petrography will provide more accurate values of the 

 parameters, but a most promising start has been made on a quantitative theory 

 of sea-ice. 



References 



Anderson, D. L., 1958. A model for determining sea ice properties. Arctic Sea Ice, 148, 



NAS-NRC Pub. No. 598, Washington. 

 Anderson, D. L., 1958a. Preliminary results and review of sea ice elasticity and related 



studies. Trans. Eng. Inst. Can., 2, 116. 

 Anderson, D. L. and W. F. Weeks, 1958. A theoretical analysis of sea ice strength. Trans. 



Amer. Geophys. Un., 39, 632. 

 Amol'd-Albiab'ev, V. I., 1939. Strength of the ice in the Barents and Kara Seas. Problemy 



Arktiki, No. 6, 21. 

 Assur, A., 1956. Airfields on floating ice sheets, for routine and emergency operations. 



SIPRE (Snow, Ice and Permafrost Research Establishment, Corps of Engineers, U.S. 



Army, Wilmette, 111.), Tech. Rep. 36. 



1 Assur (private communication) reports that much additional information was obtained 

 during the last two years which will modify and refine the relations presented in Fig. 2. 



