WATER-SUBSTRATE COOLING REQUIREMENTS 



The actual cooling requirements were estimated for freezing a 24 by 48 by 18- 

 inch (0.61 by 1.22 by 0.46 m) substrate sample. The following assumptions were made 

 in calculating the requirements: 



a. There is no appreciable water circulation in the sample. 



b. The water temperature remains constant at 40°F (4.5°C). 



c. The average temperature of the frozen sample is 0°F (-18°C). 



d. The average dry sample density is 115 lb/ft 3 (1.85 g/cm 3 ) 

 (Terzaphi and Peck 1948). 



e. The unit density of the solids is 165 lb/ft 3 (2.65 g/cm 3 ) 

 (Terzaphi and Peck 1948). 



f. Two inches (5 cm) of the periphery of the sample is rock with very 

 little ice or fine sediment because the rock may be frozen to the sample 

 on one side only. 



The constants used in calculating the cooling requirements were taken from 

 Baumester (1967). 



Specific heat (Cp) 



C p water = 1 Btu/lb (4.18 J/g°K) 



C p ice = 0.48 Btu/lb (2.01 J/g°K) 



C p rock = 0.20 Btu/lb (0.84 J/g°K) 



Heat of fusion 



Water = 144 Btu/lb (555 J/g) 



The approximate percent voids in the sample which are filled with water are 

 determined by the following equation (Terzaphi and Peck 1948) : 



i y d 



n = 1 - - — 



ys 



where 



n = percent porosity 

 yd = unit dry weight 

 ys = unit solid weight 



n 1 - (1.85/2.65) = 0.30 or 30 percent voids. 



Sample weight is calculated as follows: 



weight of rock (W ) = (volume of sample) (dry density) 



W r = (2) (4) (1.5) (115) 



W = 1,380 lb or 626 kg 



2 



