Appendix C 

 DISCUSSION OF FORM OF NORMALIZED TIME TERP 



In developing a technique for predicting the time required for 

 long-term breakout, it was determined in the main text that a plot of the 

 relative breakout force, Fj^/Fji^, versus the breakout time normalized as 

 (ptjj/D^)(B/D)^, yielded the best correlation. It was then observed that 

 this normalized term could be nondimensionalized by multiplying it by k/7, 

 where k is the soil permeability in feet per minute and 7 is the unit weight of 

 water in pounds per cubic feet. The objective of this appendix is to illustrate 

 that a nondimensional term of this nature is not unreasonable from a soil 

 mechanics point of view. 



It will first be assumed that the mechanism of long-term breakout is 

 the propagation of cracks down the side of the object. After the cracks have 

 propagated to some point close to the object bottom, water will rush into the 

 low-pressure zone beneath the object and breakout will occur. This assump- 

 tion agrees well with what was observed. 



The growth of the cracks appears associated with the flow of water 

 either through the soil to the point at which the crack is growing or into the 

 soil itself. If the water flows into the soil itself, the soil strength is reduced 

 and the soil can flow more easily. Whatever the basic mechanism, one of the 

 important relationships describing the phenomenon will be Darcy's law for 

 flow through porous media. This empirical law can be written for plane flow 

 asi^ 



Q = kh(^) (C-1) 



where = seepage rate per unit length (ft-^/min/ft) 



k = soil permeability (ft/min) 



h = total pressure head loss (ft) = Ap/7 



Ap = total pressure loss (psf) 



7 = unit weight of water (pcf) 



Nf/Nj = flow net factor, related to geometry of problem 



43 



