4 6 



TIME (et/a a ) 



Figure 8. Percentage of sand volume lost from a rectangular 

 fill as a function of dimensionless time 



Sand has to be added to the corner of the fill at the following rate: 



2y, 



Q = 



(27) 



The spread of the moving shoreline front (Equation 26) is illustrated in 

 Figure 9. 



37. It is advisable to use the analytical expressions describing shore- 

 line evolution for a rectangular fill with great care, even for rough estima- 

 tions, because the linearization procedure (Equation 8) is based on small 

 shoreline orientation angles, a condition which is violated on the sides of 

 the rectangle. In fact, the linearized transport equation implies an infi- 

 nitely large initial sand transport rate at the edges of the fill. However, 

 the original transport equation (Equation 7) gives a zero transport rate at 

 the corners; thus, a rectangular beach form is stable to parallel incident 

 waves. In reality, sand transport occurs at the corners because of 



22 



