When t = t , the end of the groin is reached by the shoreline and 

 sand begins to be bypassed around the groin. 



The boundary condition at the groin becomes oy = £ (constant) for 

 t > t . The solution then becomes (Fig. 3) : 



y = 2. E 



/4Kt 



(11) 



The curves representing the shoreline become homothetic with respect to 

 the axis oy ; i.e., 



AB 



AC 



A'B" A'C 



The area between the shoreline and the ox axis (oy x') is given by: 



f- 



2,.tl'^ 



The area of triangular fillet, oy x , is _ 

 ^ ^ o o 2 



4 N^Kt 



Hence, 



oy X 



= 2( 



/ 



Kt 



o o 



and 



ox'' = 2x 



f V^t 



4 _ 



1.27 



(12) 



The shoreline as described by equation (7) at time t = t is slightly 

 different from the shoreline defined by equation (11) at t = t " as 

 shown in Fig. 4. 



The volume of sand defined by both curves is equal when the time t. of 



equation (7) is replaced by the time t " in equation (11) in such a way 

 that 



"-{ 



2 

 16" 



0.62t 



(13) 



18 



