Therefore, the shoreline evolves initially as represented by equation 

 (7) . Then, when t = t , the shoreline keeps evolving as given by 



equation (11), as if the time were t - 0.38t 



Then', the sediment dis- 



charge , Q 



bypassing the groin is equal to the incoming discharge 



Q minus the volume of sand which accumulates per unit of time, 

 ^o ^ 



O.t) 



KDi 



TTK(t-0.38t^) 



1/2 



(14) 



I.e. , 



Q(t) = Q, 



i' 



tana [" 7TK(t-0 . 38t^) 1 



1/2 



(15) 



or again 



Q(t) = Q, 



0.638 



Rt/t^) - 0.381 



1/2 



(16) 



In dimensionless terms, the following values are obtained for equation 

 (16) (see Fig. 5) : 



1 



1.25 



1.5 



2 



3 



Q/Q, 



0.189 

 0.315 

 0.397 

 0.498 

 0.605 



0.665 

 0.703 



It takes a long time before the value of Q approaches initial dis- 

 charge, Q , downdrift of the groin. 



20 



