The above relationship for a fixed wave climate reveals that if the groin 



length is doubled, the time required for the shoreline to reach the end of the 



groin will increase fourfold. 



65. If bypassing of a groin occurs, the boundary condition at x = 



changes into y = L . A correct solution to this situation should fulfill 



this boundary condition and use as an initial condition the shoreline shape 



just before bypassing occurred, according to Equation 64. An approximate 



solution was presented by Pelnard-Considere (1956) who used the solution for a 



shoreline with fixed position y at x = (see Equation 26) and matched it 



against Equation 64 by equating sand volumes. With this criterion, the 



following relationship between the time elapsed before bypassing occurs t 



G 



(in Equation 64) and the actual time in the matching solution t , which 

 makes the sand volumes equal, is obtained: 



V IT 



66. Thus, in the case of bypassing, it is possible to use Equation 26, 



2 

 if the time t is replaced by t. = t - (1 - it /16)t_ for t > t^ . The 



* G G 



rate of sand bypassing the groin for t > t is calculated according to 



G 



Equation 8 to produce the following relationship: 



Q = 2Q o a o (l - — "t=z (68) 



\ a /Tret.. / 



for t > t G . 



Here 2Q a is the sand transport rate at equilibrium (straight beach) under 



imposed incident breaking wave angle a , and t. is the modified time in 



o * 



the matching solution using Equation 26. 



67. Formally, the solution downdrift of a groin is the same as that in 

 Equation 64 but with opposite sign. However, if the groin or jetty extends 

 far outside the wave breaker line, diffraction will occur behind the groin 

 altering the breaking wave height and angle; thus the transport capacity 



49 



