2 



t- = 2 — ^ 1.3 X 10 £ days, 



4K tan a 

 o 



In tabular form for various groin lengths, 



I ft 50 100 200 500 



Check : 



t days 3 13 52 325 



For £ = 50 feet Area Ox,y = 1.56 x Area oxy 



1.56 



I _ 0.78 I = 22,400 square feet 



2 tana tana 



Volume ^ (Area ox y) (D) = 4.5 x 10 cubic feet 



b' 

 2 ^b 



KD 

 Q = ^r- tan 2a, = 1.6 cubic feet per second 



4.5 X 10 _ _ ,„5 , „ , 

 t = ;;j = 2.8 X 10 seconds ^ 3 days. 



III. THE TWO-LINE THEORY OF BAKKER 



One limitation of the solutions of Pelnard-Considere is the assump- 

 tion of parallel depth contours. Bakker [1968a) realized that the one- 

 line theory of Pelnard-Considere and its subsequent development may, at 

 times, lead to some inaccuracy, since beach slope variations along the 

 shore were not considered. Beach slope variations with respect to time 

 (summer-winter profiles) are not important in the long-term shoreline 

 evolution. Nevertheless, if an adequate onshore-offshore profile 

 response model was available, a suitable mathematical representation of 

 it could be developed (Dean, 1973; Swart, 1974). 



Near coastal structures, the deviations of the model from prototype 

 conditions can be considerable. Pelnard-Considere finds that the accre- 

 tion and erosion patterns are symmetrical with respect to the groin as 

 shown on Fig. 12. However, in reality, the updrift profile becomes 

 steeper than the equilibrium profile and the sand moves seaward. The 

 downdrift profile is flatter than the equilibrium profile and the sand 



31 



