rectangular beach fill which is twice as long maintains its volume four times 

 as long if exposed to the same wave conditions. It is possible to calculate 

 the time it will take for a certain percentage P to be lost from the initial 

 rectangular fill. The following expression is obtained by integrating Equa- 

 tion 16 and comparing the resulting volume at a specific time to the original 

 fill volume: 



P = /t 7 " (— - ierfc — ] (22) 



where ierfc denotes the integral of the complementary error function erfc 



CO 



■/ 



ierfc z = / erfc £ d? (23) 



erfc z = 1 - erf z (24) 



Figure 8 shows the percentage of sand volume lost as a function of time. 



36. It is possible to determine the rate of sand to be supplied to the 

 fill in order to maintain the original shape. The boundary condition for this 

 case is that the end of the rectangular fill is kept at the initial position: 



y(0,t) = y Q (25) 



Note in this case that the x-axis originates from the corner of the fill 

 instead of from the middle of the fill as in Equation 16. The solution de- 

 scribing the resultant shoreline evolution is (Carslaw and Jaeger 1959, 

 p. 60): 



\2/n) 



y(x,t) = y o erfc [ ^^ ) (26) 



for t > and x > . 



21 



