Figure 6. Time history of longshore sand transport 

 past a point on the shoreline. 



where the integrals are evaluated only for those time periods when q(t) is 

 positive; the total transport to the left during t is 



% " "t / 



q(t) dt - t / 4 q(t) dt - ... - t / q(t) dt 



(4) 



where the integrals are evaluated for only those time periods when q(t) is 

 negative. The minus sign is included so that Qt will be a positive number. 

 Therefore, the net volume transport is 



Qnet = Qr " Q L 



(5) 



The gross transport, defined as the total amount of sand passing the point on 

 the beach during t is 



(6) 



"'gross 



= Qr + Ql 



Sand transport at an ideal weir- jetty system is shown in Figure 7. 

 Assuming that the net transport in the figure is from left to right (i.e., 

 Qr ^ Ql) > t ' ie m i n i mum amount of sand that should need to be bypassed for 

 erosion control is Q ne t* ^ an opt* 111 " 111 system, only Q ne t would enter the 

 deposition basin for bypassing to the downdrift beach. The amount of sand 

 carried to the weir from the updrift beach is Q^, which will be larger than 

 Q net if a net transport is to the right as assumed. An amount of sand equal 

 to Qr ~ Q n et must therefore be retained in temporary storage on the updrift 

 beach to keep the sand from moving into the deposition basin. The sand on the 

 updrift beach will then be available to replace the material trapped by the 

 downdrift jetty and be transported back up the beach during periods of trans- 

 port reversal; i.e., when the transport is to the left. The quantity of sand 

 held in temporary storage is Qj^ - Q net which, from equation (5), is equal to 

 Q^. Not all of this sand needs to be held in storage at one time. The amount 

 of storage required in the updrift beach will depend on the frequency and mag- 

 nitude of reversals in transport. A suggested analysis procedure to determine 

 the amount of storage needed is presented in Section VII. 



The bypassing requirements described above are for an ideal weir-jetty 

 system. However, several factors preclude achieving this optimum situation. 



15 



