Wave runup is estimated using the formula (Ahrens and McCartney, 

 1975)^: 



R ^ ag 

 Hj 1 + b? 



(4) 



where a = 0.692 and b = 0.504 are recommended for rubble-mound break- 

 waters and a = 0.988 and b = 0.703 are recommended for a breakwater 

 armored with two layers of dolos. g is the surf parameter given by 



S = 



tan 9 



(5) 



where 9 is the angle of the seaward face of the breakwater, and Lq is 

 the deepwater wavelength obtained from linear wave theory. Calculations 

 of wave transmission by overtopping are performed automatically in the 

 program MADSEN (see App.). 



III. WAVE TRANSMISSION THROUGH PERMEABLE BREAKWATERS 



The coefficient of wave transmission through permeable breakwaters, 

 Kyt, is estimated using the analytical model of Madsen and I'/hite 

 (1976)5. In this model the transmission coefficient is related to a 

 complex function of the size and porosity of the materials used in 

 building the breakwater (Table 1), the breakwater geometry, the seaward 



Table 1. Porosity of various armor units (after U.S. 

 Army, Corps of Engineers, Coastal Engineer- 

 ing Research Center, 1977)6. 





No. of 







Armor unit 



layers 



1 Placement 



Porosity 



Quarry stone (smooth) 



2 



random 



0.38 



Quarrystone (rough) 



2 



random 



0.37 



Quarrystone (rough) 



>3 



random 



0.40 



Cube (modified) 



2 



random 



0.47 



Tetrapod 



2 



random 



0.50 



Quadripod 



2 



random 



0.49 



Hexapod 



2 



random 



0.47 



Tribar 



2 



random 



0.54 



Dolos 



2 



random 



0.63 



Tribar 



1 



uniform 



0.47 



Quarrystone 



graded 



random 



0.37 



^AHRENS, J., and McCARTNEY, B.L., "Wave Period Effect on the Stability of 

 Riprap," Proceedings of Civil Engineering in the Oaeans/III , June 1975, pp. 

 1019-1034 (also Reprint 76-2, U.S. Army, Corps of Engineers, Coastal Engi- 

 neering Research Center, Fort Belvoir, Va., June 1976, NTIS A029 739. 



5MADSEN, O.S., and IVHITE, S.M., op. cit., p. 7. 



6U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, 

 Shore Protection Manual, 3d ed. , Vols. I, II, and III, Stock No. 008-022- 

 00077-1, U.S. Government Printing Office, Washington, D.C., 1977. 



