the Shore Protection Manual (1984), Herbich et al . (1984), and Markle (1986 

 and 1989) . 



29. Sawaragi (1966) was among the earliest researchers to attempt to 

 estimate toe scour at rubble-mound structures. In his studies, numerous 2-D 

 tests were conducted using a permeable plate having holes sufficient to 

 simulate appropriate void ratios to isolate scour depth from subsidence and 

 subsequently determine the effect of various parameters on structure 

 subsidence and toe scour. Sawaragi found that a relation existed between the 

 void ratio of the structure, the coefficient of wave reflection, and depth of 

 scour. Generally, results reported indicated that although the reflection 

 coefficient, K r = H,./^ , was roughly constant for void ratios greater than 

 20 percent, it increased quickly for smaller values of void ratio. H r and H x 

 are reflected and incident wave heights, respectively. Also, relative scour 

 depth S d /H increased with increasing reflection coefficient, with a break 

 point marked by K r = 0.25, where values of K r less than 0.25 experienced 

 significantly less scour than structures with K r greater than 0.25. For 

 breaking waves, Sawaragi noted that depth of scour is not the result of a 

 constant process - it is rather a process interspersed with episodic accretion 

 and erosional events. Finally, Sawaragi found that maximum scour depth occurs 

 in water depths approximately equal to one half the incident deepwater wave 

 height. This conclusion was based solely on one set of wave conditions and 

 may be suspect. Based on the above findings, Sawaragi proposed a composite 

 cross section similar to that shown in Figure 10 where 1 is calculated by the 

 following: 



s(R + h x ) - s'{h 2 - h x ) (40) 



tan 20° 

 and 



1 = h 2 + R c - S ( R + h) s'(h 2 -h.) (41) 



tan 20° = i i 



where R is height from seawater level to the limit of wave runup and R c is the 

 height of the top of the structure relative to sea level when the structure is 

 overtopped; h lt h 2 , s and s' are as shown in Figure 10. Equation 40 is used 

 for cases where the top of the permeable structure is higher than the upper 

 limit of wave runup and Equation 41 is used in cases where the top of the 

 permeable structure is lower than the upper limit of wave runup. 



30. Hales (1980) conducted a survey of scour protection practices in 

 the United States and found that a rule of thumb for minimum toe scour 

 protection is a toe apron measuring 2.0 to 3.0 ft thick and 4.8 ft wide. In 

 the northwest United States (including Alaska), aprons are commonly 3.0-5.0 ft 

 thick and 10.0-25.0 ft wide. Materials used vary from quarry-run stone up to 

 1.0 ft in diameter to gabions 1.0 ft thick. 



29 



