beach slope or breaker type was not determined. For breaking waves, as the beach slope 

 steepens, the wave breaking becomes more vigorous (Battjes 1974) and the slamming 

 forces increase dramatically as the waves start plunging to collapsing (Bruun 1985). 

 Van der Meer's spilling breakers were not very severe with respect to stability relative 

 to plunging or collapsing breakers. 



Equations 3.7 and 3.8 do not indicate decreasing stability as the depth to 

 wave length ratio decreases and the wave breaking becomes more severe. Carver and 

 Wright (1991) showed that stability decreases dramatically with decreasing relative 

 depth. The minimum stability condition occurs where the wave breaking is 

 characterized by plunging to collapsing breakers at the toe of the structure. Figure 3.3 

 shows some of Carver and Wright's data replotted with Hudson stability coefficient, Kj^ 

 in Equation 2.1, as a function of relative depth. Here the water depth h, at the structure 

 toe is normalized by the local wave length L^ based on the peak spectral period 

 computed using linear wave theory. It is clear that the Hudson stability coefficient 

 decreases with decreasing relative depth. This is a reflection of the severity and location 

 of the breaking wave and the resulting wave forces. As was shown in Chapter 2, the 

 critical wave forcing for incipient motion was uplift occurring under the steep wave face 

 for collapsing to plunging breakers. For depth-limited conditions, as the water depth 

 decreases relative to the wave length, the wave face steepens, and vertical forces at the 

 steep wave face are able to loosen and mobilize the stones. Therefore, for depth-limited 



49 



