4. Wave Period Effects . 



Some laboratory studies of riprap stability conducted with monochromatic 

 waves (i.e., waves of constant height and period) show a strong influence of 

 wave period (e.g., see Thomsen, Wohlt, and Harrison, 1972; Ahrens and 

 McCartney, 1975); other - studies such as Hudson and Jackson (1962) do not. A 

 comprehensive laboratory study conducted at the Hydraulic Research Station 

 (HRS) (1975) in Wallingford, England, for the Construction Industry Research 

 and Information Association (CIRIA) of the United Kingdom, concluded that there 

 was little influence of wave period on riprap stability for tests with irregu- 

 lar waves. The tests at HRS included a wide range of irregular wave conditions 

 considered to be typical of naturally occurring conditions. 



Wave period is not considered in this analysis of riprap stability because 

 (a) the monochromatic test results were inconsistent, (b) the HRS tests with 

 natural wave conditions do not indicate any period effects, and (c) there is 

 no accepted method, at present, to account for the influence of wave period 

 on riprap stability. 



5. Zero-Damage Conservatism and the Design Wave Height . 



The equation recommended for calculating the zero-damage stability numbers 

 (eq. 5) is more conservative than some other design equations; e.g., the 

 equation given in the SPM is 



Krr = — \=2.2 (6) 



3 



cot 6 



where Krr is the stability coefficient for riprap. The additional conserva- 

 tism is intended to account for the most severe wave breaking conditions and 

 the effects of irregular wave attack. Equations (5) and (6) are compared in 

 Figure 2 which shows that they give about the same stability number on a steep 

 slope (1 on 2) but diverge considerably for flatter slopes. The reason for the 

 divergence is that equation (5) is based on a small absolute measure of damage,' 

 while equation (6) is based on a 5-percent allowable damage which causes it to 

 be more slope dependent. Since a percent-damage equation is useful in eval- 

 uating the progress of damage toward failure, the following equation was devel- 

 oped for a 5-percent level of damage (also shown in Fig. 2) 



N s = 1.37(cot 6) 1/3 (7) 



Equation (7) is consistent with equation (5) since both equations were devel- 

 oped primarily from large wave tank tests of riprap stability conducted by 

 Ahrens (1975) and both were based on the most damaging wave conditions. Equa- 

 tion (7) is equivalent to Krr = 2.37 and can be used to compute the median 

 riprap weight in situations where some damage could be tolerated. In Figure 

 3, equation (7) is used to give perspective on the concept of reserve stability 

 discussed in the next subsection. 



Ahrens (1975) and ETL 1110-2-222 indicate that stability coefficients as 

 high as 4.37 can be used if damage to the riprap can be accepted. Using 

 K RR =4.37 necessitates consideration of maintenance costs and safety factors. 



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