used on trunks. Similar comparisons of test results were used to estimate 

 K„ values for armor units on structure heads. 



(5) Under similar wave conditions, the head of a rubble structure 

 normally sustains more extensive and frequent damage than the trunk of the 

 structure. Under all wave conditions, a segment of the slope of the rounded 

 head of the structure is usually subject to direct wave attack regardless of 

 wave direction. A wave trough on the lee side coincident with maximum runup 

 on the windward side will create a high static head for flow through the 

 structure. 



(6) Sufficient information is not available to provide firm guidance 

 on the effect of angle of wave approach on stability of armor units. Quarry- 

 stone armor units are expected to show greater stability when subject to wave 

 attack at angles other than normal incidence. However, an analysis of limited 

 test results by Whillock (1977) indicates that dolos units on a l-on-2 slope 

 become less stable as the angle of wave attack increases from normal incidence 

 (0") to approximately 45°. Stability increases rapidly again as the angle of 

 wave attack increases beyond 45°. Whillock suggests that structures covered 

 with dolosse should be designed only for the no-damage wave height at normal 

 incidence if the structure is subject to angular wave attack. The stability 

 of any rubble structures subjected to angular wave attack should be confirmed 

 by hydraulic model tests. 



Based on available data and the discussion above. Table 7-8 presents 

 recommended values for K^ . Because of the limitations discussed, values in 

 the table provide little or no safety factor. The values may allow some 

 rocking of concrete armor units, presenting the risk of breakage. The K^'s 

 for dolosse may be reduced by 50 percent to protect against breakage, as noted 

 in the footnote to Table 7-8. The experience of the field engineer may be 

 utilized to adjust the K^ value indicated in Table 7-8, but deviation to 

 less conservative values is not recommended without supporting model test 

 results. A two-unit armor layer is recommended. If a one-unit armor layer is 

 considered, the Kn values for a single layer should be obtained from Table 

 7-8. The indicated K^ values are less for a single-stone layer than for a 

 two-stone layer and will require heavier armor stone to ensure stability. 

 More care must be taken in the placement of a single armor layer to ensure 

 that armor units provide an adequate cover for the underlayer and that there 

 is a high degree of interlock with adjacent armor units. 



These coefficients were derived from large- and small-scale tests that 

 used many various shapes and sizes of both natural and artificial armor 

 units. Values are reasonably definitive and are recommended for use in design 

 of rubble-mound structures, supplemented by physical model test results when 

 possible. 



The values given in Table 7-8 are indicated as no-damage criteria, but 

 actually consider up to 5 percent damage. Higher values of percent damage to 

 a irubble breakwater have been determined as a function of wave height for 

 several of the armor unit shapes by Jackson (1968b). These values, together 

 with statistical data concerning the frequency of occurrence of waves of 

 different heights, can be used to determine the annual cost of maintenance as 

 a function of the acceptable percent damage without endangering the functional 

 characteristics of the structure. Knowledge of maintenance costs can be used 



7-210 



