R" = 243 (0.995) = 241 kN/m (16,500 lb/ft) 

 Similarly, for the moment 



M" = M" sin^e = 558 (sin 84°)^ 



M" = 558 (0.995)^ = 553 ^^ (124,200 ^^^ ) 



m 



ft 



The total force and overturning moment are given by the sums of the reduced 

 dynamic components and the unreduced hydrostatic components. Therefore, 



R^ = 241 + 65 = 306 kN/m (21,000 lb/ft) 



M, = 553 + 78 = 631 ^^^ (141,900 lizi^ ^ 

 v m It 



*************************************** 



7. Stability of Rubble Structures . 



a. General . A rubble structure is composed of several layers of random- 

 shaped and random-placed stones, protected with a cover layer of selected 

 armor units of either quarrystone or specially shaped concrete units. Armor 

 units in the cover layer may be placed in an orderly manner to obtain good 

 wedging or interlocking action between individual units, or they may be placed 

 at random. Present technology does not provide guidance to determine the 

 forces required to displace individual armor units from the cover layer. 

 Armor units may be displaced either over a large area of the cover layer, 

 sliding down the slope en masse, or individual armor units may be lifted and 

 rolled either up or down the slope. Empirical methods have been developed 

 that, if used with care, will give a satisfactory determination of the 

 stability characteristics of these structures when under attack by storm 

 waves . 



A series of basic decisions must be made in designing a rubble struc- 

 ture. Those decisions are discussed in succeeding sections. 



b. Design Factors . A primary factor influencing wave conditions at a 

 structure site is the bathymetry in the general vicinity of the structure. 

 Depths will partly determine whether a structure is subjected to breaking, 

 nonbreaking, or broken waves for a particular design wave condition (see 

 Section I, WAVE CHARACTERISTICS). 



Variation in water depth along the structure axis must also be considered 

 as it affects wave conditions, being more critical where breaking waves occur 

 than where the depth may allow only nonbreaking waves or waves that overtop 

 the structure. 



When waves impinge on rubble structures, they do the following: 



(a) Break completely, projecting a jet of water roughly perpendicular 

 to the slope. 



7-202 



