Line of Constant d s /gT 2 



/ /Point of Maximum Relative Runup, R/H 



•Point of Maximum Runup, R 



Wave Breaking ot or Seaward 

 of Structure Toe 



Lines of Constant R/gT 2 



Figure 13. Conditions for wave breaking on 



beach slope in front of structure. 



For structures sited on horizontal bottoms, the maximum dimensional 

 runup, R, for a given relative depth, dg/gT 2 , occurs for the maximum 

 wave steepness. The maximum steepness of an incident wave is limited 

 according to the theoretical equation (Miche, 1944), 





0.14 tanh 



27Td 



(9) 



The actual maximum wave steepness measured in runup experiments is less 

 because of reflection effects from the structure and, in laboratory 

 testing, because of difficulty in generating a nonbreaking wave of 

 such steepness. Saville's (1956) tests had maximum steepness values 

 equal to 70 percent of that predicted for the shorter wave periods, 

 and « 57 percent of that predicted for the longer periods. Only a few 

 other experiments have had greater wave steepnesses. It is unclear 

 whether these reduced wave steepness values were chosen maximums, 

 functions of equipment limitations, or experimental maximums designed 

 to prevent the wave's breaking in transit to the structure. 



For structures sited on sloping beaches, the maximum dimensional 

 runup occurs for waves breaking at or near the structure toe. Graphi- 

 cally, for constant d g /gT 2 , maximum runup, R, occurs for the wave 

 steepness where the negative slope of the R/H^ versus d s /gT 2 curve 

 becomes steeper than the slope of a line of constant R/gT 2 (Fig. 13). 



However, the smooth-slope design curves given in Section V,l do 

 not list values of dg/gT 2 . In using these curves, the following com- 

 ments on relative runup and dimensional runup are important. For struc- 

 tures sited on horizontal beaches, for a given wave steepness, both the 



37 



