A GRAPHICAL METHOD FOR CHECKING THE DESIGN HEIGHT OF 

 STRUCTURES SUBJECTED TO WAVE RUN-UP 



by 



R. P. Savage 

 Hydraulic Engineer, Beach Erosion Board 



INTRODUCTION 



Coastal engineers are often called upon to design protective struc- 

 tures for lake or ocean shores. Some of these structures, especially beach 

 fills and protective dunes, become a part of the nearshore profile of the 

 water basin. In such cases, the existing nearshore profile significantly 

 affects the design of the protective structure, especially the height to 

 which it must be built to prevent overtopping by wind-generated waves. 

 Since the nearshore profiles of most water basins vary considerably in 

 short distances from place to place along the same shore, for most designs 

 so many wave run-up computations are required that it is not feasible to 

 adequately check the design at each change in profile by existing methods. 

 This article presents a method for checking whether or not a structure 

 design is adequate by computing a "critical profile" which, when plotted 

 on transparent paper, can be overlaid on field profile plots to determine 

 if run-up from expected waves will exceed the structure height. 



WAVE RUN-UP DATA 



Much work has been done to establish the relationships between wave 

 run-up, structure slopes, and wave characteristics. This work has resulted 

 in establishment of some empirical relationships which are shown in Figure 1. 

 In this figure the relationship between the relative wave run-up, R/H' (where 

 R is the vertical height to which the wave runs up the slope and H' is the 

 deep water wave height corrected for refraction) and the slope of the beach 

 or structure in terms of a function of the deep water wave steepness H* /T^ 

 (T is the wave period) is shown. The relationships shown in this figure have 

 some limitations. First, they are valid only when the waves approach normal 

 to the beach. Second, the beach or structure must be relatively smooth and 

 impermeable. In this respect, the relationships apparently hold for beaches 

 composed of sand which is about 1 mm. or less in median diameter. When the 

 beach material is larger, conservative values of run-up will be predicted by 

 the relationships of Figure 1 and the results may become over-conservative 

 for material sizes larger than 1 ram. Third, the water depth over the toe of 

 the slope must be equal to or greater than three wave heights. The magnitude 

 of the error involved in using the data from Figure 1 for other than ex- 

 pressed limiting conditions will depend upon the extent by which the limita- 

 tions are exceeded. Other data which may be used to consider relatively 

 large wave heights at the toe of the slope and the roughness of the slope 

 are given in references 1, 2, and 3. 



