WAVE RUNUP ON ROUGH SLOPES 



by 

 Philip N. Stoa 



I. INTRODUCTION 



Prediction of wave runup on coastal structures is necessary to deter- 

 mine an adequate crest elevation if overtopping is to be prevented, or to 

 help determine the extent of overtopping. Most protective structures in 

 high-energy areas have rough, highly permeable, surfaces which absorb 

 wave energy and reduce runup, but experimental studies of runup on rough 

 slopes are complex. Consequently, runup studies have usually been lim- 

 ited in scope or have dealt with smooth slopes. Very few runup studies 

 have been conducted on rough slopes using waves which break at or near 

 the structure toe, yet this is often the design condition. This report 

 presents a method of estimating wave runup for these conditions, as well 

 as more detailed predictions for other wave conditions specifically 

 tested in the laboratory. (See Stoa, 1978a, for background information.) 



II. DEFINITION OF TERMS 



Variables used in this and related reports (Stoa 1978a, 1978b) are 

 shown in Figure 1 and are defined as: R, runup; 8, angle of structure 

 face with horizontal; d, water depth; dg, water depth at toe of struc- 

 ture; B, angle of bottom slope at structure toe; and h^, height of 

 core above toe of structure. Not shown in Figure 1 is Y^-p, the armor- 

 unit length dimension. For quarrystone, K^ is the nominal diameter; 

 for concrete armor units, K^, is a specified length dimension. L and 

 H are the. wave length and wave height, respectively, in water depth, d. 

 The same wave may be described by an equivalent deepwater wave (d/h > 0.5) 

 for which the dimensions would be L^ and H^!,. L^ is the deepwater 

 wavelength and may be determined if the wave period, T, is known (L,-, = 

 gT^/2T7) . H^ is the equivalent unrefracted deepwater wave height and is 

 used because it avoids the problem of defining the wave height in varying 

 depths over a sloping bottom where the wave may already have broken. The 

 wave height in deep water is related to the unbroken wave height in a 

 shallower depth by the shoaling coefficient, K„ = H/H^. The shoaling 

 coefficient and wavelength, L, may be determined from Tables C-1 or 

 C-2 in the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, 

 Coastal Engineering Research Center, 1977) when L^ and the depth, d, 

 are known. 



III. METHODS OF DATA PRESENTATION 



Results of runup experiments are presented in two forms. The first 

 form is more detailed and is used for results of tests which covered a 

 wide range of conditions. Relative runup, R/Hq, is given by a set of 

 design curves and is a function of structure slope (cot e), wave steep- 

 ness parameter (H^/gT^) , relative depth (d^/H^) , and relative stone size 

 (H^/k^) . 



