REVISED WAVE RUNUP CURVES FOR SMOOTH SLOPES 



by 

 Philip N. Stoa 



I. INTRODUCTION 



Wave runup is the vertical distance above Stillwater level (SWL) 

 reached by a wave incident to a structure or beach. Prediction of wave 

 runup on coastal structures is necessary to determine an adequate crest 

 elevation to prevent overtopping or to help determine the extent of 

 overtopping. Wave runup curves for structures with either smooth or 

 rough slopes have previously been presented in the Shore Protection 

 Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research 

 Center, 1977). Runup data of Saville (1956) and Savage (1959), together 

 with data from other reports, have been reanalyzed (Stoa, 1978). This 

 report presents revised smooth-slope runup curves which vary in certain 

 regions from those presented in the SPM. A scale-effect correction 

 curve is also given for application to smooth-slope runup. 



Wave runup is primarily a function of characteristics of the 

 structure and incident wave; wave characteristics are also a function 

 of water depth and bottom slope. The variables are shown in Figure 1 and 

 are defined as: R, runup; 6, angle of structure slope; d, water 

 depth; dg, water depth at toe of structure; g, angle of bottom slope 

 at the structure toe; and -£, horizontal length of the bottom slope 

 seaward of the structure toe. L and H are the wavelength and wave 

 height, respectively, as measured in a water depth, d. The same wave 

 may be described by an equivalent deepwater wave (d/L >i 0.5) for which 

 the dimensions would be Lq and H^. L^ is the deepwater wavelength 

 and Wq is the equivalent unrefracted deepwater wave height. L^ may 

 be determined if the wave period, T, is known (L^ = gT^/2iT) ; this report 

 uses gT^ as the principal measure of deepwater wavelength. H^ 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 wave height in a shallower depth 

 by the shoaling coefficient, H/H^I, or Kg. The shoaling coefficient 

 and wavelength, L, may be determined from Tables C-1 or C-2 in the SPM 

 when Lq and the required depth are known. 



The runup curves are given for three different cases: (a) horizontal 

 bottom at the structure toe; (b) 1 on 10 sloping bottom at the structure 

 toe, with a zero toe depth (d = 0); and (c) 1 on 10 sloping bottom at 

 the structure toe, with toe depths greater than zero (dg > 0). Case (c) 

 has, generally, the potential for the largest waves attacking the struc- 

 ture. A bottom slope of 1 on 10 is relatively steep for ocean coastlines, 

 and its occurrence would be restricted to beach faces with coarse sediments 

 (see Fig. 4-33 in the SPM), backshore areas subject to flooding, or some 

 nearshore areas. However, most bottom slopes would be flatter than 1 on 

 10. Experimental data for runup on structures fronted by flatter slopes 



