maximum relative runup and the maximum dimensional runup occur at the 

 minimum dg/H<J, value. For structures sited on a 1 on 10 sloping 

 bottom, maximum dimensional runup may or may not be coincident with the 

 maximum relative runup determined for a range of wave conditions. If 

 depth, d s , and wave steepness are assumed constant, then maximum 

 relative runup occurs when 1.0 < dg/H^ < 1.5, but maximum dimensional 

 runup occurs when dg/H^ is a minimum (in this study when d g > 0, 

 then (d s /tio^min = °- 6 )- In cases where a beach slope is flatter than 

 1 on 10, then for a given wave steepness, the maximum relative runup 

 will occur for somewhat higher dg/H^ values (1.5 < dg/H^ < 2.0). 

 However, if wave height, H^, and wave steepness are held constant, 

 the maximum dimensional runup will be coincident with maximum relative 

 runup as d s /H^ varies (i.e., as d s changes). The maximums 

 (R/H(>) and R) may occur at any value of dg/H^ (including dg/H^ = 0) 

 depending on the wave steepness being considered. Runup maximums would 

 occur at intermediate values of dg/H^ (1.0 < dg/H^ < 1.5) for high 

 values of H^/gT 2 , but at low values of dg/H^ for low values of 

 H o/gT 2 - F° r & given wave period and constant depth, dg , (with wave 

 steepness varying as dg/H^ varies) , maximum dimensional runup is 

 generally not coincident with maximum relative runup; furthermore, the 

 maximum dimensional runup may occur at other than the minimum dg/H^ 

 value. These relationships are highlighted in example problem 7 in 

 Section V,l,e. 



V. EXPERIMENTAL RESULTS 



1. Smooth Slopes . 



a. Past Research . Smooth slopes are simplest to construct in 

 experiments, and the results are easiest to analyze. Consequently, 

 many laboratory tests have been carried out using smooth slopes. A 

 partial listing of runup studies conducted with smooth slopes and the 

 ranges of conditions tested are given in Table 2. Wave conditions for 

 most of these studies appear to cover a wide range, but many of the 

 actual conditions tested (H^/gT 2 and d s /gT 2 pairs) are rather limited. 



Granthem (1953) was one of the earliest to investigate the effects 

 of wave steepness, relative depth, and structure slope on runup. How- 

 ever, runup values are generally below values determined from this 

 study's design runup curves based principally on data of Saville (1956) 

 and Savage (1958). Some differences are appreciable, and the reasons 

 are unclear since the model dimensions were similar. Saville (1955), 

 in conjunction with overtopping experiments, reported runup results for 

 structures sited on a 1 on 10 beach. He tabulated the maximum observed 

 runup values for each condition but the results had greater variations 

 in trends than shown by later reports using average values. Saville 

 (1956) conducted a large number of tests investigating effects of rela- 

 tive depth, relative steepness, structure slope, and beach slope. Tests 

 of beach-slope effects were limited to structures sited on the horizontal 

 wave tank bottom and on a 1 on 10 slope. 



38 



