In three of the small-scale tests (Fig. 48) , toe depths were varied 

 by a factor of two. Therefore, scale effects within the runup results 

 of each study are potentially present. 



Runup values of Saville (1955) are maximum values, although most 

 studies tend to use average values. In cases of equal wave conditions 

 (i.e., same d^/H^ and H^/gT 2 values), the larger toe depths in 

 Saville 's tests generally gave larger relative runup. The apparent 

 scale effects are large in some cases, with the larger depths giving 

 relative runup values as much as 45 percent greater than the smaller 

 depth. However, the limited data did not exhibit consistent trends 

 when analyzed. Much of the apparent scale effect may result from 

 (a) use of maximum runup rather than the average, (b) reporting runup 

 values to the nearest foot in prototype, and (c) effects of differing 

 relative bottom slope lengths (-c/L) for the different toe depths. 



Saville (1956) conducted more extensive testing, and again varied 

 the toe depths. Possible scale effects are noticed in some cases when 

 the data are plotted for equal values of d^/H^ and H^/gT 2 . However, 

 the percentage difference in runup for the two toe depths is much less 

 than in the earlier tests. The differences between results obtained in 

 the two water depths did not seem to warrant separation of the data by 

 depth (i.e., according to scale) and beach-slope length, and thus the 

 smooth-slope runup curves given previously are derived in certain cases 

 for data of different water depths but for the specific dimensionless 

 wave conditions noted. For this reason also, the data points for 

 Re = 3.9 x 10 1 * and Rg = 1.1 x 10 5 in Figure 48 are the same, having 

 been determined from the smooth-slope curves (Fig. 22) . 



The tests of Hudson, Jackson, and Cuckler (1957) were limited in 

 the range of wave steepnesses. For de/H£ * 1.5, essentially only two 

 wave steepnesses were tested, H^/gT 2 «* 0.0067 and 0.010. Variations in 

 beach-slope length were also tested for these wave conditions. For each 

 geometrical arrangement and for constant dg/H^, only two runup values 

 are available, and the values in Figure 48 are interpolated from the 

 applicable pairs of data; i.e., the values in Figure 48 for the 1 on 3 

 slope are based on two relative beach-slope lengths, each of which was 

 subjected to two different incident wave steepnesses, for a total of 

 four test conditions. The 1 on 6 slope values are based on three dif- 

 ferent relative beach-slope lengths, using two different scales (dif- 

 ferent toe depths) for a total of six test conditions. 



The range of runup values for each H^/gT 2 value at Rg = 9.0 x 10^ 

 in Figure 48 is caused by the differences in relative beach-slope length. 

 For the 1 on 3 slope, the lower runup values are associated with the 

 longer slope length, L, as expected, and that slope length is the 

 same (in relative terms) as used for the large scale (R e = 3.75 x 10 6 ) . 

 For the 1 on 6 slope, the higher runup values at R g = 9.0 x lo 4 are 

 associated with the longer slope length, t, which is not the expected 

 result; however, these runup values are essentially the same as obtained 



109 



