The functional forms of the criteria in equations (4-29) and (4-30) are 

 fairly consistent, but both classifications might be considered in predicting 

 the occurrence of eroded or accreted beaches. 



f. Slope of the Foreshore . The foreshore is the steepest part of the 

 beach profile. The equilibrium slope of the foreshore is a useful design 

 parameter, since this slope, along with the berm elevation, determines minimum 

 beach vd.dth. 



The slope of the foreshore tends to increase as the grain size increases 

 (U.S. Army Corps of Engineers, 1933; Bascom, 1951; King, 1972, p. 324.) This 

 relationship betvreen size and slope is modified by exposure to different wave 

 conditions (Bascom, 1951; Johnson, 1956); by specific gravity of beach 

 materials (Nayak, 1970; Dubois, 1972); by porosity and permeability of beach 

 material (Savage, 1958), and probably by the tidal range at the beach. 

 Analysis by King (1972, p. 330) suggests that slope depends dominantly on sand 

 size and also significantly on an unspecified measure of wave energy. 



Figure 4-35 shows trends relating slope of the foreshore to grain size 

 along the Florida Panhandle, New Jersey-North Carolina, and U.S. Pacific 

 coasts. Trends shown on the figure are simplifications of actual data, which 

 are plotted in Figure 4-36. The trends show that, for constant sand size, 

 slope of the foreshore usually has a low value on Pacific beaches, inter- 

 mediate value on Atlantic beaches, and high value on gulf beaches. 



This variation in foreshore slope from one region to another appears to be 

 related to the mean nearshore wave heights (see Figs. 4-17, 4-18, and Table 4- 

 4). The gentler slopes occur on coasts with higher waves. An increase in 

 slope with decrease in wave activity is illustrated by data from Half Moon Bay 

 (Bascom, 1951) and is indicated by the results of King (1972, p. 332). 



The inverse relation between slope and wave height is partly caused by the 

 relative frequency of the steep or high eroding waves which produce gentle 

 foreshore slopes and the low accretionary poststorm waves which produce 

 steeper beaches (see Figs. 4-1, 4-32, and 4-33). 



The relation between foreshore slope and grain size shows greater scatter 

 in the laboratory than in the field. However, the tendency for slope of the 

 foreshore to increase with decreasing mean wave height is supported by 

 laboratory data of Rector (1954, Table 1). In this laboratory data, there is 

 an even stronger inverse relation between deepvater steepness, H /L , and 

 slope of the foreshore than betvreen H and the slope. 



The following statements summarizing the results on foreshore slope for 

 design purposes are supported by available data: 



(1) Slope of the foreshore on open sand beaches depends principally 

 on grain size and (to a lesser extent) on nearshore \*ave height. 



(2) Slope of the foreshore tends to increase with increasing median 

 grain size, but there is significant scatter in the data. 



(3) Slope of the foreshore tends to decrease with increasing wave 

 height, again with scatter. 



4-86 



