This equation defines the line which is approximately tangent to the 

 dg/gT 2 lines (see Fig. 3), particularly for the higher H^/gT 2 values, 

 and is equivalent to the line of complete breaking in Figure 3 if 

 cot 9 = 2.25. The value of q can be taken from Figure 5 for the 

 appropriate structure slope. Values of q vary approximately between 

 0.4 and 0.7. If a value of q = 0.5 is used, equation (8) essentially 

 reduces to Hunt's (1959) equation (eq. 7) for H as H^; however, equa- 

 tion (8) appears to give values which agree somewhat better with experi- 

 mental values using H^. 



Equation (8) is applicable only for smooth slopes where cot 6 > 2.0. 



Alternatively, the runup curves given in Section V,l may be used for 



cot 8 > 2.0, but the curves must be used for cot < 2.0 (i.e., steeper 

 slopes) . 



Equation (8) was derived from data for a structure on a flat bottom, 

 but it may be applied to structures on sloping bottoms provided dg/H^ 

 is approximately three or greater; i.e., the equation is applicable to 

 waves which do not break before reaching the structure, but do break on 

 the structure slope. 



Basically, equation (8) will provide conservative values. Nonbreak- 

 ing waves will have relative runup equal to or less than predicted by 

 this equation because the relative runup from nonbreaking waves is also 

 a function of relative depth. Relative depth is not included in the 

 equation. If the wave climate at a location consists primarily of waves 

 of high steepness, nearly all waves will break on the structure and 

 equation (8) may be used. Such a situation would exist if the waves 

 meet the conditions of equation (5), using H^ « H. 



In contrast, some wave climates have predominantly long waves (low 

 d s /gT 2 values) of low steepness. This situation occurs, for example, 

 on the southwestern coast of the United States. Design wave conditions 

 may include waves which break on the structure slope, in front of the 

 structure because of depth limitations, or nonbreaking waves of the 

 surging type. For example, Vanoni and Raichlen (1966) tested long- 

 period surging waves for a California location. Use of equation (8) 

 to derive smooth-slope runup from surging waves or waves breaking in 

 front of the structure would give relative runup values too high, 

 although such a conservative value might be desired. Furthermore, as 

 noted later in the discussion of the qualitative aspects of runup, the 

 absolute runup, R, maximum will occur for the maximum steepness of an 

 incident wave train of constant dg/gT 2 providing the waves do not 

 break before reaching the structure. 



A flow chart for runup on a smooth structure slope fronted by a 

 horizontal bottom is given in Figure 6. Variables subscripted with 

 the letter i are incident wave characteristics at the location where 

 measured. 



23 



