The Minikin formula was originally derived for composite breakwaters 

 composed of a concrete superstructure founded on a rubble substructure; 

 strictly, D and Ljj in equation (7-85) are the depth and wavelength at the 

 toe of the substructure, and d is the depth at the toe of the vertical wall 

 (i.e., the distance from the sWl down to the crest of the rubble substruc- 

 ture). For caisson and other vertical structures where no substructure is 

 present, the formula has been adapted by using the depth at the structure toe 

 as d , while D and L^ are the depth and wavelength a distance one 

 wavelength seaward of the structure. Consequently, the depth D can be found 

 from 



D = dg + L^ m (7-88) 



where L ^ is the wavelength in a depth equal to d , and m is the nearshore 

 slope. The forces and moments resulting from the hydrostatic pressure must be 

 added to the dynamic force and moment computed above. The triangular hydro- 

 static pressure distribution is shown in Figure 7-99; the pressure is zero at 

 the breaker crest (taken at Hi/2 above the SWL), and increases linearly to 

 w(d + Hr/2) at the toe of the wall. The total breaking wave force on a wall 

 per unit wall length is 



(7-89) 



where R„ is the hydrostatic component of breaking wave on a wall, and the 

 total momeTit about the toe is 



M^ = M + \ "^ ^ ^ = M + M (7-90) 



t m 6 m s 



where M„ is the hydrostatic moment. 



Calculations to determine the force and moment on a vertical wall are 

 illustrated by the following example. 



*************** EXAMPLE PROBLEM 34 ************** 



GIVEN ; A vertical wall, 4.3 m (14 ft) high is sited in sea water with d^ = 

 2.5 m (8.2 ft). The wall is built on a bottom slope of 1:20 (m = 0.05) . 

 Reasonable wave periods range from T=6s to T=10s. 



FIND: 



(a) The maximum pressure, horizontal force, and overturning moment about 

 the toe of the wall for the given slope. 



(b) The maximum pressure, horizontal force, and overturning moment for the 

 6-second wave if the slope was 1:100. 



7-182 



