************* EXAMPLE PROBLEM 2 



************** 



GIVEN : An impermeable structure has a smooth slope of 1 on 3 



("18.4° or 0.322 radians) and is fronted by a horizontal bottom. 

 The design depth at the structure toe is d s = 10.0 meters; 

 design wave height is H = 1.25 meters; and design wave period 

 is T = 3.2 seconds. 



FIND : Using the flow chart in Figure 6, determine the expected rela- 

 tive runup of a wave approaching the structure at perpendicular 

 incidence. 



SOLUTION : This problem differs from example problem 1 only in structure 

 slope; some values are obtained from example problem 1. Following 

 the flow chart, 



sin 2 9 J2Q _ (0.316) 2 | 2(0.322) '_ Q 0022g 



2tt 2 \ tt 2tt 2 



jSE 



*° » 0.01246 > si " 29 £ 



gT 2 * 2tr 2 



Thus, the wave may be breaking. Next, 



0.031 tan 2 = 0. 031(0. 333) 2 = 0.00345. 

 Thus, 



-=— = 0.01246 > 0.031 tan 2 6 = 0.00345 , 

 gT 2 



and the wave is breaking. Also, because cot 6 = 3 > 2, equation (8) 

 may be used. 



From Figure 5, q = 0.555 for cot 9 = 3; q - 1 = -0.445. 



By equation (8) , 



£-= (cot er 1 - ^ (4.23)(io) 2 (q- 1 ) (^\ q 



H i \ gT 2 / 



= (3)- 1 - 04 (4.23)(10)" - 89 (0.01246)-°- 4 ^ 5 

 = (0.319) (4.23) (0.1288) (7.0387) 



D 



— — = 1 223 



27 



