IV. CALCULATION OF WAVE FORCE AND OVERTURNING MOMENT 



The Miche-Rundgren method in SPM Section 7.32 provides a method for deter- 

 mining wave force and overturning moment when either a wave crest or trough 

 acts against a wall. For oblique incidence some parts of the wall are acted 

 on by wave crests while others are acted on by wave troughs. Thus, there is a 

 variation in force along the wall that can be assumed in proportion to the 

 wave profile along the wall; I.e., the maximum wave force corresponds to the 

 wave crest, the minimum wave force corresponds with the wave trough, and the 

 variation in force between is assumed proportional to the ordinate of the wave 

 profile. 



It remains to select an appropriate description of the wave profile. For 

 waves in shallow water the cnoidal theory outlined in Section 2.26 of the SPM 

 provides a satisfactory description. Stream-function wave theory (Dean, 1974) 

 will also provide a satisfactory description of the profile; however, for pur- 

 poses of illustration and convenience the cnoidal theory will be used here. 



V. EXAMPLE PROBLEM 



The computation of forces and moments is best illustrated by an example 

 problem. 



GIVEN : A concrete sheet-pile groin perpendicular to shore is subjected to 

 waves 6 feet (1.83 meters) high with a period of 8.0 seconds. Waves 

 approach the groin so that the angle between the wave crest and a perpen- 

 dicular to the groin is 30°. The water depth at the end of the groin is 10 

 feet (3.05 meters). The beach profile along the windward side of the groin 

 is given in Figure 4. 



-300 -200 -100 



100 200 300 400 

 Distonce from Shoreline ( ft) 



500 600 700 



Figure 4. 



5ach and groin profile, 



FIND : Ignoring changes in wave direction as the wave propagates toward shore 

 (refraction) and changes in depth near shore (shoaling), determine the maxi- 

 mum wave force and overturning moment acting on the groin when the wave 

 crest passes a point 400 feet (121.9 meters) from shore (100 feet or 30.5 

 meters from the seaward end of the groin) and estimate the distribution of 

 force and moment along the groin at that instant. 



10 



