V. SUMMARY AND CONCLUSIONS 



This report presents the results of an analytical study of the 

 reflection and transmission characteristics of porous rubble-mound 

 breakwaters. An attempt was made at making the procedures entirely 

 self-contained by introducing empirical relationships for the hydraulic 

 characteristics of the porous material and by establishing experimentally 

 an empirical relationship for the friction factor that expresses energy 

 dissipation on the seaward slope of a breakwater. 



The results are presented in graphical form and require no use of 

 computers, although the entire approach could be programmed. The 

 procedures were developed in such a manner that the information required 

 to carry out the computations can be expected to be available. Thus, for 

 a trapezoidal, multi layered breakwater subject to normally incident, 

 relatively long waves the information required is: 



(a) Breakwater configuration: breakwater geometry and stone size and 

 porosity of the breakwater materials 



(b) Incident wave characteristics; wave amplitude, period, and water 

 depth. 



Only the porosity of the breakwater materials may be hard to come 

 by. It is recommended that the sensitivity of the results to the 

 estimate of the porosity, n, be investigated. 



The hydraulic flow resistance in the porous medium is expressed by 

 a Dupuit-Forchheimer relationship and empirical formulas are adopted. 

 The investigation shows that reasonably accurate results are obtained 

 by taking 



^o " ^-^ (177) 



a = 1150 

 o 



in equations (51) and (52). To estimate reflection and transmission 

 characteristics of a prototype structure only the value of Bq needs to be 

 known. For laboratory experiments the value of the ratio, Mq/Pq is 

 important in assessing the influence of scale effects. In a laboratory 

 setup it is possible to determine the best values of a^ and 

 simple experimental procedure used by Keulegan (1973). Thus, it was 

 found that the porous materials tested by Sollitt and Cross (1972) 

 showed a value of a^ = 2,700, a better value than that given by equation 

 (177). However, the important thing to note is that the analysis carried 

 out in Section II of this report presents a method for assessing the 

 severity of scale effects in hydraulic models of porous structures. The 

 empirical relationships for the flow resistance of porous materials have 

 been demonstrated to be fairly good for porous materials consisting of 

 gravel-size stones, diameter less than 2 inches (5 centimeters). 



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