test sections is costly both in terms of time and money, and to repeat 

 the tests a sufficient number of times to obtain data that can be ana- 

 lyzed on a statistical basis is usually not feasible. Unfortunately, 

 the shape of the armor units, the placement of the armor units, and the 

 waveforms which impinge on the structure slope are also important varia- 

 bles in stability of the structure. The waveform is a function of the 

 wave height and period and the phase relations between the incident and 

 reflected waves. Thus, large variations in stability often occur between 

 successive tests when there are no discemable differences in the test 

 conditions. When differences in stability occur, there is no recourse 

 but to repeat the test. The question then arises, because a large num- 

 ber of repeat tests may not be feasible, as to which set of test results 

 is the most representative of the conditions that will occur in the proto- 

 type considering the difficulties of reproducing the prototype wave trains 

 in the model and duplicating the placing techniques to be used by the con- 

 tractor in constructing the prototype breakwater. These and perhaps other 

 factors result in a situation where more than 100 percent variation has 

 occurred in the stability coefficient for a particular type of armor unit 

 and breakwater section; i.e., K in equation (6-4b) , obtained by two 

 different laboratories with comparable facilities and personnel. 



5. Utilization of Hydraulic Models . 



a. Problems Susceptible to Model Analysis . Hydraulic models should 

 be used only if the phenomena involved are too complicated and not under- 

 stood sufficiently to allow solution of the problems by theoretical study, 

 or have not been solved by systematic experiments already conducted. How- 

 ever, a large number of problems in hydraulic engineering cannot be solved 

 satisfactorily without the aid of scale models. Most physical systems can 

 be studied by scale models if valid scaling laws are available. Scaling 

 laws for problems involving the stability of coastal structures (derived 

 in Section VI, 2) have shown that the stability of structures subjected to 

 the forces of wave action can be investigated successfully if the scale 

 effects, resulting from the incorrect reproduction of viscous forces, can 

 be made negligible by use of relatively large models. Because of the high 

 cost of providing a shelter and constructing and operating the model, 

 smaller models can also be used when enough experimental data are avail- 

 able for wave forces on the structure as a function of Reynolds number. 



As indicated in Section VI, 2, adequate scale-effect data are not presently 

 available for all types of coastal structures. However, nearly all of the 

 major problems concerning the stability of coastal structures are believed 

 to be susceptible to scale-model analysis after experimental data become 

 available. 



b. Advantages and Disadvantages of Hydraulic Models . The engineer 

 uses scale models for more reliable solutions to design problems than can 

 be derived by mathematical analysis. When an existing structure is not 

 performing satisfactorily, or when a proposed structure cannot be designed 

 adequately by analytical means, together with information in the litera- 

 ture, the use of a scale model may be indicated. Generally, scale models 

 can be regarded as a type of analog for solving differential equations of 



368 



