(1) Rubble-Mound Structures . Surface tension and elastic forces 

 do not affect the stability of full-scale, rubble-mound structures in the 

 field, and they are also negligible in hydraulic models of such struc- 

 tures. Viscous forces are also negligible for full-scale structures, 

 but they become important in the model if the model is too small. For 

 practical reasons, all rubble-mound stability models cannot be made of 

 sufficient size to eliminate scale effects due to the lack of similar- 

 ity of the viscous forces. Therefore, special tests have been necessary 

 to determine the effects of linear scale and obtain scale-effect correc- 

 tion coefficients for the prediction or transference equations derived 

 based on Froude's law. One such series of tests was conducted by Hudson 

 and Jackson (1953) where a rubble-mound breakwater similar in cross sec- 

 tion to that of an existing breakwater in San Pedro Bay, California (Fig. 

 6-5), was modeled and tested by the Froude law using linear scales of 

 1:30, 1:45, and 1:60. The test results are compared one to the other, 

 and with storm damage to the San Pedro breakwater (Figs. 6-6 and 6-7). 

 These results indicate that for the linear scales, prototype wave di- 

 mensions, and breakwater armor units used in these tests, the Froude law 

 is sufficiently accurate for use in the design of such models. Other 

 tests, the results of which can be used to determine the scale effects 

 and corrective coefficients, were conducted by Dai and Kamel (1969). 

 Their data, plotted to show the relation between Ns and Rn, are 

 given in Figure 6-8; the data points that are in the range of values of 

 Rji between 5.0 x lo^ and 1.0 x 10^ were obtained from tests conducted 

 in the large wave flume at CERC, using waves up to 4 feet in height and 

 armor units weighing up to 162 pounds. The averge value of the stability 

 number as determined by the CERC data can be used as prototype values to 

 obtain approximate corrective coefficients (Ns)p/ (Ns)m- However, more 

 data points are considered necessary for Reynolds numbers from about 



3.0 X 10*^ to 1.0 X 10^ to ensure that accurate values of the ratio 

 (Ns)p/(Ns)in are obtained. 



A few investigations have been conducted from which the effects on 

 test results of some of the "criteria of similitude" can be estimated; 

 however, little quantitative information is available concerning these 

 effects, and more data of this type are needed. There is also a need to 

 standardize the model design and test procedures so that the differences 

 in the test results for similar model studies obtained in different lab- 

 oratories can be reduced to a minimum. 



(2) Vertical-Wall Structures . When nonbreaking waves attack a 

 vertical-wall impervious structure, the phenomena can be modeled with 

 negligible scale effects. Since accurate pressure measuring and record- 

 ing apparatus are available, and with the use of modern wave flume and 

 wave-generating facilities, wave pressures can be determined with enough 

 accuracy for design purposes when such model studies are necessary. When 

 the attacking waves break directly on vertical -wall structures, shock 

 pressures occur and cause scale effects that are difficult to define 



and measure. The magnitude and duration of shock pressures can be meas- 

 ured with enough accuracy using presently available pressure cells and 



340 



