toe of beach slope) . Holding dg constant would keep the model at the 

 same scale (same Reynolds number) to allow isolation of the effects of 

 slope length. 



(f) Testing of different armor unit sizes, with other conditions 

 remaining the same, would allow a better evaluation of the effects of 

 relative roughness. As a minimum, armor units should be tested at con- 

 ditions close to their stability limits at each of several dg/H^ 

 values (e.g., 1.0, 1.5, 3.0, 5.0, etc.). 



(g) Many small-scale runup tests have been conducted for structures 

 sited on horizontal bottoms. Large-scale tests of runup on smooth struc- 

 tures sited on horizontal bottoms have not been conducted although runup 

 experiments have been conducted at large scales using riprap slopes 

 fronted by a horizontal bottom. Additional tests of both smooth slopes 

 and slopes protected with armor units other than stone would be useful 



in evaluating scale effects. These tests would best be conducted in 

 the range 2.5 < dg/H^ < 8. Similarly, large-scale tests of runup on 

 smooth structure slopes fronted by a sloping beach have been obtained 

 for limited conditions. Additional tests would be useful if conducted 

 on both smooth and rubble slopes, and if a wide range of wave steep- 

 nesses is tested for each of several dg/H^ values (1 < d s /H^ < 5). 

 Evaluation of scale-effect tests requires use of identical geometries, 

 including the length of beach slope. Tests at intermediate Reynolds 

 numbers may help determine the minimum model scale necessary for pre- 

 diction of prototype runup. Intermediate values would be on the order 

 of 4 x 10 5 < R g < 2 x io 6 for structures on sloping beaches, or 

 2 x 10 6 < Rg < 1 x io 7 for structures on horizontal bottoms. 



VIII. SUMMARY 



Analysis of laboratory runup test results pertaining to steep struc- 

 tures and monochromatic waves was used to develop runup equation (8) for 

 smooth slopes fronted by horizontal bottoms: 



r /H 1 \^ _1 



£- = (cot er 1 -^ (4.23)(10) 2 Cq-U _£_ for cot 6 > 2 . 



«o \ gT 2 / 



Values of q are determined from Figure 5. Equation (8) gives runup 

 for waves breaking on the structure slope; nonbreaking waves will have 

 lower relative runup for a given wave steepness, H^/gT 2 . Thus, equa- 

 tion (8) is conservative and gives (R/H^) maa; for a given slope and 

 wave steepness. The demarcation between breaking and nonbreaking waves 

 is a function of relative depth and wave steepness. Waves meeting the 

 condition of equation (5) are considered breaking regardless of rela- 

 tive depth] equation (5), with H replaced by H^, is 



H» 



—r > 0.031 tan 2 6 . 

 gT 2 



