Imaginary values for P result for values of T less than 2/d in 

 the formula of Senores Castro and Briones which indicates that very- 

 steep dikes of rock-fill cannot be constructedj however large the 

 stones may be. This result is perfectly logical, but analyzing more 

 carefully one observes that the slope limit thus determined is T = 

 2/d5 which may be acceptable for values of d less or equal to 2o 

 However, for values greater than 2 the slope limit admitted by the 

 formula would be steeper than T - cot a = i or a-45°j) which is in- 

 admissible since a = 4.5° is the natiiral slope of the rock-fill o 



On the contrary, my formula admits only slopes equal to or less 

 ttian a ^ 4-5°5 therefore for values of a greater than 45° there would 

 be negative values for Po For this limit a ^ 45°? however slight 

 the height of the wave As there correspond infinite values of P, 

 which means that, however large be the stones which compose a rock- 

 fill of natural slope, the least impetus is sufficient theoretically 

 and logically to displace themo If in addition we make A = in the 

 formula then P = O/O, or it is indeterminate, which signifies that 

 if waves do not act on a rock-fill of natural slope, the fill is in 

 strict equilibrium regardless of stone sizeo 



All the results obtained from my simple formula are perfectly 

 logical and in accord with realityo 



The formula shows the great influence of the density d of the 

 stone in respect to the resistance of the rock-fill to wave attack, 

 for like conditions of wave height and slope o If, for example, we 

 consider artificial blocks of nat\iral cement of Zumaya whose density 

 is d =2, then 



d _ _2^ _ o 



If however, we consider natural stones of density 3s then the fraction 



This indicates that in rock-fill to resist the sea natural stones are 

 equivalent to those of concrete whose weight might be 2; 3/8 = 5o33 

 times greater o If, moreover, we take into account the coefficient K 

 previously determined this equivalence of weight rises to 5o33 x 19_ = 

 6o74o 15 



With a material of density d si, or one which almost floats, 

 it is impossible to construct rock-fill dikes, since p = cx> „ On the 

 contrary, if one should use a material of a density d s 4 or d = 6 

 its stones would be equal to others of concrete 13o5 or 41 times 

 heavier or even more if we take into account the relation 19/15 = 

 1„26 of the coefficients Ko 



In high dikes and in tidal seas it might be convenient and 

 economical to try to use a material denser than stone for the con- 

 struction of the upper protecting covering, with the purpose of 



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