The equation used to calculate anchor penetration in sand is: 



Q , = (A . a , + A^ . a „) k tan 4) (7) 



^ult s vl F v2 



where a = vertical effective stress 



V 



k = coefficient of passive earth pressure 



<}) = friction angle between steel and sand 



Equation 7 takes two forms, one for D >20 feet, and one for D <20 feet. 

 The equation for D >20 feet is as follows: 



Vt = (\(D-10) + Ap . D .) Y . k tan * ^g^ 



For D <20 feet the equation is: 

 d2 



Quit = (^; • ^ + ^ • °) ^ 



k tan i, (9) 



The value of (() to be used in the above equations is independent 

 of soil density (Lambe and Whitman, 1969, p. 143) and is taken as 

 (j) = 26°. The coefficient k is much more difficult to predict; various 

 researchers studying the horizontal stress acting on piles in sand 

 (Ibid, p. 501) have reported values of k from 0.5 to 3.0. It is 

 doubtful that the full passive resistance of the soil will be developed 

 during penetration because the fluke and shaft are small and will not 

 cause excessive soil movement. Also, it would seem logical that the 

 values of k used for the loose and dense sand should not differ by very 

 much because densif ication of the loose sand should occur while the anchor 

 is being embedded by vibration. Values of k between 1 and 2 are recommended 

 (Ibid, p. 500) to calculate horizontal stress acting on piles in sand. 

 For calculation purposes, k will be assumed to vary from 1.0 for loose 

 sand {4> = 30O) to 1.5 for dense sand ((}> = 40°). 



Results of the penetration analysis are presented in Table 3 for 

 both sand and clay. Since densities were assumed and since slight 

 density variations have a minimal effect on penetration, only one 

 density was used for the clay. 



Determining the adequacy of the existing vibrator was the third 

 step. Knowing the penetration capabilities of the vibratory anchor 

 system permits the use of graphs of breakout force versus 

 embedment depth to determine the theoretical breakout force of the 

 vibratory anchor. The vibratory anchor penetrations presented in Table 3 

 refer to the embedment depths of the fluke centers prior to anchor 

 keying. Field test results have shown that keying occurs in a distance 

 of approximately one-half the fluke diameter (B/2) . Therefore, breakout 

 forces in Table 3 were determined from Figures 26 and 27 by using a 



depth of embedment equal to D - B/2. 



^ ^ max 



55 



