PENETRATION 



Penetration of propeUant-embedded anchor flukes is a complex 

 phenomena that has received much research attention. True (1976) has 

 developed an analytical model for penetration prediction for high 

 velocity penetrators based on a form of Newton's second law 



dz b 1 2 3 



where M 1 = penetrator effective mass 



v = penetrator velocity 



d = differential operator 



z = depth 



W, = buoyant weight of penetrator 



F = inertial drag force 



F_ = bearing component force 



F = side adhesion force 



3.1 COHESIVE SOILS 



True developed a solution to Equation 3-1 for cohesive soils by 

 conducting a number of model and field penetration tests . The solution 

 is not closed form; thus, an incremental technique is necessary to solve 

 it. A rigorous solution would consider different values of many of the 

 parameters over the length of the penetrator and is suited for a com- 

 puter. Such a solution is beyond the scope of this report. However, 

 because anchor flukes usually penetrate a minimum of five times their 

 length, many simplifications are possible by assuming the penetrator is 

 a point object at the i depth increment. With a two-sided finite 

 difference form and substitution of parameters for M' , F,, F 2 , F„, and 

 W, per True (1975, 1976, and 1977), Equation 3-1 becomes 



33 



