Appendix A 



ANCHOR PENETRATION INTO SOIL 



by D. G. True 



The following discussion is presented to show variation in the 

 penetration behavior, and especially the ultimate embedment depth, 

 which can be expected to result from variations in soil properties 

 and projectile configurations. Although the basic equations for 

 penetration behavior and the assumptions used in evaluating coefficients 

 for those equations are open to serious question (indeed, they are 

 the subjects of current and planned research) , it is felt that they 

 are sufficiently well understood to support calculations for the 

 purpose of indicating the importance of the various aspects of anchor 

 geometry and soil deformation which contribute to penetration resistance 

 and the potential value of possible projectile modifications. 



An equation developed by Poncelet in 1839 to predict penetration is 



dv 2 /* t\ 



-ntrr = a + yv (A-i; 



at 



2 —1 

 where m = mass of projectile (FT L ) 



t = time (T) 



v = velocity of projectile (LT ) 



a,y = material property coefficients (F) 



To predict penetration of projectiles into soils, Equation A-l 

 takes the form 



A 9 



m-77 = -sN A_ - 6 sA - h P C n A_v (A-2) 



dt c F as D T 



where s = soil shear strength (FL ) (may vary with depth) 



N = bearing capacity factor (known function of soil friction 

 angle) 



6 = adhesion reduction faction 

 a 



2 

 A = side area of projectile (L ) 

 s 



A 9 



F = frontal area of projectile (L ) 



F, L, and T represent generalized units of force, length, and time, 

 respectively. 



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