4. F - The frontal resistance force was evaluated by Smith 

 using shallow footing bearing capacity equations. However, for most 

 cases of penetration, including the tests reported herein, the usage 

 of such equations for the entire penetration process is not justified. 

 This is because shallow footing equations degenerate as the penetration 

 depth becomes large relative to the least lateral dimension of the 

 penetrometer.-^^ For these tests with long slender objects, the point 

 of equation degeneration occurs early in the penetration process. 

 The case then becomes one of "deep penetration" which is more appropriately 

 predicted using pile bearing capacity equations. The frontal resistance 

 force portion of these equations is usually represented by 



-/' 



where N = frontal pressure coefficient (>1.0) 



c = soil shearing strength 



dA, = differential horizontal surface area of object 

 h 



For piles placed in a cohesive soil medium, values of N which are 

 used typically range between 7 and 9.5-"'°, a value of 10.0 was used 

 in this investigation somewhat arbitrarily as a simple, reasonable 

 number. Once again remolded and undisturbed values of Cg were used 

 as were the previously stated four values for p. 



5. Fj ~ The technique for predicting the inertial force is 

 incorporated in the technique discussed above for predicting the 

 hydrodynamic drag force. This force is considered by introducing 

 the added mass, c. 



The final form of the penetration equation is as follows: 



(m + c) a = W - Dv - (f c dA - (f 10c dA^ (16) 



where c is evaluated using Equation 14. 



This equation was solved approximately by the following numerical 

 procedure : 



The object velocities at soil entry were known for all of the 

 in situ penetration tests. For a given test the value of entry 

 velocity and a penetration depth of zero were inserted into Equation 16. 



15 



