p = mass bulk density of soil (FT L ) (may vary with depth) 



C = drag coefficient of soil (essentially constant for 

 turbulent flow) 



in which penetration resistance is expressed as a combination of static 



shear and inertial drag resistance (Christians and Meisburger, 1967; 



Thomason, et al, 1968; and Schmid, 1969). 



By integrating Equation A-l twice with the initial conditions 



t = 0, v = v , and displacement, x = 0, the final maximum penetration, 



x , can at a final velocity, v = 0, be calculated as 

 max ' 



2 



x = SL_ (i + — 9-) (a-3) 



max 2y a 



The relationships for the constants a and y in Equation A-2 are 

 used as input for Equation A-3 to obtain, for a homogeneous sediment, 



x = _^!L_ ln (1 + 1 P D ^ o } (A _ 4) 



max pC D A F sN^ + 6 a sA s 



This relationship provides a basis for predictions of penetration 

 depth for anchor-projectiles of various configurations into various 

 types of soils. For cohesive materials such as clay, the expression 

 is directly applicable. The shear strengths of terrigenous sea floor 

 clays have been observed to range from 0.2 psi at the surface to 

 3.5 psi at 10 feet (Taylor and Demars , 1970; Demars and Taylor, 19 71). 

 Extrapolating these results to the embedment depths of interest 

 (0-30 feet) gives a range for clays of 0.2 to 5 psi. The adhesion 

 reduction factor, 6 , is considered to be the inverse of soil sensitivity 

 which averages about 2.5 for typical clays; therefore & a would average 

 0.4. For sands, the fact that penetration is too rapid to permit 

 drainage of pore water causes the pore pressure to change in accordance 

 with the tendency of the sand to dilate or compress during shear. 

 Loose sands tend to compress and dense sands tend to dilate producing 

 positive and negative changes in pore pressure, respectively. Such a 

 pore pressure change acts together with the in-situ static overburden 

 stresses to cause the undrained effective confining stress to reach 

 a critical value (a' = a' crit ) after a shear strain of several percent. 

 The magnitude of this critical confining stress depends upon the void 

 ratio (density) of the sand during the undrained (zero-volume-change) 

 shearing. Thus, the strength of a saturated sand when the penetration 

 is so rapid as to prevent drainage of the sand may be represented as 



s = a' tan d>= a 1 . _ tan $ (A-5) 



crit 



31 



