e^E/p 

 0.2 0.3 









^^^"^:;::n 



> 



elast 



ic theor 



'C^- 











y y' 



approxir 



nation 



y 



















































Figure 16. Normalized vertical strain 

 versus dimensionless depth. 



By expressing this equation in terms 

 of differentials, it is possible to inte- 

 grate it over a section of the surface 

 and determine the stresses and strains 

 beneath a loaded area. This has been 

 done for a circular area, and the results 

 are presented in the literature.^ One 

 representation of these results is given 

 by Figure 16 in the form of an aver- 

 age normalized vertical strain plotted 

 versus a dimensionless depth. The 

 normalized strain is expressed by the 

 quantity 



p 



where e^ = vertical strain at depth 

 z (averaged over the 

 range of radial offset 

 distance to R) 



E = modulus of elasticity 



p = plate bearing pressure 



R = radius of loaded area 



In obtaining this quantity, an incompressible material, that is, a material 

 with Poisson's ratio equal to 0.5, was assumed. 



Two general characteristics of this relationship are of interest. First, 

 the normalized strain is predicted to be identically equal to zero at the surface. 

 This effect is primarily a result of the incompressibility assumption and will be 

 rapidly altered as drained compression or consolidation begins to occur. For 

 the small time span involved in the plate bearing test, however, this effect will 

 probably persist, at least with fine-grained soils. The second feature of inter- 

 est indicated by Figure 16 is the occurrence of a maximum strain at a depth 

 which varies linearly with the radius of the loaded area. Combining this 

 feature with the first implies that the plate penetration process involves 

 pressing a slightly strained soil volume, the thickness of which varies with 

 the size of the loaded area, into a heavily strained zone. The significance 

 of this will be discussed below. 



19 



