If the soil tested with the plate bearing device were indeed linearly 

 elastic and homogeneous, and if the elastic parameters could be determined, 

 it would be a simple matter to determine settlement, S, in terms of surface 

 load. This would be done by means of a numerical integration of the 

 Figure 1 6 data according to Equation 1 . 



-I 



e,dz (1) 



It may readily be seen that this would lead to a linear relationship 

 between settlement and plate width, a well-known result which has been 

 presented in the literature^ and which was discussed in an earlier report 

 on the plate bearing device.'' Unfortunately, this relationship apparently 

 does not apply to any of the plate bearing test data. This is best exempli- 

 fied by the Series 1 1 1 data in which settlement was found to be independent 

 of the plate width. 



It is felt that these deviations are produced by variations in soil stiffness 

 with depth. According to the data presented in Figure 16, as the plate radius, 

 R, is increased, the thickness of the zone of high normalized strain increases 

 linearly. With a constant modulus this results in a linear increase in settlement. 

 However, the depth below the surface of the zone of high normalized strain 

 also increases, as noted above. If the modulus should increase with depth, 

 then, by the definition of normalized strain, the actual magnitude of strain 

 would decrease. It may be seen that if the modulus increases linearly from 

 a value of zero at the surface, the magnitude of the strain produced will 

 decrease with plate size at exactly the same rate as the thickness of the 

 strained zone increases. The net effect is an amount of settlement which 

 is independent of plate width. If the modulus has a non-zero value at the 

 surface and also increases with depth, an intermediate settlement— plate 

 width relationship results. Qualitatively, these results compare well with 

 the plate bearing data, assuming vane shear strength to be an indicator of 

 soil stiffness. 



Analytically this sort of behavior may be predicted by allowing the 

 soil stiffness, as reflected by the elastic modulus, to vary linearly with depth. 



E = K(H + z) (2) 



where K and H are constants which relate E to z. 



20 



