The function A(p) may be evaluated empirically from the test data 

 as follows: K' and H' may be estimated using a linear least squares fit of the 

 vane shear strength versus depth data. Since K' and H' may vary depending 

 upon the range of depths considered, a reasonable rule is to consider only 

 the data between z = and z = 2 D, the assumed region of stressing. With 

 H' = H known, any set of D, p, and S values obtained using the plate bearing 

 device will determine a quantity K according to Equation 4 (Figure 17). This 

 K divided by K' will yield a quantity A(p). 



Values of A(p) were calculated for each plate diameter or width tested 

 at each site using the average pressure— displacement curves. For any given 

 value of p, it was found that the experimentally determined values of A(p) 

 were distributed approximately normally. Assuming that these values were 

 indeed random samples from a population with a normal distribution, the 

 statistical characteristics of future tests were estimated. The expected value 

 of A(p) for a particular pressure at a future test site was taken to be the aver- 

 age of the previously calculated values of A(p) for that pressure. This quantity, 

 plotted versus p in Figure 18, is statistically the best possible prediction on the 

 basis of these data. It may be incorrect, however, and the magnitude of error 

 which may occur is indicated by the 95% confidence limits shown in Figure 18. 

 The probability that a value of A(p) obtained in a future test will lie within 

 these limits is 0.95. The limits were calculated on the basis of the scatter of 

 the experimental data using statistics theory. 



Figure 18 may be applied as follows: The expected value of A(p) is 

 taken from the graph and used to calculate the expected settlement. Values 

 of A(p) taken from the 95% confidence limits curves are used to estimate the 

 range of settlement values which can be expected. 



Two characteristics of Figure 18 should be noted. 



1 . Except at very low pressures, the range of data scatter is small 

 considering the usual magnitude of error present in settlement 

 prediction schemes. 



2. The amount of data scatter varies inversely with pressure. 



Therefore, it may be concluded that for relatively large pressures the 

 errors introduced by the various assumptions which led to Equation 4, including 

 the violation of the Boussinesq assumption, are small. 



Bearing Capacity Solution 



Skempton^ has proposed the following equation for the bearing capacity 

 of an embedded rectangular footing with width B and length L. 



p = 5c (l + 0.2 -^jM + 0.2 f ) + T^Df (10) 



B /\ L 



23 



