exact quantitative evaluation cannot be made. It will, therefore, be necessary 

 to resort to empirical correlations in order to obtain practical results for 

 engineering analysis. 



Empirical Derivation of Elastic Coefficients 



It has been suggested that the modulus of elasticity of soil varies 

 approximately linearly with the undrained shear strength.^' ^ 



E = Ac (5) 



where A = constant of proportionality 



c = undrained shear strength of soil 



For the nonlinear stress— strain curves of typical soils, secant moduli, 

 which are functions of the stress state, are often substituted for E. Using the 

 bearing pressure p as a measure of the stress state. Equation 5 may be rewritten 

 as 



E(p) = A(p)c (6) 



where E(p) = secant modulus as a function of p 



A(p) = coefficient of proportionality, also a function of p 



If the shear strength is assumed to vary linearly with depth, then 



c = K'(z + H') (7) 



where K' and H' are soil profile parameters. 



Combining Equations 2, 6, and 7 yields 



„, . K /H + z 



A(p) = -rn- 



K' \H' + z, 

 A(p) should be independent of z. Therefore, 



H = H' (8) 



and K = A(p) K' (9) 



22 



