SOIL STIFFNESS
The effective elastic modulus, E', or the shear modulus, G, and the effective bulk modulus, K', characterize soil stiffness. In practice, E' or G and K' are commonly obtained from triaxial or simple shear tests. We can obtain an estimate of E' or G and K' using the critical state model and results from axisymmetric, isotropic consolidation tests. The void ratio during unloading/reloading is described by
V
Loading and unloading/
reloading (elastic) response of soils in
(ln p', e) space.
where ek is the void ratio on the unloading/reloading line at p' =1 unit of stress . The unloading/reloading path BC is reversible, which is a characteristic of elastic materials. Differentiating Equation gives
The elastic volumetric strain increment is
But, from Equation
Therefore,
Solving for K9, we obtain
From Equation
Equations indicate that the elastic constants, E' and G, are proportional to the mean effective stress. This implies nonlinear elastic behavior, and therefore calculations must be