Resilient Behaviour

In dealing with granular materials, the elastic properties are often defined by the resilient modulus (which replaces the modulus of elasticity to indicate the nonlinearity of the behaviour) and Poisson’s ratio. A common approach in dealing with the stress dependency of granular materials stiffness is the K-θ model, which expresses resilient modulus as a function of the sum of the principal stresses, or bulk stress.
                                                                                                                                (1)
Thanks to its simplicity, this model has been widely adopted for analysis of stress dependence of material stiffness. However, it has the drawbacks of assuming a constant Poisson’s ratio and of ignoring the effect of other stress parameters apart from the bulk stress. For this reason, several more elaborated versions of this model have been suggested such as, for instance, the so called “Universal Model”, first suggested by Uzan and then adopted by the ME-PDG:
                                                                                             (2)
This model includes the 3D effect of shear, or deviator, stress by means of the octahedral stress. Most of the models of this family have empirical origins and are mainly used in the US.
A more theoretical approach is taken by those models that characterise the non-linear behaviour by decomposing stresses and strains into volumetric and shear components. In this case, resilient modulus and Poisson’s ratio are replaced by bulk and shear moduli:
                                                                                                                                                  (3)
                                                                                                                                                (4)
where
                                                                                                                                 (5)
                                                                                                                                            (6)
                                                                                                                                 (7)
                                                                                                                            (8)
In 1980 Boyce used this type of approach to develop a theoretical nonlinear elastic model for the stress-strain relationship of granular materials:
                                                                                                                         (9)
                                                                                                                         (10)
this model has then been employed by many other researchers, particularly in mainland Europe. It is important to note that it is possible to express resilient modulus and Poisson’s ratio in terms of bulk and shear moduli:
                                                                                                                                   (11)
                                                                                                                                          (12)
This can be useful considering that our current approach to including the effect of moisture content in granular materials makes use of the resilient modulus.

Posted in: granular, materials, model