Simulating stiffness degradation and damping in soils via a simple visco-elastic-plastic model

Stiffness degradation and damping represent some of the most well-known aspects of cyclic soil behavior. While standard equivalent linear approaches reproduce these features by (separately) prescribing stiffness reduction and damping curves, in this paper a multiaxial visco-elastic-plastic model is developed for the simultaneous simulation of both cyclic curves over a wide cyclic shear strain range. The proposed constitutive relationship is based on two parallel resisting/dissipative mechanisms, purely frictional (elastic-plastic) and viscous. The frictional mechanism is formulated as a bounding surface plasticity model with vanishing elastic domain, including pressure-sensitive failure locus and non-associative plastic flow – which are essential for effective stress analyses. At the same time, the use of the parallel viscous mechanism is shown to be especially beneficial to improve the simulation of the overall dissipative performance. In order to enable model calibration on few standard experimental data, the constitutive equations are purposely kept as simple as possible with a low number of material parameters. Although the model performance is here explored with reference to pure shear cyclic tests, the multiaxial formulation is appropriate for general loading conditions.