Nonlinear viscoelastic wave propagation: An extension of nearly constant attenuation models

Hysteretic damping is often modeled by means of linear viscoelastic approaches such as "nearly constant attenuation" models (e.g. NCQ model). These models do not take into account nonlinear effects either on the stiffness or on the damping, which are well known features of soil dynamic behavior. The aim of this paper is to propose a mechanical model involving nonlinear viscoelastic behavior for isotropic materials under dynamic excitations. This model simultaneously takes into account nonlinear elasticity and nonlinear damping. On one hand, the shear modulus is a function of the excitation level; on the other, the description of viscosity is based on a generalized Maxwell body involving nonlinearity. This formulation (X-NCQ) is implemented into a one-dimensional finite-element approach for a dry soil. The validation of the model shows its ability to retrieve low amplitude seismic ground motion. For larger excitation levels, the analysis of seismic wave propagation in a nonlinear soil layer over an elastic bedrock leads to results which are physically satisfactory (lower amplitudes, larger time delays, higher frequency content).