Dynamic Soil Response for Strong Earthquakes: A Simplified Non Linear Constitutive Model

Abstract eng:
The seismic soil response can be analyzed in the frequency (linear or equivalent linear approaches) as well as in the time domain (e.g. complex constitutive models). The nonlinear constitutive properties of soils being difficult and costly to determine, the present work proposes a simplified constitutive model to analyze the dynamic soil response for moderate or strong earthquakes at large scales (alluvial basins). In this work, we consider a non linear viscoelastic constitutive model involving both non linear elasticity as well as non linear viscous behavior. The non linear elastic part of the model is described by a hyperbolic law. The description of the viscosity starts from a Nearly Constant Quality Factor (NCQ) model able to fulfil the causality principle for seismic wave propagating in dissipative materials. In the NCQ model, we introduced a dependence on the excitation level in order to consider the variations of moduli and the increasing damping ratio. This dependence is controlled during the 3D stress-strain path by the variation of the second order invariant of the strain tensor. Applications are performed to study the rheological response of the materials without considering wave propagation, and then to study the effects of nonlinearity on the generation of higher harmonics and shift of spectral frequencies during wave propagation in a sedimentary layer. Starting from the here proposed mechanical formulation including the main features of soil nonlinear behavior, the analysis of the nonlinear response of a sedimentary layer submitted by a vertical SH wave is then performed thanks to a discretization by the finite element method. Validations of the model for different inputs show its ability to recover low amplitude ground motion response. For larger excitation levels, the analysis of wave propagation in sedimentary layer leads to interesting results: at the free-surface the spectral peaks are shifted to lower frequency values (when compared to the input motion); higher frequency components are not overdamped as for the equivalent linear model; the amplification level is generally lower. These results show the ability of this simplified nonlinear model to investigate, in the near future, site effects in 2D/3D alluvial deposits for strong earthquakes.

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