A HIGH-ORDER DISCONTINUOUS GALERKIN METHOD FOR 1D WAVE PROPAGATION IN NON-LINEAR HETEROGENEOUS MEDIA

Abstract eng:
During strong earthquakes, non-linear behaviour of soils is observed when the strain goes beyond the elasticity limit. In particular, this behaviour results in a shift of amplification peaks towards lower frequencies, the generation of high frequency harmonics, and the increase of hysteretic attenuation.These phenomena can have serious impacts on engineering structures at the surface. Therefore, it needs to be better understood and this understanding goes, for instance, through numerical simulations. Recent advances in computing power has led to the development of modern and efficient numerical methods for modelling seismic wave propagation in complex media. Among them, the discontinuous Galerkin finite element method (DG-FEM) constitutes one of the most interesting methodologies as it merges both the flexibility of finite element methods, the accuracy of high-order methods and the computational efficiency of fully local discretization of the wave equation. In this paper, we present a high-order discontinuous Galerkin method for 1D wave propagation in non-linear media. We propose a numerical upwind flux established for heterogeneous media, including the non-linear constitutive relationship between stress and strain. The proposed flux is quite general and can be extended as long as an explicit relationship between stress and strain is available. In the non-linear homogeneous context, the accuracy and the numerical convergence are studied by comparing numerical results with an analytical solution derived for this study. The expected theoretical convergence order is obtained, proving the good properties of the numerical method. Two applications are studied, first, the 1D wave propagation in non-linear elastic heterogeneous media and then, the 1D wave propagation in non-linear elastoplastic media including hysteresis. Both applications are compared to the linear elastic case considering the time history solutions and its frequency content. In particular, we discuss the impact of the non-linear model on the shift of the amplification peaks towards lower frequencies and the high frequency generation phenomena.

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