Model for Soil Amplifications Studies Involving Soil Failure

This paper presents a numerical model for soil amplification studies based on a variational formulation of the wave propagation problem of solids with strong discontinuities adapted to represent strain localization in soil deposits induced by the propagation of seismic waves. The approximation of the wave propagation problem in soils is formulated through finite elements, conventional for undamaged conditions and with embedded discontinuities once a failure process initiates. The paper deals with a formulation which takes into account the internal strain energy and the kinetic energy due to wave passage. It is shown that the developed energy functional of the solid with discontinuities has as stationary conditions the strong formulation of the dynami-cal problem, i.e., the governing equations of the corresponding boundary value problem. Some advantages of this variational formulation are that the stiffness and mass matrices of its finite element model approximation: 1) satisfy the inner continuity stresses at the localization band and the simulated rigid body movements of the finite element parts generated by the discontinuity are consistent, and 2) are symmetric, reducing the involved computational effort and the number of numerical problems encountered during its application. The develop-ment of a local material failure (shear bands as localization zones) is in terms of continuum constitutive mod-els furnished with strain softening capabilities. Representative numerical examples illustrate the results of the presented formulation. A discussion of the implications of local soil failure during earthquakes is included.JRC.G.5-European laboratory for structural assessmen