Abstract
Presented here is a numerical investigation that (re-)appraises standard rules for space/time discretization in seismic wave propagation analyses. Although the issue is almost off the table of research, situations are often encountered where (established) discretization criteria are not observed and inaccurate results possibly obtained. In particular, a detailed analysis of discretization criteria is carried out for wave propagation through elastic and elastic-plastic media. The establishment of such criteria is especially important when accurate prediction of high-frequency motion is needed and/or in the presence of highly non-linear material models. Current discretization rules for wave problems in solids are critically assessed as a conditio sine qua non for improving verification/validation procedures in applied seismology and earthquake engineering. For this purpose, the propagation of shear waves through a 1D stack of 3D finite elements is considered, including the use of wide-band input motions in combination with both linear elastic and non-linear elastic-plastic material models. The blind use of usual rules of thumb is shown to be sometimes debatable, and an effort is made to provide improved discretization criteria. Possible pitfalls of wave simulations are pointed out by highlighting the dependence of discretization effects on time duration, spatial location, material model and specific output variable considered.
Highlights
The study of wave motion is of utmost importance in many applied sciences, as it supports the understanding of transient phenomena in many natural and anthropic dynamic systems
When linear elastic wave problems are considered, either time-domain or frequency-domain solutions may be sought, whereas time-domain approaches are usually needed in the presence of non-linearities
Since the Real earthquakesoil structure-interaction (ESSI) program is based on a displacement Finite Element (FE) formulation, displacement components are the most reliable output; some attention is paid to accelerations, postcalculated through second-order central differentiation
Summary
The study of wave motion is of utmost importance in many applied sciences, as it supports the understanding of transient phenomena in many natural and anthropic dynamic systems. When linear elastic wave problems are considered, either time-domain or frequency-domain solutions may be sought, whereas time-domain approaches are usually needed in the presence of non-linearities (constitutive or geometrical). In this respect, it should be remarked that much interest in earthquake engineering is nowadays on non-linear wave phenomena, since they govern (i) the occurrence of natural catastrophes (e.g., landslides and debris flows) induced by soil instabilities, such as liquefaction and strain localization [18, 24, 63]; (ii) the interaction between geomaterials and man-made structures [13, 16, 20, 28, 53, 59].
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