Discretization effects in the finite element simulation of seismic waves in elastic and elastic-plastic media

Abstract

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.

On the implementation and validation of a three‐dimensional pressure‐dependent bounding surface plasticity model for soil nonlinear wave propagation and soil‐structure interaction analyses

“…Moreover, numerical examples were limited to material point simulations. A following paper 22 illustrated the response of the original PJ model in the context of a 1D site response analysis, which is still limited; the original paper 7 was cited and no additional details on the model were provided. This somewhat hindered the understanding of the robustness issues surrounding the model, especially when complex loading conditions were to be considered.…”

“…The model features deviatoric‐volumetric coupling and has only a few parameters, both of which are desirable for practical numerical simulations. The details of the stress update procedure for the original PJ model, however, was not discussed, and the model response has been shown only through material point simulations 7 and 1D site response analysis 22 . Furthermore, the original PJ model adopted an unrealistic definition of plastic strain rate direction, as it assumes that the plastic strain rate occurs always along the stress‐ratio rate direction, which has been discussed in Dafalias and Taiebat 13 …”

“…The details of the stress update procedure for the original PJ model, however, was not discussed, and the model response has been shown only through material point simulations 7 and 1D site response analysis. 22 Furthermore, the original PJ model adopted an unrealistic definition of plastic strain rate direction, as it assumes that the plastic strain rate occurs always along the stress-ratio rate direction, which has been discussed in Dafalias and Taiebat. 13 Here, we utilized a more commonly used function of plastic strain rate direction, 12,13 which ensures the zero elastic range and improves the numerical stability when stress paths are close and in a tangential direction to the bounding surface (see more discussions about this in Dafalias and Taiebat 13 ).…”

Earthquake soil‐structure interaction of nuclear power plants, differences in response to 3‐D, 3 × 1‐D, and 1‐D excitations

“…Accurately resolving the wave amplitudes for a given maximum frequency imposes restrictions on the spatio-temporal discretization, which are more stringent than just meeting the Nyquist criterion. 43 For finite elements with linear displacement interpolation functions involving linear material and geometrical response, it has been shown many times (see Watanabe et al 44 for a recent discussion) that at least 10 elements per shortest wavelength are required to accurately resolve displacement amplitudes. In addition to that, the time step is limited by the Courant-Friedrichs-Lewy condition 45 ; eg, the time step must be chosen such that the distance traveled by the fastest phase is less than the smallest spacing between grid nodes for all points in the mesh.…”

Transient response of offshore wind turbines on monopiles in sand: role of cyclic hydro–mechanical soil behaviour

“…Further, Krylov-Newton step iterations (Scott and Fenves, 2003) are arrested when an error criterion on the incremental displacement norm is satisfied with relative tolerance equal to 7.5 × 10 −4 (Mazzoni et al, 2007). Although smaller time-steps may suit better the integration of highly non-linear soil models (Jeremić et al, 2009;Watanabe et al, 2016), the selection of ∆t (and of the error tolerance) is largely driven by computational cost…”