Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain

Chen Xia,Xiaozhao Li,Chengzhi Qi

doi:10.1155/2018/7982342

Abstract

Transmitting boundaries are important for modeling the wave propagation in the finite element analysis of dynamic foundation problems. In this study, viscoelastic boundaries for multiple seismic waves or excitations sources were derived for two-dimensional and three-dimensional conditions in the time domain, which were proved to be solid by finite element models. Then, the method for equivalent forces’ input of seismic waves was also described when the proposed artificial boundaries were applied. Comparisons between numerical calculations and analytical results validate this seismic excitation input method. The seismic response of subway station under different seismic loads input methods indicates that asymmetric input seismic loads would cause different deformations from the symmetric input seismic loads, and whether it would increase or decrease the seismic response depends on the parameters of the specific structure and surrounding soil.

Highlights

The 1995 Kobe earthquake caused a major collapse of the Daikai subway station in Kobe, which represents the first modern underground structure failure during a seismic event
The seismic response of subway station under different seismic loads input methods indicates that asymmetric input seismic loads would cause different deformations from the symmetric input seismic loads, and whether it would increase or decrease the seismic response depends on the parameters of the specific structure and surrounding soil
Similar to the proposed 2D viscoelastic boundary equations in Section 2, the proposed two-dimensional viscoelastic boundary is extended to the three-dimensional condition

Summary

Introduction

The 1995 Kobe earthquake caused a major collapse of the Daikai subway station in Kobe, which represents the first modern underground structure failure during a seismic event. A two-dimensional viscoelastic boundary for the multiple input waves or excitation sources would be developed based on an approximation of the form of the outward traveling waves. To obtain the shear stiffness parameter for two-dimensional viscoelastic boundary conditions under multiple seismic excitation sources input, three kinds of shear stiffness parameters are proposed. To employ the proposed viscoelastic boundary equations in the finite element analysis model, discrete springs and dashpots should be implemented on the corresponding boundary nodes, which would make the shear stresses and displacements approximate to the real ones. This is because the free surface boundary has no stiffness to recover from elastic deformation and no damping to absorb the energy of transmitting waves. From the above calculated results and analysis and considering that the distances between the excitation sources and boundaries could be distinctly different, it is suggested to estimate the shear stiffness parameter K by the both sources

The 3D Viscoelastic Boundary Conditions

Input Equivalent Forces of Seismic Waves

Findings

Conclusions