Seismic Response of Irregular Triangular Alluvial Valleys under Shear Waves Using Spectral Elements

The present study investigates seismic response problems of triangular uniform irregular alluvial valleys under shear waves using a finite element spectral method. Alluvial valleys; affect the shape and properties of alluvial materials on the response and seismic behavior of the valley surface due to the geometry conditions. Therefore this study aims to illustrate the plots and magnitude of amplification values for irregular alluvial valleys in a two-dimensional triangular manner, with the characteristics of homogeneous alluvial materials and different geometric characteristics. The analysis in the time domain was performed based on the finite element method of the spectral element (SFEM) using NASEM software, developed by Najafizadeh. The valleys are analyzed with the slope angles of 15, 30, 45 and 60 degrees on one side and in opposite directions with a slope of 45 degrees and with a maximum depth of 50 meters for the alluvial valley. The horizontal amplification curves in the alluvial valley's points from the analysis reach a maximum value at a given frequency, which can be an ideology for determining the frequency of irregular triangular alluvial valleys under different slope valley angles. The results of natural valley frequencies indicate that with decreasing slope of the valley, the natural frequency of the valley decreases, as well as amplification plots are related to the slope of the valley.

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Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain

Mathematical Problems in Engineering ◽

10.1155/2018/7982342 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11

Author(s):

Chen Xia ◽

Chengzhi Qi ◽

Xiaozhao Li

Keyword(s):

Finite Element ◽

Seismic Response ◽

Time Domain ◽

Seismic Waves ◽

Three Dimensional ◽

Seismic Loads ◽

Element Analysis ◽

Artificial Boundaries ◽

The Time Domain ◽

Transmitting Boundaries

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.

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Time-Domain Stability of Artificial Boundary Condition Coupled with Finite Element for Dynamic and Wave Problems in Unbounded Media

International Journal of Computational Methods ◽

10.1142/s0219876218500998 ◽

2019 ◽

Vol 16 (04) ◽

pp. 1850099 ◽

Cited By ~ 6

Author(s):

Mi Zhao ◽

Huifang Li ◽

Xiuli Du ◽

Piguang Wang

Keyword(s):

Boundary Condition ◽

Finite Element ◽

Time Domain ◽

The Finite Element Method ◽

Artificial Boundary ◽

Artificial Boundary Condition ◽

Unbounded Media ◽

The Time Domain ◽

Wave Problems ◽

Domain Stability

The finite element modeling of the dynamic and wave problems in unbounded media requires an artificial boundary condition to simulate the truncated infinite domain. The Dirichlet-to-Neumann boundary condition has been transformed from frequency to time domain by using the rational function approximation and auxiliary variable technique. It is extended to three-dimensional layer problem here. The resulting artificial boundary condition is stable itself in time domain, whereas the time-domain instability of the artificial boundary condition coupled with the finite element method is found for the foundation vibration recently and for the wave propagation here. A simple and effective method that introduces the damping proportional to the stiffness matrix in the finite element method is given to cure such coupling instability completely. The stabilized damping is so small that it does not affect the solution accuracy nearly. The numerical examples show the instability phenomenon and indicate the effectiveness of the damping method. The time-domain stability studies here can be a reference for the other artificial boundary conditions.

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