Comparison of Earthquake Input Methods in Soil-structure Interaction Analysis
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摘要: 地震作用下土-结构动力相互作用的整体有限元分析需要在人工边界处输入地震动。目前可能采用的地震输入方法包括黏弹性边界自由场输入方法、自由场应力方法、自由场位移方法以及侧边界自由方法。由于采用近似人工边界条件或者未完全考虑地震自由场，上述地震输入方法均为近似方法。本文以大开地铁车站二维有限元分析为例，根据规范建议的边界位置，研究了上述地震输入方法的精度，研究成果可为土-结构相互作用分析的合理地震输入提供一定参考。
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关键词:
- 土-结构动力相互作用 /
- 地震输入 /
- 黏弹性边界 /
- 自由场 /
- 有限元分析
Abstract: The earthquake input is required in the finite element analysis of the seismic soil-structure interaction. The earthquake input methods that can be used in engineering at present include the free-field input method based on viscous-spring boundary, the free-field stress method, the free-field displacement method, and the free lateral boundary method. The results from these methods are all approximate due to the approximate artificial boundary condition or no consideration of the seismic free field. In this paper, the accuracies of the results by these methods are compared by the 2-dimensional finite element analysis of the Daikai subway station where the artificial boundary position is determined according to the code. This work can give a reference on the earthquake input in the soil-structure interaction analysis. -
图 1 地震作用下土-结构相互作用分析模型示意图
Figure 1. Dynamic soil-structure interaction model under earthquake
图 4 大开车站的土-结构系统有限元模型
Figure 4. Finite element model of soil-structure system of Daikai station
图 5 黏弹性边界自由场输入方法的计算结果（采用文献（刘晶波等，2005a）的黏弹性边界）
Figure 5. Results of the free field input method based on viscous-spring boundary (after Liu et al., 2005a)
图 6 黏弹性边界自由场输入方法的计算结果（采用文献（杜修力等，2006a）的黏弹性边界）
Figure 6. Results of the free field input method based on viscous-spring boundary (from Du et al., 2006)
图 7 黏弹性边界自由场输入方法的计算结果
Figure 7. Results of the free field input method based on viscous-spring boundary
图 8 土-结构相互作用与自由场分析在左侧人工边界深度5.1m处的水平位移
Figure 8. Horizontal displacement at depth 5.1m of left artificial boundary from soil-structure interaction and free field analyses
图 9 自由场应力方法和自由场位移方法的计算结果
Figure 9. Results of the free field stress and displacement methods
图 10 左侧人工边界深度5.1m处水平位移频谱（自由场应力法和自由场位移法）
Figure 10. Horizontal displacement spectrum at depth 5.1m of left artificial boundary based on the free field stress and displacement methods
图 12 左侧人工边界深度5.1m处水平位移频谱（侧边界自由方法）
Figure 12. Horizontal displacements spectrum at depth 5.1m of left artificial boundary based on the free lateral boundary method
表 1 场地的几何及材料常数
Table 1. Geometry and material constants of the site
土层 深度/m 密度/kg·m－3 弹性模量/MPa 泊松比 1 0—1.0 1900 99.3 0.333 2 1.0—5.1 1900 110.0 0.488 3 5.1—8.3 1900 164.0 0.493 4 8.3—11.5 1900 204.0 0.494 5 11.5—17.3 1900 326.0 0.490 6 17.3—39.3 2000 648.0 0.487 7 39.3—∞ 2100 1540.0 0.470 
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表 2 黏弹性边界的常数
Table 2. Constants of the viscous-spring boundary
参考文献 边界法向均布弹簧常数 边界切向均布弹簧常数 边界法向均布阻尼常数 边界切向均布阻尼常数 刘晶波等，2005a $\frac{2G}{r}$ $\frac{3G}{2r}$ $\rho {{c}_{\text{P}}}$ $\rho {{c}_{\text{S}}}$ 杜修力等，2006a $\frac{\lambda +2G}{3.6r}$ $\frac{G}{3.6r}$ $1.1\rho {{c}_{\text{P}}}$ $1.1\rho {{c}_{\text{S}}}$
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