地下结构抗震分析的振动法与波动法对比研究

A Comparison between Vibration and Wave Methods in Seismic Analysis of Underground Structures

摘要:

针对地下结构抗震分析中应用广泛的波动方法与振动方法，从物理方程和有限元格式出发，明确了两种方法的区别与联系。通过标准数值试验，证明了振动方法是波动方法采用下卧刚性基岩假设和地层水平无限延伸假设，仅考虑SV波垂直向上入射的一种特例。采用波动方法模拟弹性地基，对比振动方法结果，表明弹性地基和刚性地基上地表位移响应和隧道结构内力响应均有显著差异。建议应根据具体场地条件，选择振动或波动方法进行地下结构抗震设计研究。

Abstract:

The wave and vibration methods of seismic analysis are widely employed with underground structures. Comparisons between the two approaches were conducted in the paper. First, the wave method, i.e., the viscoelastic artificial boundary and pertinent equivalent nodal force method, is introduced briefly. Second, the governing equation and finite element formulation of the problem are presented to clarify the interrelation and distinction between the two methods. On the basis of standard numerical tests, it was proved that the vibration method is only applicable to degraded cases, with assumptions of a rigid base and an SV propagating vertically upward. Then, the comparison between the rigid base and the elastic base was conducted. The rigid base was simulated through the vibration method, while the elastic base was simulated using the equivalent nodal force method. The results showed that there are significant differences between elastic and rigid bases in terms of ground surface displacement response and internal force response of tunnel structures. Therefore, the influence of different site conditions was far from negligible, and the analysis method should be carefully selected based on site conditions and whether a rigid or elastic base is incorporated into the seismic design of underground structures.