Numerical Modeling Techniques of Rayleigh Wave Field and Its Application
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摘要: 本文总结了Rayleigh波场数值模拟的4种思路和各自特点，根据Lamb问题的理论分析成果提出了基于地表激振的Rayleigh波场数值模拟技术，论述了地表集中震源作用下引起地表波动场的特点及主要影响因素。在此基础上，利用Plaxis 2D有限元软件实现了Rayleigh波场的数值模拟，并结合算例验证了所提方法的可行性和结果的合理性。最后，针对多层建筑结构，研究了不同地震动输入模式下结构动力反应的特点。结果表明，Rayleigh波作用下结构的动力反应特性明显区别于在底部输入剪切波时的结果，不同地震动输入模式对结构的振动形态和破坏模式有着明显的影响。Abstract: Four different approaches about numerical modeling techniques of Rayleigh wave field were summarized. The techniques base on vertical harmonic point load on the free surface has been proposed in this paper. The main research achievements of Lamb issues, such as the characteristics of Rayleigh wave field under point load and its main influencing factors were discussed. On this basis the numerical modeling of Rayleigh wave field with Plaxis 2D was conducted and the effectiveness of the approach was verified with an example. The dynamic response of a multi-story building structure during propagation of Rayleigh wave was analyzed using the proposed method, and the results were compared to that from the traditional methods. Numerical analysis results show that different wave motion input methods have great effect on the dynamic response of building structures. The vibration shape and failure modes of the structure were greatly influenced by seismic input modes.
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Key words:
- Rayleigh wave /
- Lamb issues /
- Plaxis 2D software /
- Numerical modeling /
- Wave motion input /
- Multi-story building
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图 1 Rayleigh波场数值模拟的有限元网格划分
Figure 1. The finite element model for Rayleigh wave field simulation
图 2 不同时段有限元网格变形示意图
Figure 2. Illustration of deformation of finite element nets in different time domains
图 6 含建筑结构的场地有限元模型
Figure 6. The finite element model for soil-structure interaction analysis
图 7 Rayleigh波作用下不同时刻建筑物的振动形态
Figure 7. Deformation diagram by finite element model under Rayleigh wave
图 8 Rayleigh波作用下建筑物顶层两侧角点的水平和竖向位移时程
Figure 8. The displacement time histories in horizontal and vertical at the top of building under Rayleigh wave
图 9 剪切波作用下不同时刻建筑物的振动形态
Figure 9. Deformation diagram by finite element model under shear wave
图 10 剪切波作用下建筑物顶层两侧角点的水平和竖向位移时程
Figure 10. The displacement time histories in horizontal and vertical at the top of building under shear wave
图 11 剪切波与Rayleigh波联合作用下建筑物顶层两侧角点的水平和竖向位移时程
Figure 11. The displacement time histories in horizontal and vertical at the top of building under Rayleigh and shear wave
表 1 Plaxis 2D中土层材料参数
Table 1. Soil material parameters in the Plaxis 2D
材料模型 饱和重度 弹性模量 泊松比 线弹性 20kN/m3 5×104kN/m2 0.3 
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表 2 Plaxis 2D中振动基础材料参数
Table 2. Foundation material parameters in the Plaxis 2D
材料模型 重度 弹性模量 泊松比 轴向刚度 线弹性，各向同性 5kN/m3 2.4×104kN/m2 0.2 7.6×106kN
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表 3 建筑物材料属性（板单元）
Table 3. The material parameters of the building
材料类型 轴向刚度 抗弯刚度 重度 泊松比 上部结构：线弹性，各向同性 9.6×106kN 6.75×104kN·m2 10kN/m3 0.2 地下室：线弹性，各向同性 1.2×107kN 1.6×105kN·m2 20kN/m3 0.2
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表 4 点对点锚杆材料属性
Table 4. The material parameters of the central pillar
材料类型 轴向刚度 平面外间距 线弹性 2.5×106kN 3.0m
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