Seismic Response of the Adjacent Semi-cylindrical Hill in Layered Half Space for Incident SV Wave
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摘要: 采用有限元方法计算SV波入射下层状半空间相邻2个半圆形凸起地形的地震响应，比较分析相邻凸起之间的相互影响。研究结果表明：（1）当无量纲频率
$\eta $ 较小时，凸起间距对地表位移谱放大系数$\beta $ 的影响明显大于高频；凸起间距越小，右侧凸起对左侧凸起的影响越大，而左侧凸起对右侧凸起的影响还受入射角度限制。（2）当无量纲频率$\eta $ > 1.0 时，对于相同的入射波频率和入射角度，凸起间距越大，对谱放大系数的影响越小。（3）当输入地震波波长大于凸起地形宽度时，相邻凸起的影响可忽略。（4）与SV波入射下均匀半空间半圆形凸起地形的地震响应相比，无论是单个半圆形凸起还是相邻2个半圆形凸起，在$ \left|x/a\right| $ ≤1.0范围内，层状半空间地表位移谱放大系数明显大于均匀半空间地表位移谱放大系数；在$ \left|x/a\right| $ ≥1.0范围内，偶尔会出现层状半空间地表位移谱放大系数小于均匀半空间地表位移谱放大系数的情形。Abstract: In this paper, the seismic response of two adjacent semi-cylindrical hills in layered half space for incident SV wave is calculated by finite element method. The interaction between adjacent hills is compared and analyzed, and the conclusions are as follows: (1) When the dimensionless frequency$\eta $ is small, the effect of the hill distance L on the spectral amplification coefficient$\beta $ is significantly greater than that of high frequencies. In addition, the smaller the hill distance is, the greater the influence of the right hill on the left hill. And the influence of the left hill on the right hill is also affected by the incident angle. (2) When$\eta $ >1.0, for the same incident wave frequency and incident angle, the larger the hill distance, the smaller the influence on the spectral amplification coefficients$\beta $ . (3) When the input wave wavelength is greater than the width of the hill, the interaction between adjacent hill could be ignored. (4) Compared with the seismic response of the semi-cylindrical hill in the half space, whether it is a single hill or two adjacent hills, in the range of$| x /a | $ ≤1.0, the surface displacement spectrum amplification coefficient of the layered half space is obviously larger than that of the uniform half-space. In the range of$| x /a | $ ≥1.0, occasionally the amplification coefficient of the surface displacement spectrum of the layered half-space is smaller than that of the uniform half-space. -
图 1 结构-地基系统动力反应分析示意
Figure 1. Schematic diagram of dynamic response analysis of structure-foundation system
图 2 人工边界附近节点（一维波动模型）
Figure 2. Node number near artificial boundary（One-dimensional wave model）
图 4 本文计算结果与文献（Kamalian等，2006）
Figure 4. Comparison of results from this paper and reference（Kamalian et al.，2006）
图 6 计算模型示意（相邻2个凸起半圆地形）
Figure 6. Schematic diagram of calculation model- two adjacent cylindrical hills
图 7 不同凸起间距下左侧凸起地表位移谱放大系数（模型A，
$ \theta $ =0°）Figure 7. Spectral amplification of surface observation points of left hill with different hill distance （Model A,
$ \theta $ =0°）
图 8 不同凸起间距下左侧凸起地表位移谱放大系数（模型A，
$ \theta $ =15°）Figure 8. Spectral amplification of surface observation points of left hill with different hill distance （Model A,
$ \theta $ =15°）
图 9 不同凸起间距下左侧凸起地表位移谱放大系数（模型A，
$ \theta $ =30°）Figure 9. Spectral amplification of surface observation points of left hill with different hill distance （Model A,
$ \theta $ =30°）
图 10 不同凸起间距下右侧凸起地表位移谱放大系数（模型B，
$ \theta $ =0°）Figure 10. Spectral amplification of surface observation points of right hill with different hill distance （Model B,
$ \theta $ =0°）
图 11 不同凸起间距下右侧凸起地表位移谱放大系数（模型B，
$ \theta $ =15°）Figure 11. Spectral amplification of surface observation points of right hill with different hill distance （Model B,
$ \theta $ =15°）
图 12 不同凸起间距下右侧凸起地表位移谱放大系数（模型B，
$ \theta $ =30°）Figure 12. Spectral amplification of surface observation points of right hill with different hill distance （Model B,
$ \theta $ =30°）
图 13 左侧凸起地表位移谱放大系数比较（L = a
） Figure 13. Comparison of the surface spectral amplification of the left hill （L=a ）
图 14 右侧凸起地表位移谱放大系数比较（L = a
） Figure 14. Comparison of the surface spectral amplification of the right hill （L=a ）
表 1 无量纲频率对应的实际频率
Table 1. Actual frequency corresponding to the dimensionless frequency
$ \eta $ 0.25 0.5 0.75 1 2 4 $ f $/Hz 1.25 2.5 3.75 5 10 20 
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