Numerical parametric study of seismic dynamic response and amplification effects of slope topography
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摘要: 本文采用隐式动力有限单元法研究了不同的边坡角度和边坡高度对地形放大效应的影响，并以位移峰值放大系数为衡量地震动放大效应的标准，计算了不同边坡角度和边坡高度条件下的地震响应，在此基础上对模型关键监测点的输出波形以及位移峰值放大系数的变化趋势进行了分析，获得了不同监测点处的地震动时程曲线，揭示了坡角和坡高对单体边坡地震动放大效应的定量作用规律。数值结果表明，相同高度处坡面监测点的水平向位移峰值放大系数大于坡内监测点的，地形放大效应在水平方向具有趋表效应。由于坡面存在入射波和反射波的叠加，因此竖直向位移峰值放大系数的最大值出现在坡体内部。Abstract: In this paper, the implicit dynamic finite element method was applied to analyze the seismic dynamic response and amplification effects of slope topography with different slope angles and heights. With the peak displacement amplification factor （PDA） as the measurement of the amplification effects of seismic waves, the seismic dynamic response based on the PDA under the different conditions was investigated. And then the topographical amplification effects of seismic waves were investigated by analyzing the output waveforms of key monitoring points in the numerical model as well as the variation trend of PDA. Consequently, the time history curves of ground motion at the different monitoring points were obtained. The peak displacement amplification effects induced by different slope angles and heights were quantitatively analyzed and discussed. The numerical results showed that, when the monitoring points were at the same height, the PDAs at the slope surface were larger than those inside the slope. The PDA had the surface effect in horizontal direction. Namely, the more close to the surface was, the larger PDA was. Due to the superposition of the incident seismic waves and the reflected waves induced by the slope surface, the maximum amplification factor of vertical peak displacement appeared inside the slope. The numerical results can provide some guidance in predicting and evaluating the vibration intensity and disaster degree of slopes to some extent.
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图 3 本模型输入的雷克子波的位移（a）和加速度（b）时程曲线
Figure 3. Displacement （a） and acceleration （b） time-history curves of input Ricker wavelet
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图 4 入射点沿x向（a）和y向（b）的入射波形以及总入射波形（c）
Figure 4. Input waveform in x （a） and y （b） directions and total incident waveform （c）
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图 5 不同坡角α条件下关键监测点的总位移输出
Figure 5. Total displacement output of key monitoring points under different slope angles α
（a） α＝30°；（b） α＝45°；（c） α＝60°；（d） α＝75°
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图 6 不同坡角α时各监测点的位移峰值放大系数
（a） 水平向位移峰值放大系数；（b） 竖直向位移峰值放大系数；（c） 总位移峰值放大系数
Figure 6. Peak displacement amplification factor （PDA） of the monitoring points under different slope angle α
（a） Horizontal PDA；（b） Vertical PDA；（c） Total PDA
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图 7 各监测点位移峰值放大系数随坡角α的变化
（a） 水平向位移峰值放大系数；（b） 竖直向位移峰值放大系数；（c） 总位移峰值放大系数
Figure 7. Variation of peak displacement amplification factor of monitoring points with slope angle α
（a） Horizontal PDA；（b） Vertical PDA；（c） Total PDA
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图 8 不同坡角工况下坡表面监测点位移放大系数
（a） 水平向位移峰值放大系数；（b） 竖直向位移峰值放大系数；（c） 总位移峰值放大系数
Figure 8. PDA of observation points under different slope angle α
（a） Horizontal PDA；（b） Vertical PDA；（c） Total PDA
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图 9 不同位置监测点的放大效应规律
（a） 水平向位移峰值放大系数；（b） 竖直向位移峰值放大系数；（c） 总位移峰值放大系数
Figure 9. Amplification effect of the monitoring points at different locations
（a） Horizontal PDA；（b） Vertical PDA；（c） Total PDA
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图 10 边坡高度对各监测点放大效应的影响
（a） 水平向位移峰值放大系数；（b） 竖直向位移峰值放大系数；（c） 总位移峰值放大系数
Figure 10. Amplification effect of the monitoring points under different slope height
（a） Horizontal PDA；（b） Vertical PDA；（c） Total PDA
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图 11 不同坡高工况下坡表面监测点的位移峰值放大系数
（a） 水平向位移峰值放大系数；（b） 竖直向位移峰值放大系数；（c） 总位移峰值放大系数
Figure 11. PDA of the observation points under different slope height
（a） Horizontal PDA；（b） Vertical PDA；（c） Total PDA
表 1 本文模型的材料参数
Table 1 Material parameters of the model in this study
材料 密度/（kg·m−3） 弹性模量/GPa 泊松比 岩体 2 400 50 0.25 节理 2 320 5 0.30 
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