地震波斜入射下岩质边坡放大效应的数值模拟研究

Numerical study on the amplification effect of rock slopes under obliqueincidence of seismic waves

近源地震中,地震波入射角对岩质边坡的放大效应影响显著。基于黏弹性人工边界理论和等效节点力原理,结合有限单元法建立了可以考虑地震SV波和P波斜入射的地震动输入方法,研究了岩质边坡的坡角、地震波入射角以及入射波类型对边坡放大效应的影响规律。边坡峰值地面加速度(peakgroundacceleration,简称PGA)放大系数结果表明,若仅考虑地震波垂直入射的情况,边坡的动力放大效应可能会被严重低估。此外,边坡坡角的变化和入射波类型的改变也对边坡的放大效应有显著的影响。将计算得到的PGA放大系数与相关规范中建议的放大系数对比发现,规范建议值在一些情况下低估了放大效应。边坡坡顶的加速度频谱结果显示,地震波入射角对坡顶加速度傅里叶谱的主频影响较小,但对其傅里叶谱的幅值影响较大。随着SV波入射角的增大,坡顶水平加速度傅里叶谱幅值整体上变化不显著,而竖向加速度傅里叶谱幅值逐渐增大;随着P波入射角的增大,坡顶竖向加速度傅里叶谱幅值逐渐减小而水平向幅值逐渐增大。引入谱比曲线定量评估了不同入射条件下边坡坡顶的谱放大效应,获得了坡顶谱比峰值的变化规律。

The influence of the incident angle of seismic waves on the amplification effect of rock slopes is obvious in near-source earthquakes.Based on the theory of viscous-spring artificial boundary and the principle of equivalent nodal force,a seismic input method for oblique incidence of seismic SV and P waves is established and implemented in the finite element method.Various influencing factors such as slope inclination,incident angle of seismic wave,and type of incident wave are considered,and then a numerical study is conducted to investigate the amplification effect of rock slopes.The results of the peak ground acceleration(PGA)amplification factor of the slope show that the amplification effect of the rock slope may be significantly underestimated if only the vertical incidence of seismic waves is considered.In addition,the slope inclination and the type of incident wave also have a significant influence on the amplification effect.By comparing the calculated results of the PGA amplification factor with those suggested by the Code for Seismic Design of Buildings(GB50011―2010),it is found that the values suggested by the seismic code may underestimate the amplification effect in some cases.The results of the spectral characteristics of the acceleration at the slope crest reveal that the incident angle of the seismic waves has little effect on the main frequency of the Fourier spectrum but has a significant effect on the Fourier amplitude.As the incident angle of the SV-wave increases,the Fourier amplitude of vertical acceleration at the slope crest increases,while the variation of Fourier amplitude of horizontal acceleration is not obvious.As the incident angle of P-wave increases,the Fourier amplitude of vertical acceleration at the slope crest decreases while that of horizontal acceleration increases.Finally,the spectral ratio curve is introduced to quantitatively evaluate the effects of different influencing factors on the spectral amplification of slope crest,and the variation pattern of the peak spectral ratio under different incident conditions is obtained.