坡体几何参数与弹性模量对岩质斜坡地震动力响应的影响：IBEM求解

doi:10.13722/j.cnki.jrme.2018.1511

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摘要提出一种用于求解层状半空间中斜坡动力响应的间接边界元方法，研究坡体几何参数和弹性模量对岩质斜坡场地地震效应的影响规律。本方法通过在边界上施加斜线和水平线虚拟均布荷载来模拟斜坡地形产生的散射波场，避免了传统边界元方法中的奇异性问题，具有计算精度高、求解速度快的显著优点。文中对该方法的正确性和模型的收敛性进行验证与讨论，进而开展相应的数值计算分析。研究结果表明：(1) 地震作用下岩质斜坡动力响应具有显著的高程放大效应，随着相对高程的增加，斜坡坡面加速度峰值(PGA)放大系数呈非线性增大，且水平向大于竖直向，算例中软质岩和硬质岩对应的最大水平加速度分别是其竖向的1.51和1.14倍；(2) 坡体几何参数和弹性模量对岩质坡顶斜坡动力响应均有重要影响，随着坡角和坡高的增加，PGA放大系数表现为增大趋势，而随着弹性模量的增加，PGA放大系数表现为衰减趋势；(3) 经比较发现，《建筑抗震设计规范》(GB50011—2010)给出的放大系数未考虑岩性的影响，同时也在一定程度上低估了地形效应；(4) 根据不同输入地震波的分析结果，提出斜坡坡顶动力响应规律随几何参数和弹性模量变化的经验公式，方便了结果的定量描述；(5) 通过分析斜坡坡顶的傅里叶谱特征(峰值、形状和卓越频率)，得到了斜坡动力响应随几何参数和弹性模量变化的频谱规律，进而引入谱比曲线定量评估了不同坡角、坡高和弹性模量对应的斜坡坡顶地震动谱放大效应。

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	巴振宁1
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关键词 ：边坡工程, 斜坡场地, 地震响应, 间接边界元, 放大系数, 频谱特性

Abstract：An indirect boundary element method for solving the dynamic response of slopes in layered half-space was proposed，and the influence of geometric parameters and elastic modulus on seismic effect of rock slopes was studied. The method simulates the scattered wave field generated by the slope topography by applying inclined and horizontal fictitious distributed loads on corresponding boundaries，avoiding the singularity problem in the conventional boundary element method and thus obtaining higher calculation accuracy and faster solution speed. The correctness and convergence of the developed method were analyzed，and the corresponding numerical calculations were carried out. Results show that the seismic dynamic response of rock slopes has significant elevation amplification effect，i. e.，the peak acceleration(PGA) amplification factor of the slope surface increases nonlinearly with increasing the relative elevation and the horizontal acceleration response is greater than the vertical. The ratios of the horizontal amplification factor to the vertical respectively corresponding to soft rock and hard rock can reach 1.51 and 1.14 in the calculation examples. The geometric parameters and elastic modulus of the slope have important influence on the dynamic response of the top of the slope. The PGA amplification factor increases with increasing the angle and height of the slope while attenuates with rising the elastic modulus. Comparisons indicate that the amplification factor calculated by the Code for Seismic Design of Buildings (GB50011—2010) does not take into account the influence of lithology and at the same time underestimates the topographic effect to some extent. According to the analysis results with different input seismic waves，an empirical formula for evaluating the dynamic response of the rock slope with the changes of geometric parameters and elastic modulus was proposed，which facilitates the quantitative description of research results. By analyzing the Fourier spectrum characteristics(of rock slopes such as peak value，shape and predominant frequency)，the spectrum law of dynamic response at the top with changing geometric parameters and elastic modulus was obtained，and then the spectral ratio curve was introduced to quantitatively evaluate the spectral amplification effect of ground motion with different angles，heights and shear wave velocities.

Key words： slope engineering slope site seismic response indirect boundary element amplification factor spectrum characteristics

引用本文:

巴振宁1，2，吴孟桃1，2，梁建文1，2. 坡体几何参数与弹性模量对岩质斜坡地震动力响应的影响：IBEM求解[J]. 岩石力学与工程学报, 2019, 38(8): 1578-1592.
BA Zhenning1，2，WU Mengtao1，2，LIANG Jianwen1，2. Influence of geometric parameters and elastic modulus on seismic dynamic response of rock slopes by IBEM#br#. , 2019, 38(8): 1578-1592.

链接本文:

http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2018.1511 或 http://www.rockmech.org/CN/Y2019/V38/I8/1578

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