Ground motion variability of a mountain-canyon site near a strike-slip fault considering uncertainty of source
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摘要:
由于震源不确定性客观存在且对近地表地震动特性产生显著影响，尝试将乘子降维法应用至考虑震源不确定性的近断层复杂场地地震动变异性求解，将不确定性分析问题转换为有限次确定性分析，获得与蒙特卡洛模拟一致的地震动参数统计矩，其中单次确定性分析采用边界元法模拟断层破裂—传播路径—场地放大的整个物理过程。基于乘子降维法，以近走滑断层高山峡谷场地为例，分析了在近断层效应、场地效应和震源不确定性三者耦合作用下的场地地震动峰值加速度（PGA）、峰值速度（PGV）的空间分布变异性，以及关键地表点谱加速度（SA）的统计值。结果表明：乘子降维法适用于含震源参数不确定性的近断层复杂场地随机地震动求解；高山峡谷地形对地震波的散射效应叠加近断层效应后可引起断层上盘PGA和PGV均值的显著增大，可放大至两倍以上；震源不确定性经由场地传播，导致地表地震动变异性，PGA变异性强于PGV；考虑一倍均方差时，震源不确定性对结构反应的影响可达30%以上，大跨度工程结构还应考虑近断层地震动变异性的空间分布差异。
Abstract:A large number of railways and highways in the western part of China are located in near-fault mountain-canyon sites. The bridges and tunnels account for a large proportion due to the complex topography, and many important projects are faced with severe seismic risk. The ground motions in the near-fault mountain-canyon sites are very complex. On the one hand, velocity pulses and large vertical amplitudes are typical characteristics of the ground motions in near-fault regions; on the other hand, the topography of mountains and canyons leads to amplification and non-uniformity effects on ground motions. For example, the 1992 Hualien earthquake records show that the peak ground acceleration on the sidewalls of the Feitsui canyon in Taiwan is 2.69 times than that of the canyon bottom. In the 2008 Wenchuan earthquake, the peak ground acceleration in the east-west direction at the top of Xishan Mountain in Zigong is 1.77 times than that at the foot of the mountain. Theoretical and numerical analyses reveal that the physical essence of the amplification and non-uniformity effect is the scattering and local focusing of seismic waves by the topography of mountain-canyon sites.
In addition, the current technologies of geophysical prospecting make it difficult to finely determine the physical parameters of faults, interface slip characteristics, etc. It means that the fault rupture process has uncertainty. Based on the previous studies, the uncertainty of source existed objectively and had a significant impact on the characteristics of near-surface ground motions. In this study, it is an issue of quantifying uncertainty in ground motion parameters at near-fault mountain-canyon sites. Monte Carlo simulations and logic trees are commonly used to quantify the uncertainty in this problem. The main purpose is to construct different seismic scenarios, focusing on comparing the standard deviation of the spatial distribution of ground motions in the actual regional site with the standard deviation in the ground motion prediction model. It is worth pointing out that the Monte Carlo simulation has low efficiency to carry out the multidimensional uncertainty analysis. Besides, the simulation of ground motions in near-fault mountain-canyon sites needs to take into account near-fault and topography effects. Meanwhile, the uncertainty of the seismic source will cause random scattering of the seismic waves in mountain-canyon sites, which will lead to the variability of the ground motion parameters at various surface locations. However, the existing studies have not explored the propagation mechanism in depth.
In this paper, the multiplicative dimensional reduction method （M-DRM） is applied to solve the ground motion variability of complex sites near-fault considering the uncertainty of the source. The uncertainty analysis problem is converted into a finite deterministic analysis to obtain statistical moments of ground motion parameters consistent with Monte Carlo simulation. The deterministic analysis uses the boundary element method to simulate the entire physical process. Based on this method, the mountain-canyon site near a strike-slip fault was discussed as an example. The spatial distribution variability of the peak acceleration （PGA） and peak velocity （PGV） under the coupling of near-fault effect, site effect and source epistemic uncertainty was analyzed, as well as statistical values of spectral acceleration （SA） at some surface points.
The results indicated that the M-DRM is applied to the ground motion variability problem of near-fault mountain-canyon sites caused by seismic source uncertainty, which has higher computational efficiency compared with the conventional Monte Carlo simulation. This method can be used for the stochastic ground motion simulation of the complex sites based on the phylsical model and considering the uncertainty of seismic source. When there is a mountain-canyon topography in the near-fault region, the coupling of the near-fault effect and the local site effect causes a significant amplification of the mean values of the PGAs at the sites, which shows significant spatial variations, especially in the canyon. It can be up to 2.69 times that of the result without the local topography. The mean values of the variability of the PGVs at the different surface points are smaller than those of the PGAs. The structural periods corresponding to the maximum values of the surface ground motion acceleration response spectrum are basically the same under the conditions with and without mountain-canyon topography. The seismic source uncertainty is propagated through the site, which is finally manifested in the spatial distribution variability of PGAs and PGVs. Due to the different energy distributions of ground motion acceleration and velocity, there are differences in the variability of PGAs and PGVs. PGAs have larger coefficients of variation. The variability of PGAs and PGVs is different from that of a single parameter under different rupture scenarios when both the asperity intensity and the rupture velocity uncertainty are taken into account. However, the results of the acceleration response spectrum are more complicated. The variability of the structural response at different locations may be lower or higher than the superposition of single-parameter uncertainty variability, and it is affected by the location of the asperity.
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Keywords:
- site effect /
- near-fault effect /
- source uncertainty /
- boundary element method
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图 9 近断层场地PGV空间分布变异性
（a） 考虑凹凸体强度不确定性；（b） 考虑破裂速度不确定性；（c） 同时考虑凹凸体强度和破裂速度不确定性
Figure 9. Spatial distribution variability of PGVs in the near-fault site
（a） Considering asperity intensity uncertainty ；（b） Considering rupture velocity uncertainty；（c） Considering asperity intensity and rupture velocity uncertainty
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图 1 近走滑断层高山峡谷场地计算模型示意图
Figure 1. Calculation model of mountain-canyon site near a strike-slip fault
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图 2 不同断层角度下本文方法与Kara和Trifunac （2014）方法所得地表位移结果对比
（a） 倾角为π/24；（b） 倾角为π/4；（c） 倾角为π/2
Figure 2. Comparison of surface displacement results obtained by the proposed method and the method in reference Kara and Trifunac （2014） under different fault angles
（a） Dip angle of π/24；（b） Dip angle of π/4；（c） Dip angle of π/2
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图 3 用于验证的计算模型
（a） 场地计算模型，图中A，B，C，D，E，F为地表参考点；（b） 断层模型
Figure 3. Calculation model for verification
（a） Calulation model of sites，and A，B，C，D，E and F are the surface reference point；（b） Fault model
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图 4 不同入射频率波下高山峡谷场地位移幅值均值（a）及其均方差（b）
Figure 4. Mean values of displacement amplitude of mountain-canyon site （a） and mean square deviation of displacement amplitude of mountain-canyon site （b） under different incident frequency waves
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图 5 考虑凹凸体位置不确定性的破裂情景
Figure 5. Rupture scenarios considering uncertainty of asperity positions
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图 6 考虑凹凸体强度不确定性时近断层场地PGA空间分布变异性
（a） 破裂情景1；（b） 破裂情景2；（c） 破裂情景3
Figure 6. Spatial distribution variability of PGAs in the near-fault site considering asperity intensity uncertainty
（a） Rupture scenario 1；（b） Rupture scenario 2； （c） Rupture scenario 3
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图 7 考虑破裂速度不确定性时近断层场地PGA空间分布变异性
（a） 破裂情景1；（b） 破裂情景2；（c） 破裂情景3
Figure 7. Spatial distribution variability of PGAs in the near-fault site considering rupture velocity uncertainty
（a） Rupture scenario 1；（b） Rupture scenario 2； （c） Rupture scenario 3
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图 8 考虑凹凸体强度和破裂速度不确定性时近断层场地PGA空间分布变异性
（a） 破裂情景1；（b） 破裂情景2；（c） 破裂情景3
Figure 8. Spatial distribution variability of PGAs in the near-fault site considering asperity intensity and rupture velocity uncertainty
（a） Rupture scenario 1；（b） Rupture scenario 2；（c） Rupture scenario 3
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图 10 考虑凹凸体强度不确定性时近断层场地SA空间分布变异性
（a） A点；（b） B点；（c） C点；（d） D点；（e） E点；（f） F点。μ1和μ2分别代表有、无高山峡谷地形时观测点SA均值，σ为存在高山峡谷地形时观测点SA均方差，阻尼比取为0.05，下同
Figure 10. Spatial distribution variability of SAs in the near fault site considering asperity intensity uncertainty
（a） Point A；（b） Point B；（c） Point C ；（d） Point D；（e） Point E；（f） Point F. μ1 and μ2 represent mean SAs at observed points with and without the mountain-canyon site， σ represents the root mean squares of SAs at observed points with the mountain-canyon site，and the damping ratio is 0.05，the same below
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图 12 同时考虑凹凸体强度和破裂速度不确定性时近断层场地SA空间分布变异性
（a） A点；（b） B点；（c） C点；（d） D点；（e） E点；（f） F点
Figure 12. Spatial distribution variability of SAs in the near-fault site considering asperity intensity and rupture velocity uncertainty
（a） Point A；（b） Point B； （c） Point C ；（d） Point D；（e） Point E；（f） Point F
表 1 边界元法数值稳定性验证 （η＝0.25）
Table 1 Numerical stability verification of boundary element method （η＝0.25）
x/a 边界元法参数 解析解 N＝600，
L＝561N＝1 000，
L＝801N＝1 400，
L＝1 041−2.0 0.070 3 0.070 7 0.070 4 0.070 4 −1.5 0.091 3 0.090 9 0.090 8 0.090 8 −1.0 0.518 9 0.519 9 0.522 6 0.522 6 −0.5 0.495 0 0.516 7 0.551 2 0.551 2 0.5 0.744 8 0.749 8 0.754 7 0.754 7 1.0 0.494 2 0.547 7 0.551 2 0.551 2 1.5 0.097 8 0.099 2 0.100 3 0.100 3 2.0 0.083 3 0.084 0 0.084 6 0.084 6 
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