Probabilistic seismic slope displacement hazard analysis based on Newmark displacement model：Take the area of Tianshui，Gansu Province，China as an example
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摘要: 本文以天水地区为研究区，结合地震潜在震源区模型和Newmark位移预测方程，采用概率地震危险性分析方法，计算了该地区50年超越概率10%水平下的Newmark位移。同时，根据天水地区50年超越概率10%下的阿里亚斯烈度，并结合Newmark位移与阿里亚斯烈度的关系式，计算了天水地区在遭受50年超越概率10%下的阿里亚斯烈度影响时，潜在滑坡体产生的Newmark位移分布。通过比较上述两种方法得到的天水地区不同Newmark位移的分布特征，本文认为二者虽然存在较大差异，但其空间分布特征均能反映天水地区每个场点处的相对滑坡危险性。对滑坡危险性水平进行分区的结果显示，天水地区60%以上的区域具有高地震滑坡危险性，50%以上的区域具有甚高地震滑坡危险性。本文的研究结果可以作为天水地区地震危险性及风险评估的参考资料，也可以作为天水地区城市规划、土地使用规划、地震应急准备以及其它公共政策制定的参考资料。Abstract: Earthquake-induced landslide is a kind of destructive earthquake secondary disaster, which could cause serious casualties and property damage. The Tianshui area of Gansu Province has suffered severe landslides caused by several strong earthquakes. In this paper, based on the model of potential seismic sources and the prediction equation of Newmark displacement, we adopt the method of probabilistic seismic hazard analysis to study the probabilistic seismic landslide hazard in Tianshui area, and to calculate the values of Newmark displacement under the 10% probability of being exceeded in 50 years. Meanwhile, according to the Arias intensity under the 10% probability of being exceeded in 50 years in Tianshui area, combined with the relationship between Newmark displacement and Arias intensity, we also calculate the Newmark displacement of potential landslides when Tianshui area suffered from the Arias intensity under the 10% probability of being exceeded in 50 years. We compare the two sets of the values of Newmark displacement obtained by these two different methods, and find that there are significant difference, but still can reflect the relative landslide hazard of each site in Tianshui area. According to the results of landslide hazard zoning, more than 60% of the area in Tianshui has high earthquake-landslide hazard, and more than 50% of the region in Tianshui has very high earthquake-landslide hazard. The research results of this paper can be used as the reference materials of seismic hazard and risk assessment of Tianshui area, and can also be used as the reference materials of city planning, land use planning, earthquake emergency preparedness and other public policy making in Tianshui area.
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图 1 Newmark位移滑块模型（引自Jibson et al，1998）
Figure 1. Sliding-block model of Newmark displacement （after Jibson et al，1998）
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图 2 Newmark位移计算示意图（Wilson， Keefer，1983）
Figure 2. Demonstration of the Newmark-analysis algorithm （after Wilson，Keefer，1983）
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图 3 研究区周缘潜在震源区（a）及研究区具体范围（b）
Figure 3. Potential seismic sources around the Tianshui region （a） and the scope of the studied region （b）
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图 4 概率地震滑坡危险性分析计算流程图
Figure 4. Flow chart showing steps involved in producing a seismic landslide hazard map
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图 6 采用机器学习方法得到的覆盖层厚度分布图
Figure 6. Map showing the slab thickness obtained from machine learning method
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图 9 50年超越概率10%的Newmark位移D
Figure 9. Predicted Newmark displacements D with 10% probability of exceedance in 50 years
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图 10 不同临界加速度ac下Newmark位移的超越概率曲线
Figure 10. Newmark displacement hazard curves under different critical accelerations
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图 11 受到50年超越概率10%下的地震动（阿里亚斯烈度）影响时的Newmark位移
Figure 11. Newmark displacement hazard for shaking conditions related to 50-year exceedance probabilities of 10%
表 1 天水地区地质单元的剪切强度参数
Table 1 Shear strengths of geologic units in Tianshui
岩性 权重 c′ /kPa ϕ′ /° γ/（kN·m−3） 软岩（如泥岩等） 0.2 30 25 23.0 极软岩（如第四纪覆盖层） 0.8 24 21 15.4 
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表 2 Du和Wang （2016）计算的Newmark位移预测方程参数
Table 2 Coefficients of the Newmark displacement prediction equation proposed by Du and Wang （2016）
ac c1 c2 c3 c4 c5 c6 c7 h ν1 τ σ σt c8 c9 c10 c11 0.02 g 8.15 −0.14 −5.04 0.45 0.54 −2.25 − 6.32 −1.26 0.45 1.33 1.40 1.04 1.46 −1.71 −0.37 0.05 g 8.23 −0.18 −4.57 0.31 0.64 −4.84 0.31 5.72 −1.26 0.39 1.55 1.59 3.69 0.97 −1.74 −0.51 0.075 g 7.11 −0.08 −5.17 0.40 0.75 −3.21 0.09 4.19 −0.92 0.50 1.56 1.63 4.52 0.76 −1.76 −0.52 0.1 g 7.29 −0.14 −4.10 0.22 0.72 −4.67 0.38 4.23 −0.86 0.54 1.60 1.70 4.13 0.64 −1.78 −0.39 0.15 g 7.13 −0.21 −2.77 − 0.80 −1.35 − 4.55 −0.55 0.45 1.78 1.84 4.10 0.37 −1.51 −0.37 0.2 g 6.12 −0.25 −2.42 − 0.74 −1.65 − 5.53 −0.57 0.42 1.78 1.82 2.76 0.28 −1.27 −0.25 0.25 g 15.21 −0.27 −5.33 − 1.04 −0.72 − 14.30 −0.43 0.29 1.76 1.78 1.53 0.26 −1.14 −0.15
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