Vulnerability analyses of masonry structure under induced earthquake
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摘要:
为揭示诱发地震和天然地震对建筑结构影响及其破坏概率分布的影响，本文以我国典型砌体结构为研究对象，开展了考虑诱发地震影响的易损性研究。首先建立了典型三层和六层砌体结构分析模型，然后以40条震级和震中距都接近的天然地震地震动和诱发地震地震动为输入开展Pushover分析，分别建立基于峰值加速度PGA和结构基本周期加速度反应谱值Sa的易损性曲线，最后采用循环往复加载方法对两次诱发地震作用下的结构倒塌易损性进行了分析讨论。结果表明：当以PGA作为易损性输入地震动参数时，天然地震地震动作用下的易损性显著高于诱发地震地震动；当以Sa作为易损性输入地震动参数时，三层砌体结构由于以基本振型为主导，在两类地震动作用下其易损性曲线比较接近，而六层砌体结构高阶振型由于对结构地震响应具有一定影响，且诱发地震地震动的高频成分较天然地震地震动丰富，因此六层砌体结构在诱发地震地震动作用下的易损性高于天然地震。此外，对两次诱发地震作用下的砌体结构易损性分析结果表明两次地震作用下结构的损伤概率明显增加。
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关键词:
- 诱发地震 /
- 天然地震 /
- 砌体结构 /
- Pushover分析 /
- 地震易损性分析
Abstract:The impact of earthquake induced by shale gas mining has attracted the attention of the government, academia and the public. It is of scientific significance and application value for the prevention and control of earthquake disaster risk to carry out seismic vulnerability research of induced earthquakes. There are significant differences between induced earthquakes and natural earthquakes in ground motion characteristics, and their seismic responses to engineering structures are also very different. In order to reveal the influence of induced earthquake and natural earthquake on the seismic effects of building structure and the distribution of failure probability of masonry structure, this paper takes typical masonry structure as the research object and develops the vulnerability study considering the effects of induced earthquake. At first, analysis models of typical three-story and six-story masonry structures are established, and then 40 natural ground motions and induced seismic ground motion with similar magnitude and epicenter distances are selected as inputs to the Pushover analysis. Finally vulnerability curves based on peak ground acceleration （PGA） and basic periodic acceleration response spectrum value Sa of the structure are established respectively. The cyclic loading method is used to analyze and discuss the structural collapse vulnerability under two induced earthquakes. The analysis shows that the induced seismic ground motion contains more high frequency components, while the natural ground motion has more low frequency components, when PGA is used as the vulnerability parameter, the vulnerability of natural ground motion is significantly higher than that of induced seismic ground motion. When Sa is used as the vulnerability parameter to input ground motion, the vulnerability curves of the three-story masonry structure are close to each other under the action of two kinds of ground motions because the basic mode is dominant. However, the high-order mode of six-story masonry structure has some influence on the seismic response of the structure, and the high-frequency components of induced seismic ground motion are more abundant than those of natural ground motion, so the vulnerability of six-story masonry structure under induced seismic ground motion is higher than that of natural ground motion. In addition, the cyclic loading method is used to analyze the vulnerability of masonry structures under the two induced earthquakes. The results show that the damage probability of structures increases obviously under the action of two induced earthquakes.
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图 3 砌体结构层间剪切模型示意图
Figure 3. Schematic diagram of interlayer shearing model of masonry structure
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图 4 三线性恢复力模型示意图（张令心等，2002）
Figure 4. Schematic diagram of trilinear restoring of masonry structure force model （after Zhang et al，2002）
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图 5 诱发地震（a）和天然地震（b）的地震动加速度反应谱
Figure 5. Ground motion acceleration response spectra of induced earthquake （a） and natural earthquake （b）
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图 6 诱发地震与天然地震的平均地震动加速度反应谱
Figure 6. Mean ground motion acceleration response spectra of induced and natural earthquakes
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图 7 诱发地震（a）与天然地震（b）的三层结构地震概率需求模型
Figure 7. Probabilistic seismic demand models of three-story structure for induced earthquakes （a） and natural earthquakes （b）
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图 8 三层（上）、六层（下）砌体结构基于PGA （a）和Sa （b）的易损性曲线
Figure 8. Vulnerability curves of three-storey （top） and six-storey （bottom） masonry structures based on PGA （a） and Sa （b）
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图 9 基于PGA归一化后的天然地震和诱发地震的平均地震动加速度反应谱
Figure 9. Mean ground motion acceleration response spectra of natural and induced earthquakes after PGA normalization
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图 10 基于Sa （0.15 s）（a）和Sa （0.34 s）（b）归一化后的天然地震与诱发地震的平均地震动加速度反应谱
Figure 10. Mean ground motion acceleration response spectra of natural earthquakes and induced earthquakes after Sa （0.15 s）（a） and Sa （0.34 s）（b） normalization
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图 11 两次诱发地震作用下三层（a）、六层（b）砌体结构毁坏的易损面
Figure 11. Vulnerable surfaces of three-story （a） and six-story （b） masonry structure collapse under two induced earthquakes
表 1 砌体结构延性系数与破坏等级之间的关系（郝敏等，2007）
Table 1 Relationship between ductility coefficient and damage grade of masonry structure （Hao et al，2007）
破坏等级 延性系数μ 能力参数限值 基本完好 μ≤0.68 轻微破坏 0.68＜μ≤1.3 0.68 中等破坏 1.3＜μ≤3.5 1.3 严重破坏 3.5＜μ≤6.5 3.5 毁坏 μ＞6.5 6.5 
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表 2 砌体墙段开洞影响系数
Table 2 Influence coefficient of masonry wall with opening
开洞率 影响系数φ0 开洞率 影响系数φ0 0.9 0.98 0.6 0.76 0.8 0.94 0.5 0.68 0.7 0.88 0.4 0.56
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表 3 天然地震地震动与诱发地震地震动记录的基本信息
Table 3 Basic information of ground motion records of natural and induced earthquakes
诱发地震 天然地震 诱发地震 天然地震 M 震中距
/kmPGA
/（cm·s−2）M 震中距
/kmPGA
/（cm·s−2）M 震中距
/kmPGA
/（cm·s−2）M 震中距
/kmPGA
/（cm·s−2）4.7 12.95 14.04 4.79 13.55 38.97 4.9 31.4 27.71 4.92 31.71 30.24 4.7 2.71 63.94 4.7 2.84 158.0 4.9 15.02 69.84 4.92 14.94 38.79 5.7 27.29 62.39 5.7 27.78 36.42 4.3 3.95 197.5 4.27 3.69 20.02 4.8 27.63 63.60 4.88 27.89 103.6 4.4 6.02 231.6 4.45 6.46 33.72 4.5 5.17 36.20 4.6 5.2 184.5 4.5 7.28 43.7 4.45 7.46 63.36 4.5 10.04 19.55 4.6 10.16 12.10 4.1 2.0 261.5 4.12 1.42 167.51 4.5 4.47 367.8 4.45 4.7 29.43 4.1 4.23 97.21 4.1 4.41 99.87 4.3 2.47 215.5 4.27 2.67 48.83 4.4 6.71 114.9 4.37 6.48 6.004 4.3 5.66 267.6 4.3 5.28 37.54 4.4 4.9 162.1 4.45 4.7 29.44 4.1 2.76 284.6 4.05 2.93 21.93 4.4 1.7 341.5 4.45 1.0 159.68 4.1 5.42 380.0 4.1 5.39 84.58 4.4 4.53 116.1 4.5 4.62 57.93 4.4 2.88 152.7 4.45 2.38 216.77 4.7 27.22 49.30 4.77 26.39 8.036 4.3 8.57 154.4 4.2 8.32 54.57 4.4 6.9 38.51 4.5 6.35 26.75 4.3 8.55 144.4 4.3 8.76 68.84 4.7 23.32 30.87 4.7 23.47 15.42 4.3 2.48 666.5 4.3 2.67 48.83 4.7 16.2 51.80 4.7 16.05 16.94 4.3 6.96 51.38 4.26 7.34 14.54 4.3 3.39 255.1 4.26 3.45 44.97 4.9 17.91 72.05 4.9 18.46 26.19 4.2 3.68 284.8 4.2 3.34 71.14 4.9 24.25 47.49 4.92 24.5 36.80 4.2 7.92 33.5 4.2 7.98 120.56 4.9 28.69 37.40 4.92 29 59.15 4.2 5.52 19.80 4.3 5.14 24.57 4.9 21.21 37.72 4.9 21.48 28.98 4.2 5.84 413.7 4.2 5.31 245.06
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表 4 不同地震及结构类型关于PGA和Sa的拟合参数
Table 4 Fitting parameters of different seismic and structural types
结构类型 地震类型 地震动参数 拟合结果 拟合优度 均方根误差 三层砌体 诱发地震 PGA lnDM＝1.11 lnPGA＋2.60 0.78 0.62 天然地震 PGA lnDM＝1.20 lnPGA＋2.90 0.71 0.56 诱发地震 Sa lnDM＝1.05 lnSa＋1.46 0.84 0.36 天然地震 Sa lnDM＝1.17 lnSa＋1.54 0.77 0.50 六层砌体 诱发地震 PGA lnDM＝1.04 lnPGA＋1.50 0.73 0.55 天然地震 PGA lnDM＝1.20lnPGA＋2.28 0.81 0.51 诱发地震 Sa lnDM＝0.97lnSa＋1.64 0.63 0.71 天然地震 Sa lnDM＝1.16lnSa＋1.61 0.64 0.69 注：DM为结构延性系数。
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