Seismic Fragility Analysis of Shallow-Buried Subway Station Structure in Loess Strata
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摘要:
为研究黄土场地地铁车站的地震易损性，以黄土地区某典型两层三跨地铁车站结构为例，基于黏弹性边界的地震动输入方法对该地铁车站结构进行增量动力分析（IDA），对37个地震动强度指标的有效性、实用性和效益性进行综合评价，选出适合该场地条件和车站结构断面形式的地震动强度指标，并采用双参数对数正态分布模型建立该地铁车站结构的地震易损性曲线和破坏状态概率曲线，以此得到该地铁车站结构在某一强度地震作用下各性能水准的超越概率和发生不同破坏状态的概率. 结果表明：加速度、速度相关型指标更适合作为地震动强度指标来预测地下结构的地震响应，位移相关型以及比值型指标不宜作为地震动强度指标；多遇地震作用下车站结构发生破坏的概率较小，设防地震作用下车站结构以轻微破坏为主，罕遇地震作用下车站结构以轻微破坏和中等破坏为主. 研究可为黄土地层基于性能的地铁车站的抗震设计提供参考.
Abstract:In order to study the seismic fragility of subway stations situated in loess sites, a typical two-story three-span subway station structure in a loess area was chosen as a representative example, and incremental dynamic analysis (IDA) was conducted on the subway station structure by using the ground motion input method based on viscoelastic boundaries. The results of IDA were then used to comprehensively evaluate 37 seismic intensity indices in terms of their effectiveness, practicality, and benefit. Based on this evaluation, seismic intensity indices that were suitable for the site conditions and structural configuration of the subway station were selected. Seismic fragility curves and damage state probability curves for the subway station structure were established using a double-parameter lognormal distribution model. These curves facilitated the determination of the probability of the subway station structure exceeding various performance levels and encountering different damage states under specific seismic intensities. The findings suggest that acceleration-related and velocity-related indices are more suitable as seismic intensity indices for predicting the seismic response of underground structures, while displacement-related and ratio-related indices are not appropriate. Under frequent seismic events, the probability of the subway station structure experiencing damage is relatively low. For design-level seismic events, the structure primarily sustains slight damage. In the case of rare seismic events, the subway station structure is more prone to slight and moderate damage. The results provide a reference for the seismic design of performance-based subway stations constructed on loess strata.
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图 1 基于IDA方法的地下结构地震易损性分析流程
Figure 1. Seismic fragility analysis of underground structures based on IDA method
图 2 土-地铁车站结构相互作用有限元模型（单位：m）
Figure 2. Finite element model of soil-subway station structure interaction （unit: m）
图 3 黏弹性人工边界等效节点荷载
Figure 3. Equivalent nodal loads in viscoelastic artificial boundary
图 9 不同IIM指标的IDA结果线性回归分析
Figure 9. Linear regression analysis of IDA results ofifferent intensity measure （IIM） indices
图 10 不同IIM指标的有效性${\beta _{\text{d}}}$
Figure 10. Effectiveness ${\beta _{\text{d}}}$of different IIM indices
图 12 不同IIM指标的效益性$\zeta $对比
Figure 12. Benefit $\zeta $comparison of different IIM indices
图 14 地铁车站结构破坏状态概率曲线
Figure 14. Damage state probability curves of subway station structure
表 1 主要计算参数
Table 1. Main calculation parameters
材料 密度/（kg·m−3） 弹性模量/GPa 泊松比 黏聚力/kPa 内摩擦角/（°） 土体 1 650 0.07 0.30 0.03 22 墙、板 2 500 32.50 0.20 2.50 55 中柱（折减） 329 4.14 0.20 2.50 55 
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表 2 不同性能水准功能描述及损伤限值标定
Table 2. Function description and damage limit calibration for different performance levels
性能水准 功能状态 $ \theta_{\text {max }} $限值/% LS1 结构抗震关键构件基本完好，设备功能完好，可以正常运行 0.21 LS2 结构抗震关键构件发生中等损伤，设备功能整体正常，经修复后可以正常使用 0.46 LS3 结构抗震关键构件发生不可修复的严重破坏，设备功能失常，可保证安全 0.72 LS4 结构功能完全丧失，结构强度和刚度基本退化，可能发生倒塌 1.00
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表 3 地震动强度指标选择
Table 3. Selection of seismic intensity indices
类型 编号 名称 定义 加速度相关型 1 地表峰值加速度 ${P_{{\mathrm{PGA}}}} = \max |a(t)|$ 2 加速度谱强度 $ A_{\text{ASI}} = \displaystyle\int_{0.1}^{0.5} {{S_{\mathrm{a}}}} (T,\xi ){\mathrm{d}}T $ 3 加速度平方积分 ${E_{\text{a}}} = \displaystyle\int_0^{{t_{\max }}} {{a^2}} (t){\mathrm{d}}t$ 4 根平方加速度 ${A_{{\text{rs}}}} = \sqrt {\displaystyle\int_0^{{t_{\max }}} {{a^2}} (t){\mathrm{d}}t} $ 5 Housner加速度强度 ${P_{\text{a}}} = \dfrac{1}{{{t_{\mathrm{d}}}}}\displaystyle\int_{{t_1}}^{{t_2}} {{a^2}} (t){\mathrm{d}}t$ 6 Housner均方根加速度 ${A_{{\text{rms}}}} = \sqrt {\dfrac{1}{{{t_{\mathrm{d}}}}}\displaystyle\int_{{t_1}}^{{t_2}} {{a^2}} (t){\mathrm{d}}t} $ 7 地震动均方根加速度 ${a_{{\text{rms}}}} = \sqrt {\dfrac{1}{{{t_{\max }}}}\displaystyle\int_0^{{t_{\max }}} {{a^2}} (t){\mathrm{d}}t} $ 8 累计绝对速度 $C_{\text{CAV}} = \displaystyle\int_0^{{t_{\max }}} | a(t)|{\mathrm{d}}t$ 9 谱加速度峰值 $P_{\text{PSA}} = \max \left( {{S_{\mathrm{a}}}\left( {T,\;\;\xi = 0.05} \right)} \right)$ 10 Arias强度 $ A_{\text{AI}} = \dfrac{{\text{π}} }{{2g}}\displaystyle\int_0^{{t_{\max }}} {{a^2}} (t){\mathrm{d}}t $ 11 修正的Arias强度 ${I_{{\text{AM}}}} = A_{\text{AI}}/v_0^2$ 12 特征强度 $ {I_{\text{c}}} = A_{{\mathrm{rms}}}^{1.5}\; \cdot \;t_{\mathrm{d}}^{0.5} $ 13 复合加速度 ${I_{\text{a}}} = P_{\text{PGA}} \cdot t_{\mathrm{d}}^{1/3}$ 14 Faifar强度 ${I_{\text{f}}} = P_{\text{PGV}} \cdot t_{\mathrm{d}}^{0.25}$ 速度相关型 15 地表峰值速度 $P_{\text{PGV}} = \max |v(t)|$ 16 速度谱强度 $ V_\text{VSI}={\displaystyle {\displaystyle\int }_{0.1}^{2.5}{S}_{{\mathrm{v}}}}(T,\xi ){\mathrm{d}}T $ 17 速度平方积分 ${E_{\text{v}}} = \displaystyle\int_0^{{t_{\max }}} {{v^2}} (t){\mathrm{d}}t$ 18 根平方速度 $ {V_{{\text{rs}}}} = \sqrt {\displaystyle\int_0^{{t_{\max }}} {{v^2}} (t){\mathrm{d}}t} $ 19 Housner速度强度 ${P_{\text{v}}} = \dfrac{1}{{{t_{\mathrm{d}}}}}\displaystyle\int_{{t_1}}^{{t_2}} {{v^2}} (t){\mathrm{d}}t$ 20 Housner均方根速度 ${V_{{\text{rms}}}} = \sqrt {\dfrac{1}{{{t_{\mathrm{d}}}}}\displaystyle\int_{{t_1}}^{{t_2}} {{v^2}} (t){\mathrm{d}}t} $ 21 地震动均方根速度 ${v_{{\text{rms}}}} = \sqrt {\dfrac{1}{{{t_{\max }}}}\displaystyle\int_0^{{t_{\max }}} {{v^2}} (t){\mathrm{d}}t} $ 22 累计绝对位移 $C_{\text{CAD}} = \displaystyle\int_0^{{t_{\max }}} | v(t)|{\mathrm{d}}t$ 23 谱速度峰值 $P_{\text{PSV}} = \max \left( {{S_{\mathrm{v}}}\left( {T,\;\;\xi = 0.05} \right)} \right)$ 24 Housner强度 $ S_{\text{SI}} = \displaystyle\int_{0.1}^{2.5} P_{{\mathrm{PSV}}} (T,\xi = 0.05){\mathrm{d}}T $ 25 复合速度 ${I_{\text{v}}} = P_{{\text{PGV}}}^{2/3} t_{\mathrm{d}}^{1/3}$ 位移相关型 26 地表峰值位移 $P_{\text{PGD}} = \max |d(t)|$ 27 位移谱强度 $D_{\text{DSI}} = \displaystyle\int_{2.5}^{4.0} {{S_{\mathrm{d}}}} (T,\xi ){\mathrm{d}}T $ 28 位移平方积分 ${E_{\text{d}}} = \displaystyle\int_0^{{t_{\max }}} {{d^2}} (t)dt$ 29 根平方位移 ${D_{{\text{rs}}}} = \sqrt {\displaystyle\int_0^{{t_{\max }}} {{d^2}} (t)dt} $ 30 Housner位移强度 ${P_{\text{d}}} = \dfrac{1}{{{t_d}}}\displaystyle\int_{{t_1}}^{{t_2}} {{d^2}} (t)dt$ 31 Housner均方根位移 ${D_{{\text{rms}}}} = \sqrt {\dfrac{1}{{{t_d}}}\displaystyle\int_{{t_1}}^{{t_2}} {{d^2}} (t)dt} $ 32 地震动均方根位移 ${d_{{\text{rms}}}} = \sqrt {\dfrac{1}{{{t_{\max }}}}\displaystyle\int_0^{{t_{\max }}} {{d^2}} (t)dt} $ 33 累计绝对能量 $C_{\text{CAI}} = \displaystyle\int_0^{{t_{\max }}} | d(t)|dt$ 34 谱位移峰值 $P_{\text{PSD}} = \max \left( {{S_{\mathrm{d}}}\left( {T,\;\;\xi = 0.05} \right)} \right)$ 35 复合位移 ${I_{\text{d}}} = P_{\text{PSD}} t_{\mathrm{d}}^{1/3}$ 比值型 36 峰值速度与峰值加速度比值 ${{F_1}} = {{P_{\mathrm{PGV}} / P_{\mathrm{PGA}}}}$ 37 峰值位移与峰值速度比值 ${{F_2}} = {{P_{\mathrm{PGD}} / P_{\mathrm{PGV}}}}$
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表 4 不同频遇地震各性能水准超越概率
Table 4. Exceedance probability of each performance level for earthquakes with different frequencies
地震频遇 设计基本加速度/（ × g） 超越概率/% 轻微破坏 中等破坏 严重破坏 倒塌 多遇地震 0.07 3.58 0.16 0.01 0.00 设防地震 0.20 54.70 15.20 4.29 2.03 罕遇地震 0.41 92.37 60.90 34.26 23.14
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表 5 不同频遇地震各破坏状态出现概率
Table 5. Occurrence probability of each damage state in earthquake with different frequencies
地震频遇 设计基本加速度（ × g） 出现概率/% 基本
完好轻微
破坏中等
破坏严重
破坏倒塌 多遇地震 0.07 96.42 3.43 0.14 0.01 0.00 设防地震 0.20 45.30 39.68 10.73 2.26 2.03 罕遇地震 0.41 7.63 31.47 26.44 11.12 23.14
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