Analysis on Seismic Intensity Measures for Underground Structures Based on the PCA Method
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摘要: 地震动强度指标（IM）蕴含丰富的地震动特性信息，是连接地震危险性与结构响应的重要参数指标，选择与结构响应相关性较高的地震动强度指标参数，可以有效提高结构地震响应评估结果的准确性。本文以地铁地下结构抗震评估为目标，针对某II类场地地下结构响应评估中地震动强度指标选取开展了系统研究。首先，收集近场速度脉冲型地震动记录、远场类谐和地震动记录、普通地震动记录各20条，对地铁车站-隧道-场地地震响应进行数值模拟，然后采用主成分分析法（PCA）对12种地震动强度指标进行分析，并对地震动强度指标与结构响应之间的相关性进行探讨。结果表明，在利用单一强度指标表征地下结构地震响应方面，近场速度脉冲型地震动以峰值速度（PGV）和Housner谱强度(SI)两种速度型指标相关性最强，远场类谐和地震动以谱相关型指标SI相关性最强，普通地震动以峰值加速度（PGA）和Arias强度(AI)两种加速度型指标相关性最强；三类地震动可以分别组成为如下综合强度指标，近场速度脉冲型地震动： $ \ln {I}_{\text{p}}=0.36\ln {V}_{\max }+0.09\ln {C}_{\text{AV}} $；远场类谐和型地震动： $ \ln {I}_{\text{p}}=0.50\ln {I}_{\text{H}}+0.05\ln {A}_{\text{rms}} $；普通地震动： $ \ln {I}_{\text{p}}= 0.79\ln {a}_{\max }+ $$ 0.02\ln {I}_{\text{H}} $。相较于单一地震动强度指标，地震动综合强度指标更适用于本案例场地地铁地下结构抗震性能评估。Abstract: The seismic intensity measures (IM) contain rich information about seismic motion characteristics and serve as crucial parameters linking seismic hazard to structural response. Selecting the IM with high correlation to structural response can significantly improve the accuracy of evaluating structural seismic response. With the objective of seismic assessment for subway underground structures, this study conducted a systematic investigation into the selection of IMs for evaluating the response of underground structures in a Class II sites. Twenty near-field velocity pulse-like ground motion records, twenty far-field harmonic-like ground motion records, and twenty ordinary ground motion records were collected. Numerical simulations were conducted on the seismic response of station-tunnel-site. The principal component analysis (PCA) was applied to analyze 12 IMs, and the correlation between IMs and structural response was explored. The results indicate that, in characterizing the seismic response of underground structures, PGV and SI are the preferred IMs for near-field velocity pulse-like ground motionsSI is the preferred IM for far-field harmonic-like ground motions, and PGA and AI are the preferred IMs for ordinary ground motions; For the three types of ground motions, three composite IMs were proposed respectively: $ \ln {\boldsymbol{I}}_{\text{p}}=0.36\ln {\boldsymbol{V}}_{\max }+0.09\ln {\boldsymbol{C}}_{\text{AV}} $is for near-field velocity pulse-like ground motions, $ \ln {\boldsymbol{I}}_{\text{p}}=0.50\ln {\boldsymbol{I}}_{\text{H}}+0.05\ln {\boldsymbol{A}}_{\text{rms}} $ is for far-field harmonic-like ground motions, and $ \ln {\boldsymbol{I}}_{\text{p}}=0.79\ln {\boldsymbol{a}}_{\max }+0.02\ln {\boldsymbol{I}}_{\text{H}} $ is for ordinary ground motions. Compared to single parameter IMs, the composite seismicintensitymeasures are more suitable for assessing the seismic performance of underground structures in the case.
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图 4 车站结构底部与顶部加速度反应谱对比
Figure 4. Acceleration response spectra of the bottom and top of the shaker experiment station structure
图 6 所选地震动强度指标的相关系数
Figure 6. Correlation coefficients of the selected seismic intensity indicators
图 7 近场速度脉冲型相关性对比
Figure 7. Correlation comparison chart for near-field velocity pulse type
图 8 中柱下层最大层间位移角与各IM指标的对数线性回归
Figure 8. Log-linear regression of the maximum interlayer displacement angle in the lower part of the middle column on each IM index
图 9 远场类谐和型相关性对比
Figure 9. Correlation comparison chart for far-field quasi-harmonic type
图 10 中柱下层最大层间位移角与各IM指标的对数线性回归
Figure 10. Log-linear regression of the maximum interlayer displacement angle in the lower part of the middle column on each IM index
图 12 中柱下层最大层间位移角与各IM指标的对数线性回归
Figure 12. Log-linear regression of the maximum interlayer displacement angle in the lower part of the middle column on each IM index
表 1 地震动强度指标（韩俊艳等，2026）
Table 1. Seismic intensity measures（Han et al.，2026）
地震动强度指标名称 符号 定义 单位 指标类型 峰值加速度（PGA） amax $ \text{max}|\boldsymbol{a}(\boldsymbol{t})| $ m/s2 加速度型 Arias强度（AI） IA $ \dfrac{\boldsymbol{\text{π} }}{2\boldsymbol{g}}\displaystyle\int\nolimits_{0}^{{\boldsymbol{T}}_{\text{d}}}\,[\boldsymbol{a}(\boldsymbol{t}){]}^{2}\text{d}\boldsymbol{t} $ m/s 均值方根加速度（Arms） Arms $ \sqrt{\dfrac{1}{{T}_{d}}\displaystyle\int\nolimits_{0}^{{T}_{d}}{[a\left(t\right)]}^{2}\text{d}t} $ m/s2 加速度谱强度（ASI） Asi $ \displaystyle\int\nolimits_{0.1}^{0.5}\,\,{S}_{\text{a}}(T,\xi =\left.0.05\right)\text{d}T $ m/s 累计绝对速度（CAV） CAV $ \displaystyle\int\nolimits_{0}^{{T}_{\text{d}}}\,|a(t)|\text{d}t $ m/s 峰值速度（PGV） Vmax $ \text{max}|\nu (t)| $ m/s 速度型 均值方根速度（Vrms） Vrms $ \sqrt{\dfrac{1}{{T}_{d}}\displaystyle\int\nolimits_{0}^{{T}_{d}}{[v\left(t\right)]}^{2}\text{d}t} $ m/s 速度谱强度（VSI） Vsi $ \displaystyle\int\nolimits_{0.1}^{0.5}\,\,{S}_{\text{v}}(T,\xi \text{=0.05)d}T $ m/s Housner谱强度（SI） IH $ \dfrac{\text{π} }{2 g}\displaystyle\int\nolimits_{0.1}^{2.5}\,\,{S}_{\text{v}}(T,\xi \text{=0.05)d}T $ m/s 峰值位移（PGD） dmax $ \text{max}|d(t)| $ m 位移型 均值方根位移（Drms） Drms $ \sqrt{\dfrac{1}{{T}_{\text{d}}}\displaystyle\int\nolimits_{0}^{{T}_{\text{d}}}\,\,[d(t){]}^{2}\text{d}t} $ m 速度/加速度（PGV/PGA） R amax/Vmax s — 
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表 2 土层材料参数
Table 2. Soil material parameters
土层 土类 土层深度/m 密度/(kg·m3) 剪切波速/(m·s−1) 泊松比 黏聚力/kPa 内摩擦角/(°) 1 填土 0～5.8 1 800 177.4 0.3 5 10 2 粉土 5.8～8.5 1 935 227.8 0.325 39 23 3 粉砂 8.5～11.5 1 980 310.8 0.26 1 40 4 中砂 11.5～16.5 1 940 323.8 0.24 1 40 5 粉质黏土 16.5～23.1 1 960 269.8 0.295 42 24 6 砂土 23.1～28.5 2 075 398.0 0.22 1 40 7 粉质黏土 28.5～45.5 1 946 328.3 0.3 55 12
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表 3 混凝土材料参数
Table 3. Concrete material parameters
混凝土标号 密度/(kg·m−3) 弹性模量/MPa 泊松比 轴心受压强度/MPa 轴心受拉强度/MPa C40 2 400 32 500 0.2 39.5 2.94
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表 4 地震动震级及断层距
Table 4. Earthquake intensity and fault distance
编号 近场速度脉冲型地震动 远场类谐和型地震动 普通地震动 震级 断层距/km 震级 断层距/km 震级 断层距/km 1 6.7 5.9 7.2 366.03 6.69 21.36 2 6.7 5.9 7.2 366.03 6.69 21.36 3 6.9 1 7.51 207.81 6.69 39.91 4 6.9 1 7.51 207.81 6.69 39.91 5 7.5 4.8 7.62 66.64 6.9 17.85 6 7.5 4.8 7.62 66.64 6.9 17.85 7 7.6 19.8 7.62 92.81 6.9 19.15 8 7.6 19.8 7.62 92.81 6.9 19.15 9 7.6 19.9 7.14 188.7 7.51 15.37 10 7.6 19.9 7.14 188.7 7.51 15.37 11 7.1 6.6 7.13 123.79 6.5 102.15 12 7.1 6.6 7.13 123.79 6.5 102.15 13 6.5 12.9 6.63 222.42 6.53 22.03 14 6.5 12.9 6.63 222.42 6.53 22.03 15 7.9 2.7 7.2 57.95 6.61 173.16 16 7.9 2.7 7.2 57.95 6.61 173.16 17 6.9 5 7.3 144.9 6.93 41.86 18 6.9 5 7.3 144.9 6.93 41.86 19 7.3 34.9 7.3 157.41 7.28 148.07 20 7.3 34.9 7.3 157.41 7.28 148.07
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表 5 前两个主成分的方差贡献率及载荷（近场速度脉冲型地震动）
Table 5. Variance contribution rate and loadings of the first two principal components （near-field velocity pulse-type like seismic ground motions）
主成分及方差贡献率 强度指标 PGA PGV AI SI Arms CAV ASI 第一主成分（76.58%） 0.35 0.47 0.24 0.36 0.38 0.46 0.34 第二主成分（13.24%） −0.30 0.22 −0.01 0.00 −0.55 0.68 −0.30
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表 6 前两个主成分的方差贡献率及载荷（远场类谐和型地震动）
Table 6. Variance contribution rate and loadings of the first two principal components （far-field harmonic-like ground motions）
主成分及方差贡献率 强度指标 PGA PGV PGD SI Arms Drms CAV 第一主成分（87.32%） 0.35 0.47 0.24 0.36 0.38 0.46 0.34 第二主成分（9.35%） −0.30 0.22 −0.01 0.00 −0.55 0.68 −0.30
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表 7 前两个主成分的方差贡献率及载荷（普通地震动）
Table 7. Variance contribution rate and loadings of the first two principal components （ordinary ground motions）
主成分及方差贡献率 强度指标 PGA PGD AI SI 第一主成分（95.20%） 0.83 0.37 0.35 0.44 第二主成分（3.22%） −0.63 0.30 0.12 0.71
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