Response Analysis of Twin Tunnels Under Horizontal and Vertical Earthquake Loading
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摘要: 基于有效的土-结相互作用有限元数值模拟方法，利用有限元软件ABAQUS对水平及竖向地震共同作用下双线盾构隧道的地震响应进行分析研究。地震动输入选取近场地震Loma、ChiChi、Mammoth和WoLong的基岩水平及竖向加速度时程记录。结果表明，不同近场地震记录对隧道结构的作用不同，隧道的地震反应与场地性质及地震动的频谱特性密切相关。对比隧道在水平及竖向地震动共同作用下的响应与单向水平地震动作用下的响应，发现隧道的最大地震附加内力及其分布均发生较大的变化，在隧道结构抗震设计中需引起重视。另外，分析中还考虑了在双向地震动共同作用下，隧道间距、土-结接触面的摩擦系数、土-结相对刚度、输入的地震记录和竖向地震动相对强度对隧道地震响应的影响等，研究结果对隧道工程的抗震设计具有一定的参考价值。Abstract: Based on an effective Finite Element procedure for soil-structure interaction, the seismic response of twin tunnels under combined horizontal and vertical earthquake loading were analyzed by using the ABAQUS package. The horizontal and vertical acceleration time history records at bedrock from the near-field earthquakes of Loma, ChiChi, Mammoth and WoLong were selected as the input ground motions. The results showed that the seismic responses of the tunnels were different as the input earthquake records changed, and the seismic responses of the tunnels were related to the field properties and the vibration frequency characteristics of the input ground motions. By comparing the seismic responses under bi-directional and unidirectional earthquake loadings, it was found that both the distributions and the magnitudes of the seismic additional internal forces were changed greatly, which should be taken into account in the seismic design of tunnels. In addition, parametric studies were carried out on the effects of the space between two tunnels, friction coefficient of contact surface between soil and tunnels, relative stiffness of the soil-structure system, input earthquake motion and relative intensity of vertical earthquake motion. The results may provide a good reference for the seismic design of tunnels.
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图 1 有限元模型示意图及各土层动剪切模量比和阻尼比随剪应变变化图
Figure 1. Schematic diagram of the finite element model and the relation curves of dynamic shear module ratio and damp ration shear strain for soils
图 2 近场地震记录的水平地震动、竖向地震动加速度时程和水平加速度反应谱
Figure 2. Acceleration time histories of the horizontal and vertical ground motions and horizontal acceleration response spectra of the near-field seismic records
图 3 Loma地震记录双向地震动作用下不同隧道间距的附加内力
Figure 3. Additional internal forces of tunnel linings with different tunnel spacings under the loading of Loma seismic record
图 4 不同的土-结接触面摩擦系数下的隧道最大附加内力变化曲线（Loma地震记录作用下）
Figure 4. The variation curves of maximum additional internal forces of the tunnel with different friction coefficients of the contact surface between the soil and tunnel(Under the loading of Loma seismic record)
图 5 隧道最大附加内力与隧道刚度的关系（Loma地震记录作用下）
Figure 5. The relationship between the maximum additional internal forces of the lining and the lining stiffness(Under the loading of Loma seismic record)
图 6 不同近场地震记录作用下隧道的附加弯矩
Figure 6. The additional bending moments of the lining under the loadings of different near-field seismic records
图 7 不同近场地震记录作用下隧道的附加轴力
Figure 7. The additional axial forces of the lining under the loading of different near-field seismic records
图 8 土层加速度放大系数和标准加速度反应谱分析
Figure 8. The analysis of soil acceleration amplification coefficient and standard acceleration response spectrum
图 9 不同近场地震记录的水平地震动作用下，土层自由场各深度处的水平加速度放大系数
Figure 9. The horizontal acceleration amplification coefficients of the free field under the loadings of the horizontal ground motions of different near-field seismic records
图 10 隧道在Wolong地震记录的不同竖向地震动相对强度作用下的附加内力
Figure 10. Additional internal forces of the lining with different V/H ratios of the WoLong seismic inputs
图 11 Wolong地震记录作用下不同的竖向地震动相对强度下隧道的最大附加内力和土层自由场最大平均剪应变
Figure 11. Variation trends of maximum additional internal forces of the lining and maximum average shear strain of the free field under loading of Wolong seismic record
图 12 不同近场地震记录下隧道在单向和双向地震荷载作用下最大附加内力
Figure 12. The maximum additional internal forces of the lining under unidirectional and bidirectional loads resulted by different near-field earthquake records
表 1 土层的相应参数
Table 1. Corresponding parameters of soil layers
土层类别 厚度/m 初始剪切模量/MPa 密度/×103 kg·m-3 A 2B r0 /×10-4 泊松比 黏性土 18 50.67 1.94 1.12 0.82 9.00 0.35 砂质黏性土 4 100.84 1.98 1.00 0.76 7.38 0.32 中粗砂 5 149.73 1.98 1.00 0.70 9.67 0.30 砂层 13 300.84 1.98 1.10 0.74 9.50 0.30 砾质黏性土 16 361.57 1.96 1.20 0.74 10.03 0.30 
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表 2 隧道管片的相应参数
Table 2. Corresponding parameters of the tunnel segments
杨氏模量/GPa 泊松比 密度/kg·m-3 外径/m 厚度/m 35.5 0.2 2600 6.2 0.35
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表 3 近场地震记录加速度幅值
Table 3. Acceleration amplitudes of the near-field seismic records
近场地震记录 水平向加速度峰值/g 竖直向加速度峰值/g 竖直/水平 Arias intensity/m·s-1 Loma 0.2 0.106 0.53 0.32 ChiChi 0.2 0.132 0.66 0.88 Mammoth 0.2 0.056 0.28 0.09 WoLong 0.2 0.200 1.00 0.54
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