Seismic response analysis of the subway station structure under the coupling action of P and S seismic waves with the time difference
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摘要: 以北京实测地震波作为输入，运用二维显示有限差分程序对北京地区常见的3层3跨矩形断面结构地铁车站进行了动力模拟分析，探讨了纵横波时差耦合作用下车站结构加速度、位移放大效应及动应力变化规律。计算结果表明地震纵横波时差耦合作用导致浅埋地铁车站结构受力变形过程为：首先纵波作用使得结构产生较大的竖向加速度，导致结构产生一定的正应力；继而纵横波时差耦合作用使得结构产生较大的水平加速度，此时结构内力达到最大，容易使得结构产生较大的拉应力；最终随着地震动力作用逐渐减小至消失，结构内力减小，恢复稳定。在地震动力作用下，地铁车站侧墙、中柱等结构的加速度自下而上均发生放大效应，且竖向加速度的放大程度远高于水平加速度。因地震纵波产生较大的竖向加速度，并且具有较强的放大效应，需重视距离震源较近地区的地下结构竖向抗震性能；而纵横波时差耦合作用下，结构的内力往往能达到最大值，是地下结构发生破坏的主控因素。Abstract: Ground motion records of Beijing from the Tangshan earthquake was selected as the seismic input, and then the seismic simulation of a three-layer and three-span subway station with a rectangle cross-section in Beijing was carried out using the finite difference procedure. The variation law of dynamic acceleration, displacement amplification effect and dynamic stress of the subway station structure under the coupling action of P and S seismic waves with time difference was discussed. It is shown that, the process of impact on dynamic response and stress of the typical subway structure could be clear, which is, firstly, the P wave makes the station structure gain the largest vertical acceleration, and then, the structure gains the largest horizontal acceleration and stress through the coupling action of P and S seismic waves with the time difference, and finally, as the seismic force gradually reduces to disappear, the structure restore stability. The amplification effect of parameters in the dynamic response of the structure showed that the amplification coefficient of the side wall and column structures increases gradually from bottom to top and the amplification coefficient of the vertical acceleration is much larger than that of the horizontal acceleration. As the P wave can cause a large vertical acceleration and strong amplification effect, particular emphasis should be placed on the vertical anti-seismic performance of underground structures near the source. The structure gains the largest horizontal acceleration and tension stress under the coupling action of P and S seismic waves with the time difference, which is the key factor in structure destruction.
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图 1 纵横波作用下模型边界条件示意图
Figure 1. Diagram showing the boundary conditions of the model with P and S seismic waves
图 3 输入数值模型的水平、竖向加速度时程曲线
Figure 3. Time-history curves of the horizontal and vertical accelerations inputted in the numerical model
图 4 模型监测点(底部输入、中柱顶部)加速度时程曲线
a—水平加速度; b—竖向加速度
Figure 4. Time-history curves of the acceleration at the monitoring points in the numerical model
(a) Horizontal acceleration; (b) Vertical acceleration
图 5 结构动力加速度峰值及放大系数
a—加速度放大系数随高差变化规律曲线; b—结构上加速度峰值分布规律包络图
Figure 5. Amplification coefficient and peak value of the structural dynamic acceleration
(a) Curves of acceleration amplification coefficient with a height difference; (b) Envelope diagram of the structural acceleration peaks
图 6 地铁车站结构各监测点处地震应力峰值
Figure 6. Seismic stress peak at each monitoring point of the structures of the subway station
表 1 土层参数
Table 1. Soil parameters
名称 厚度/m 重度/(kN·m-3) 剪切波速/(m·s-1) 泊松比 黏聚力/kPa 内摩擦角/(°) 杂填土 3.0 1.81 200 0.30 10.00 10 圆砾卵石 4.0 2.10 363 0.31 20.00 23 卵石 7.0 1.93 405 0.30 0.00 35 卵石 9.0 2.10 523 0.30 0.00 40 卵石 8.0 2.13 623 0.30 0.00 42 卵石 19.0 2.16 666 0.30 0.00 42 
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表 2 结构参数
Table 2. Structural parameters
部位 重度/(kN·m-3) 弹性模量/GPa 几何尺寸/m 柱 25.0 34.5 直径：0.7 梁、板 24.0 33.5 上中下长度：9.55、2、9.55
单位宽度：1.0
厚度：0.4车站结构框架 25.0 30.0 长度：24.1
单位宽度：1.0
厚度：0.7
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