Seismic Analysis of Single-arch and Large-span Subway Station Structure under Bidirectional Ground Motion
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摘要: 地铁车站结构作为现代城市交通工程的重要组成部分，其抗震问题已成为城市工程抗震和防灾减灾研究的重点与难点。以深圳地铁3号线四期低碳城单拱大跨车站为研究对象，采用近场波动有限元方法，建立三维土-结构相互作用整体有限元分析模型。选取3条人工波和3条天然波作为输入地震动，分析水平单向地震动、水平与竖向双向地震动作用下单拱大跨地铁车站结构三维地震响应规律。研究结果表明，双向地震动作用下单拱大跨无柱结构及矩形框架有柱结构的水平位移及层间位移均略小于单向地震动作用下，但矩形框架有柱结构在竖向地震动作用下的中柱轴压比明显增加，说明单拱大跨车站结构可有效降低双向地震动作用下中柱轴压比变大的风险；双向地震动作用下的结构峰值弯矩大于单向地震动作用下，说明进行结构设计时应适当考虑竖向地震动作用的影响；单拱大跨无柱结构拱顶弯矩明显小于矩形框架有柱结构顶板跨中弯矩，改善了常规矩形框架结构顶板受力性能，但由于单拱大跨无柱结构缺少中柱竖向支撑作用，其底板及侧墙底部弯矩明显大于矩形框架有柱结构，尤其在双向地震动作用下更明显，因此单拱大跨无柱结构需加强底板及侧墙的厚度与配筋，以抵抗较大的弯矩响应。Abstract: As subway being an important part of modern urban transport engineering, the earthquake resistance of subway station structure has become the key and difficult point in the research of earthquake resistance and disaster prevention and reduction of urban engineering. In this paper, a three-dimensional finite element model of soil-structure interaction for a single-arch long-span structure in the fourth phase of Shenzhen Metro Line 3 is established by using the near-field wave finite element method. Three artificial waves and three natural waves were selected as input ground motions to analyse the three-dimensional seismic response of the single-arch and large-span subway station structures under horizontal unidirectional ground motions and horizontal and vertical bi-directional ground motions. The numerical results show that the horizontal displacement and interstory displacement of single-arch long-span column-free structure and rectangular frame column-free structure under bi-directional earthquake are slightly less than those under unidirectional earthquake. However, the axial compression ratio of the columns in the rectangular frame structure increases obviously under the action of the vertical seismic motion, which indicates that the single-arch and long-span station structure can effectively avoid the risk of the increase of the axial compression ratio of the columns under the action of bi-directional ground motions; The peak moment of structure is larger than that of the structure under the action of bi-directional ground motions, which indicates that the effect of vertical earthquake motion should be considered in the structure design; The bending moment of the single-arch and large-span column-free structure is obviously smaller than that of the rectangular frame with columns, which improves the mechanical behaviour of the roof of the conventional rectangular frame structure. However, the bending moment of the bottom plate and the bottom of the side wall is obviously larger than that of the column structure of the rectangular frame, especially under the action of bi-directional ground motions. Therefore, it is necessary to strengthen the thickness and reinforcement of the soleplate and the side wall of the single arch long-span column-free structure to resist the large moment response.1)
1 1 李洋，2018. 浅埋地下框架结构地震破坏机理研究. 北京：北京工业大学. -
图 6 人工波相应反应谱对目标谱的拟合曲线
Figure 6. The fitting of the corresponding response spectrum of artificial wave to the target spectrum
图 8 地铁车站结构最大水平位移时刻结构变形云图（单位：米）
Figure 8. Cloud diagram at the moment of maximum horizontal displacement of subway station structure (Unit: m)
图 9 C—C′断面顶、底板相对位移时程曲线
Figure 9. Relative displacement time history of the top and bottom plates of the C—C′ section
图 10 D—D′断面顶、底板相对位移时程
Figure 10. Relative displacement time history of the top and bottom plates of the D—D′ section
图 11 C—C′断面弯矩云图（单位：千牛·米）
Figure 11. Bending moment cloud diagram of C—C′ section（Unit：kN·m）
图 12 D—D′断面弯矩云图（单位：千牛·米）
Figure 12. Bending moment cloud diagram of D—D′ section（Unit：kN·m）
图 13 车站柱网轴力云图（单位：牛）
Figure 13. Axial force cloud diagram of column grid in station（Unit: N）
表 1 场地土物理参数
Table 1. Physical parameters of ground soil
层号 土层描述 层厚/m 密度/（g·cm−3） 剪切波速/（m·s−1） 泊松比 1 素填土 2.4 1.90 155.0 0.35 2 粉质黏土 6.4 1.92 220.8 0.35 3 砂质黏性土 5.4 1.95 282.4 0.28 4 全风化花岗岩 8.2 1.97 362.0 0.33 5 强风化花岗岩 13.1 2.10 470.6 0.25 
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表 2 土层模量比和阻尼比
Table 2. Modulus ratio and damping ratio of soil layer
土类 参数 剪应变γ/10−4 0.05 0.1 0.5 1 5 10 50 100 素填土 $ G/{G_{\max }} $ 0.960 0 0.950 0 0.800 0 0.700 0 0.300 0 0.200 0 0.150 0 0.100 0 $ \lambda $ 0.025 0 0.028 0 0.030 0 0.035 0 0.080 0 0.100 0 0.110 0 0.120 0 粉质黏土 $ G/{G_{\max }} $ 0.995 0 0.988 0 0.939 0 0.876 0 0.572 0 0.401 0 0.145 0 0.075 0 $ \lambda $ 0.015 0 0.026 0 0.043 0 0.044 0 0.069 0 0.074 0 0.094 0 0.098 0 砂质黏性土 $ G/{G_{\max }} $ 0.996 2 0.910 0 0.964 0 0.931 3 0.737 3 0.593 6 0.236 7 0.138 0 $ \lambda $ 0.012 0 0.015 9 0.030 1 0.039 3 0.068 8 0.082 6 0.106 0 0.110 9 全、强风化岩 $ G/{G_{\max }} $ 0.990 0 0.970 0 0.900 0 0.850 0 0.700 0 0.550 0 0.320 0 0.200 0 $ \lambda $ 0.004 0 0.006 0 0.019 0 0.030 0 0.075 0 0.090 0 0.110 0 0.120 0
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表 3 车站结构变形
Table 3. The deformation of the station structural
工况 结构最大水平位移/mm C—C′断面 D—D′断面 位移差/mm 位移角 位移差/mm 位移角 1 13.6 9.18 1/1 810 5.52 1/3 011 2 11.4 7.79 1/2 134 5.38 1/3 089 3 13.6 10.54 1/1 577 7.45 1/2 231 4 12.4 8.99 1/1 849 5.28 1/3 148 5 11.7 7.66 1/2 170 5.12 1/3 246 6 13.9 9.23 1/1 801 6.89 1/2 412 7 11.4 6.57 1/2 530 2.48 1/6 702 8 12.5 7.12 1/2 334 3.57 1/4 655 9 11.2 6.42 1/2 589 2.47 1/6 729 10 11.8 6.39 1/2 601 2.25 1/7 387 11 12.1 6.83 1/2 433 3.12 1/5 327 12 11.6 6.25 1/2 659 2.08 1/7 990
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表 4 车站结构标准断面弯矩
Table 4. Bending moment of standard section at station structure
工况 C—C′断面/（kN·m） D—D′断面/（kN·m） 拱顶 拱底 侧墙（左） 拱顶 拱底 侧墙（左） 1 287 2 147 1 211 371 1 192 589 2 298 2 334 1 275 406 1 223 594 3 322 2 561 1 390 465 1 373 619 4 441 3 015 1 768 583 1 636 654 5 467 2 994 1 638 591 1 669 668 6 481 3 269 1 841 621 1 791 709 7 218 2 056 1 460 297 1 118 570 8 341 2 589 1 648 331 1 325 651 9 235 2 152 1 463 285 1 211 581 10 67.2 2 280 1 724 223 1 258 344 11 92 2 558 1 889 371 1 568 473 12 74 2 317 1 759 245 1 301 371
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表 5 车站结构柱网最大轴力及轴压比
Table 5. Maximum axial force and axial compression ratio of station structural column network
工况 最大轴力/kN 最大轴压比 工况 最大轴力/kN 最大轴压比 1 11 421 0.618 7 10 513 0.569 2 11 060 0.598 8 10 947 0.592 3 11 380 0.616 9 10 695 0.597 4 11 504 0.622 10 12 271 0.664 5 11 145 0.603 11 12 341 0.668 6 11 393 0.616 12 12 314 0.666
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