Comparative Study of Pile Foundation Seismic Simplify Model for Urban Railway Bridge
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摘要: 以郑州城郊铁路工程中独柱高架车站为例，将土体化为一系列弹簧，描述土体的变形性质。通过比较《城市轨道交通结构抗震设计规范》中的非线性土弹簧、《铁路桥涵地基和基础设计规范》中的m系数法弹簧及Mindlin解弹簧进行建模计算得到的车站结构的地震响应，由结果可知结构地震响应对承台处弹簧刚度最为敏感。另外，将分布弹簧模型等代为六弹簧模型进行地震反应计算，结果表明桩体质量的影响与承台质量相比很小。Abstract: Based on the single column station in Zhengzhou suburb railway engineering, soil material is considered as a series of springs to describe the deformation properties.A comparative study of non-linear spring from Code for Seismic Design of Urban Rail Transit Structures, m coefficient method from Code for Design on subsoil and foundation of railway bridge and culverts, and soil modulus in Mindlin model is conducted, which explains that the seismic response of bridge structure is most sensitive to spring stiffness around pile cap.In addition, a six-spring model is gained based on the primary distributed spring model to calculate the seismic response, which shows that the influence of pile mass is very small compared with the influence of pile cap mass.
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Key words:
- Soil-pile interaction spring /
- Stiffness coefficient values /
- Soil nonlinear /
- Pile cap mass /
- Pile mass
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图 1 桩基础集中参数模型示意图
Figure 1. Sketch map of concentration parameter model of pile foundation
图 9 《规范》线性弹簧、m系数法、Mindlin土弹簧下的车站结构响应
Figure 9. The response of station structure in "code" linear spring, m method and Mindlin model
图 10 《规范》线性弹簧与m系数法、Mindlin法弹簧刚度取值情况
Figure 10. Stiffness values in "code" linear spring model, m method and Mindlin model
图 11 水平地基抗力和变形之间的关系
Figure 11. Relationship between horizontal soil resistance and deformation
图 12 《规范》与m系数法，Mindlin法计算得到承台处的“地基系数”
Figure 12. "Foundation coefficient" around pile cap in "code" linear spring, m method and Mindlin model
图 13 m系数法、Mindlin法承台处弹簧刚度修正后的车站结构响应比较
Figure 13. The response of station in condition of m method, Mindlin model modified
图 14 反应承台处弹簧刚度影响程度的Rp值
Figure 14. Rp value representing pile cap spring stiffness influence
图 15 结构是线弹性情况下线性分布弹簧与非线性分布弹簧约束下的桥梁结构响应比较
Figure 15. The response comparison between linear distributed spring and nonlinear distributed spring (structure is in linear elasticity)
图 16 结构是线弹性情况下分布弹簧进入非线性的状态
Figure 16. State of nonlinear distributed spring (structure is linear elasticity)
图 18 墩进入非线性时线性分布弹簧与非线性分布弹簧的计算结果比较
Figure 18. The response comparison between linear distributed spring and nonlinear distributed spring (piers go into nonlinear)
图 19 墩柱进入非线性时分布弹簧进入非线性的状态
Figure 19. State of nonlinear distributed spring (piers go into nonlinear)
图 21 桩体进入非线性时线性分布弹簧与非线性分布弹簧的计算结果比较
Figure 21. The calculation result comparison between linear distributed spring and nonlinear distributed spring (piles go into nonlinear)
图 22 桩体进入非线性时分布弹簧进入非线性的状态
Figure 22. State of nonlinear distributed spring (piles go into nonlinear)
图 23 墩底和桩顶弯矩-转角关系曲线
Figure 23. Bending moment-corner curve at the bottom of pier and on the top of pile
图 24 墩柱和桩体进入非线性时线性分布弹簧与非线性分布弹簧的计算结果比较
Figure 24. The calculation result comparison between linear distributed spring and nonlinear distributed spring (piers and piles both go into nonlinear)
图 25 墩柱和桩体进入非线性时分布弹簧进入非线性的状态
Figure 25. State of nonlinear distributed spring (piers and piles both go into nonlinear)
图 27 结构是线弹性情况下分布弹簧与六弹簧的墩柱反应计算结果比较
Figure 27. The pier response calculation result comparison between distributed spring and six-spring model (structure is in linear)
图 28 结构是线弹性情况下分布弹簧模型中桩体的地震响应
Figure 28. The pile response of distributed spring model (structure is in linear)
表 1 桥梁结构的工程材料
Table 1. Materials of bridge structure
上部结构框架梁、板、柱 桥梁墩柱 上部结构盖梁承台 桩基和承台 C45混凝土 C45混凝土 C50混凝土 C35混凝土 
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表 2 土体基本参数
Table 2. Basic parameters of soil
土层 天然密度
ρ/g·cm-3水平基床系数
/kPa·m-1竖向基床系数
/kPa·m-1压缩模量
Es/kPa地基系数的比例系数
m/kPa·m--2⑤1粉土 1.65 45000 15000 6000 6000 ⑥5黏土 1.65 62200 20733 12900 13000 ⑥5黏土 1.65 62200 20733 12900 13000 ⑥4细砂 2.01 43300 14433 20000 13000 ⑥6泥质胶结黏性土 1.71 50000 16667 11000 11000 ⑦4细砂 2.01 55000 18333 20000 15000 ⑦4细砂 2.01 55000 18333 20000 15000 ⑦3泥质胶结砂土 1.97 60000 20000 35000 26000 ⑧7泥质胶结黏性土 2.10 65000 21667 20000 23000 ⑧7泥质胶结黏性土 2.10 65000 21667 20000 23000 ⑧7泥质胶结黏性土 2.10 65000 21667 20000 23000 ⑧4泥质胶结砂土 2.30 60000 20000 40000 28000
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表 3 《规范》线性弹簧与m系数法、Mindlin法弹簧刚度值
Table 3. Stiffness values in "code" linear spring model, m method and Mindlin model
深度/m Mindlin/103kN·m-1 m/103kN·m-1 规范/103kN·m-1 Mindlin/规范 m/规范 -2.75(承台) 143.80 350.63 843.75 0.17 0.42 -7 127.87 472.5 337.5 0.38 1.40 -12 554.97 1755 466.5 1.19 3.76 -17 821.63 2486.25 466.5 1.76 5.32 -22 1686.06 3217.5 324.75 5.19 9.91 -27 1154.52 3341.25 375 3.07 8.91 -32 2513.18 5400 412.5 6.09 13.09 -37 2928.06 6243.75 412.5 7.09 15.14 -42 5851.30 12285 450 13.00 27.30 -47 3759.67 12161.25 487.5 7.71 24.95 -52 4176.15 13455 487.5 8.56 27.60 -57 4592.95 14748.75 487.5 9.42 30.25 -62 10020.06 19530 450 22.26 43.40
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