Study on the influence of above-crossing tunneling on the existing shield tunnels based on timoshenko beam
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摘要: 采用修正的Loganathan理论研究了盾构上跨过程中土体损失引起的既有隧道纵向位移，考虑剪切变形的Timoshenko梁理论分析隧道内力变化及管片间错台量，基于弹性力学理论中的剪切效应建立了隧道纵向变形微分方程并求解，研究了隧道剪切刚度、土体损失率对隧道弯矩、剪力、管片间错台量变化规律。将计算结果与已发表监测数据对比，分析了Timoshenko梁发生弯曲变形后梁横截面不再与中性轴垂直，与不考虑剪切变形的Euler-Bernoulli梁的差异。研究表明：考虑剪切变形的理论解能准确预测隧道纵向变形，能矫正不考虑剪切变形条件下弯矩、剪力内力值过大以及无法计算管片错台量的缺陷。研究为预测盾构近距离上跨对既有隧道影响分析提供一种有效方法。
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关键词:
- Timoshenko梁 /
- 盾构上跨 /
- 土体损失 /
- 纵向变形
Abstract: Based on the modified Loganathan theory, the longitudinal displacement of an existing tunnel caused by the ground loss in the process of shield crossing was studied. Timoshenko beam theory considering shear deformation was used to analyze the change of tunnel internal force and the amount of the dislocation between the adjacent rings. Based on the shear effect in elastic mechanics theory, the differential equation of tunnel longitudinal deformation was established and solved. After the bending deformation of Timoshenko beam, the difference between the beam cross-section of euler-Bernoulli beam which was not perpendicular to the neutral axis was analyzed. Furthermore, the variation of tunnel bending moment, shear force, and displacement between tunnel segments on tunnel shear stiffness and the ground loss ratio was studied. The results showed that the theoretical solution considering the shear deformation of the tunnel could predict the longitudinal deformation of the tunnel accurately. The proposed theory can correct the excessive internal forces such as bending moment and shear force without considering shear deformation and make up for the defect of unable to calculate the dislocation between the adjacent ring misalignment without considering shear deformation. The research results provide an effective method for predicting the influence of shield on existing tunnels.-
Key words:
- Timoshenko beam /
- above-crossing tunneling /
- ground loss /
- longitudinal deformation
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图 1 Timoshenko梁与Euler-Bernoulli梁变形示意图
Figure 1. Schematic diagram of timoshenko beam and Euler-Bernoulli beam deformation
图 2 盾构斜穿既有隧道示意图
Figure 2. Schematic diagram of shield tunneling up-crossing existing tunnel at a certain angle
图 3 盾构开挖对既有隧道的纵向变形影响示意图
Figure 3. Schematic diagram of the influence of shield tunneling on longitudinal deformation of existing tunnels
图 6 外滩通道上跨2号线隧道示意图
Figure 6. Schematic diagram of the Bund Passage up-crossing Line-2 tunnel
图 7 实测数据与本文解析解对比
Figure 7. Comparison between measured tunnel displacement and analytical solutions
图 8 上海地铁8号线上跨2号线示意图
Figure 8. Schematic diagram of Shanghai Metro Line 8 up-crossing Line 2
图 9 2号线监测数据与本文解析解对比图
Figure 9. Comparison between Line-2 measured tunnel displacement and analytical solutions
图 10 Timoshenko梁与Euler-Bernoulli梁模型对隧道变形及内力影响的对比
Figure 10. Calculation of tunnel longitudinal deformation and internal force by Timoshenko beam and Euler-Bernoulli beam
图 11 等效剪切刚度对既有管片错台量的影响
Figure 11. The effect of equivalent shear stiffness on the dislocation of segmen
图 12 地层损失率对隧道变形及内力影响
Figure 12. Effects of ground volume loss ratio on dislocations and internal forces of tunnel
表 1 现场地层力学参数
Table 1. Soil parameters of the site
土层 含水率ω/% 重度/(kN·m-1) 孔隙比e0 塑性指数Ip 液性指数IL 压缩系数α0.1-0.2/MPa-1 压缩模量Es0.1-0.2/MPa 十字板剪切试验cu/kPa 江滩土 34.7 18 0.986 14.5 1.08 0.29 6.85 47.6 灰色泥质黏土 49.4 16.9 1.386 21.3 1.25 0.99 2.41 23.2 灰色黏土 36.7 17.8 1.065 18.0 0.85 0.54 3.85 50.1 灰色粉质黏土 34 17.9 1.005 15.5 0.88 0.41 4.94 82.3 
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表 2 2号线隧道管片参数
Table 2. Line-2 tunnel segment parameters
隧道参数 数值 外径D/m 6.2 内径Di/m 5.5 管片厚度t/m 0.35 管片长度/m 1.2 弹性模量/MPa 3.45 环向螺栓数n 17 螺栓直径/m 30 螺栓长度lb/mm 400 螺栓弹性模量Eb/(105 MPa) 2.06
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表 3 现场地层力学参数
Table 3. Soil parameters of the site
土层名称 含水率ω/% 重度/(kN·m-1) 孔隙比e0 液性指数IL 塑性指数Ip 压缩系数α0.1-0.2/MPa-1 压缩模量Es0.1-0.2/MPa 粉质黏土 38.7 2.73 1.07 36.7 20.9 0.50 4.16 泥质粉质黏土 56.0 2.74 1.54 37.5 19.8 1.50 1.71 泥质黏土 65.1 2.76 1.81 45.0 21.8 1.69 1.68 粉质黏土 33.5 2.72 0.97 33.1 19.3 0.50 3.98
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