A 2.5-D COUPLED FE-BE MODEL FOR THE DYNAMIC INTERACTION BETWEEN TUNNEL AND SATURATED SOIL
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摘要: 针对饱和土中异形隧道的三维动力响应问题，建立了2.5维有限元与边界元耦合模型.将隧道结构视为弹性体，采用2.5维有限元建立隧道模型；将地基土视为饱和多孔介质，采用2.5维边界元建立饱和土体模型.借助组合辅助问题基本解消除了边界积分方程的奇异性.利用饱和土与隧道接触面的位移、面力连续和完全透水或完全不透水边界条件，实现2.5维有限元和边界元模型的耦合求解.模型具有计算效率高、适用范围广的优点.通过与完全透水和完全不透水边界条件下轴对称问题的半解析解以及单相介质的2.5维有限元与边界元耦合模型对比，验证了本文模型的正确性.最后利用该模型计算了饱和土体中类矩形隧道在移动载荷作用下的三维动力响应，分析了不同土体渗透性下位移及孔隙水压力沿隧道轴向、环向和深度的分布规律.结果表明：（1）孔隙水压力随土体渗透性增大而显著减小，位移受土体渗透性影响小；（2）位移及孔隙水压力在隧道环向主要分布在距载荷作用点两侧约2 m的范围内；（3）孔隙水压力沿深度的衰减比土体位移快，且孔隙水压力和轴向位移沿深度的分布受土体渗透性影响大.Abstract: This paper presents a 2.5-D coupled FE-BE model to simulate the three-dimensional dynamic interaction between saturated soils and tunnels with arbitrary sections.The tunnel is modeled using 2.5-D FEM and the ground is modeled using 2.5-D BEM for saturated porous media.The auxiliary problems are introduced to eliminate the Cauchy singularity of the 2.5-D boundary integral equation.The coupled FE-BE equations are obtained using the continuity conditions on the soil-tunnel interface.The presented model is appropriate for tunnels with arbitrary sections and high computational efficiency.The model is verified through the comparison with the existing models.Finally, a case study of dynamic responses of a quasi-rectangular tunnel in saturated soil due to moving loads is presented.The effects of soil permeability on displacements and pore pressure are investigated.The results show that:(1) The pore pressure decreases drastically with the increment of soil permeability, while displacements are not susceptible to soil permeability;(2) the pore pressure and displacements are mainly distributed in the vicinity of 2m around the loading point;(3) In the direction of gravity, the dissipation of the pore pressure beneath the tunnel is faster than that of displacements;the distributions along the depth to tunnel invert of pore pressure and axial displacement are evidently influenced by the soil permeability.
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Key words:
- saturated soil /
- special-section tunnel /
- dynamic response /
- coupled FE-BE /
- Fourier transformation
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图 5 类矩形盾构断面形式及网格划分
Figure 5. Section form and element mesh of the quasi-rectangular tunnel
图 6 载荷作用位置正下方的隧道底部处位移及孔隙水压力沿轴向分布
Figure 6. Soil displacement and pore pressure at tunnel invert where loads acting varied with $z'$
图 7 不同$b$值时位移及孔隙水压力沿隧道环向分布
Figure 7. Soil displacement and pore pressure varied with tunnel ring for different values of $ b$
图 8 不同$b$值时位移及孔隙水压力沿深度分布
Figure 8. Soil displacement and pore pressure varied beneath the tunnel invert for different values of $ b$
表 1 隧道参数
Table 1. Parameters of tunnel
表 2 饱和土体参数
Table 2. Parameters of saturated soil
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