Analytical Solution for the Longitudinal Response of Tunnels under Combined Seismic-fault Misalignment
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摘要: 隧道穿越地震活动断层带时可能遭受严重破坏，以内马铁路一期三标段工程为依托，对地震动和断层错动联合作用下隧道结构纵向响应进行研究。针对穿越断层破碎带的隧道结构，基于地下结构抗震拟静力法，将其简化为弹性地基梁，并将地震动和断层错动位移简化为作用在隧道上的静荷载，建立地震动和断层错动联合作用下隧道纵向响应理论模型并进行求解，利用有限元数值模拟方法验证解析解的正确性。通过解析解进行参数敏感性分析，揭示断层错动位移、两侧围岩地基系数与断层破碎带地基系数比及围岩与隧道结构刚度比对隧道结构纵向响应的影响规律。研究结果表明，断层错动位移增加使隧道结构截面弯矩、剪力峰值接近线性增加，隧道内力沿隧道纵向分布的影响范围不变，且断层破碎带界面出现了截面剪力突变；两侧围岩地基系数与断层破碎带地基系数比对隧道结构截面剪力的影响较大，在地震动和断层错动联合作用下隧道结构剪力在断层破碎带界面急剧减小；随着围岩与隧道结构刚度比的减小，地震动引起的隧道挠度减小，断层错动作用引起的隧道挠度变化范围增大，同时隧道结构内力响应明显增大。Abstract: China is one of the countries that has the most severe seismic hazards in the world, and tunnels may suffer severe damage when crossing seismically active fault zones. In this paper, the longitudinal response of the tunnel structure under the joint action of earthquake and fault misalignment is investigated based on the third standard section of the first phase of the Nairobi-Malaba railway as a project. For the tunnel structure crossing the fault fragmentation zone, based on the idea of seismic anthropomorphism of underground structure, it is simplified into elastic foundation beam, and the ground vibration and fault misalignment displacement are simplified into static load acting on the tunnel, the theoretical model of tunnel longitudinal response under the joint action of earthquake - fault misalignment is established and solved, and the correctness of the analytical solution is verified by using the finite element numerical simulation method. Parametric sensitivity analysis is carried out to reveal the influence of the fault misalignment displacement, the ratio of the foundation coefficient of the surrounding rock to the foundation coefficient of the fault fragmentation zone, and the ratio of the surrounding rock to the tunnel structure stiffness on the longitudinal response of the tunnel structure. The results show that the increase of fault misalignment displacement makes the tunnel structure cross-sectional moment and tunnel structure cross-sectional shear peak close to linear increase, the influence range of tunnel internal force distribution along the tunnel longitudinal direction remains unchanged, and there is a sudden change of cross-sectional shear at the interface of fault fragmentation zone; the ratio of surrounding rock foundation coefficient and fault fragmentation zone foundation coefficient on both sides has a greater influence on the tunnel structure cross-sectional shear, under the combined effect of earthquake - fault misalignment tunnel The shear force of the tunnel structure decreases sharply at the interface of the fault zone; the ratio of surrounding rock to tunnel structure stiffness decreases, the tunnel deflection caused by the earthquake decreases, and the range of deflection caused by fault misalignment increases, while the internal force response of the tunnel structure increases significantly.
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Key words:
- Tunnel /
- Seismic shaking /
- Fault dislocation /
- Analytical solution /
- Foundation beam /
- Quasi-static method
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图 1 地震动和断层错动联合作用下隧道响应示意
Figure 1. Schematic diagram of tunnel response under earthquake-fault dislocation
图 4 El Centro地震波加速度时程曲线
Figure 4. El Centro seismic wave acceleration time-history curve
图 5 理论解析解与数值解隧道纵向变形及内力对比
Figure 5. Comparison of theoretical and numerical solutions for longitudinal deformation and internal forces in tunnels
图 6 断层错动位移对隧道变形及内力的影响
Figure 6. Effect of fault misalignment changes on tunnel deformation and internal forces
图 7 两侧围岩地基系数与断层破碎带地基系数比对隧道变形及内力的影响
Figure 7. Influence of fault fracture zone foundation coefficient on tunnel deformation and internal force
图 8 围岩与隧道结构刚度比对隧道变形及内力的影响
Figure 8. Influence of tunnel structure and surrounding rock stiffness ratio on tunnel internal force deformation
表 1 计算参数
Table 1. Calculation parameter table
材料 弹性模量/GPa 围岩泊松比 围岩密度/（kg·m−3） 地基系数/MPa 隧道截面惯性矩/m4 隧道宽度/m 强风化粗面岩 6.5 0.32 2 400 1 083.4 — — 断层破碎带 2.0 0.30 2 200 332.7 — — 隧道衬砌 35.0 0.20 — — 173.63 6.2 
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