隧道开挖引起上覆既有隧道受力变形解析解

为了精确且快捷地评估隧道开挖对上覆既有隧道的影响,首先基于Loganathan公式获得隧道开挖引起周围土体竖向自由位移解,然后将上覆既有隧道视为搁置在Vlasov地基模型的欧拉梁,综合考虑隧道两侧土体对既有隧道受力变形的影响,最后采用积分法获得既有隧道纵向变形解析解。案例分析结果表明：该方法计算结果与实测数据接近；与该方法的退化解析对比,该方法更贴近实测数据。进一步参数研究表明：增大地层损失率会引起既有隧道纵向位移和内力呈现线性增加的趋势；既有隧道抗弯刚度的增强会导致其纵向位移的减小,且会造成其内力增强；新旧隧道竖向距离和土体模量的增大会有效地减小既有隧道纵向位移和内力。

Analytical solution of Stress and Deformation of Overlying Existing Tunnel Induce by Tunneling

In order to analyze the effect of tunneling on overlying existing tunnel accuracy and rapidly. Firstly, the Loganathan formulas is adopted here to obtain the vertical soil-free displacement, then the existing tunnel is treated as a Euler-Bernoulli beam laying on the Vlasov foundation model and taking the tunnel lateral soil effect into consideration, finally an analytical longitudinal deformation solution of existing tunnel can be solved by using the integration method. Cases study shows that the calculation results of the proposed method are close to the measured data. Compared with the degradation analysis from the proposed method, the proposed method is closer to the measured data. Further study shows that the trend of longitudinal displacement and inner force of existing tunnel increase linearly with the increment of volume loss. Increasing the bending stiffness of existing tunnel will reduce the longitudinal displacement of existing tunnel, but the inner force of tunnel will increase. Increasing the vertical distance between new and old tunnels and soil modulus will effectively reduce the tunnel longitudinal displacement and inner force.