Tunneling underneath is bound to induce the free displacement of surrounding soil, which will further significantly affect the overlying tunnel's deformation. Based on this, a simplified method for calculating the deformation of the overlying tunnel due to shield tunnel excavation is proposed. Firstly, the Loganathan formula is selected to solve the additional stress along the pre‐existing tunnel induced by tunneling underlying, then the overlying tunnel is further simplified into an infinitely Euler‐Bernoulli beam resting on the Pasternak foundation. The influence of the lateral soil reaction on the existing tunnel is introduced, then adopting the energy method to describe the soil and tunnel response. The minimum potential energy principle is utilised to solving the variational energy solutions due to new tunnel excavation underlying and further obtain the explicit solutions of tunnel response. The proposed method's effectiveness is confirmed through comparisons with centrifuge tests and field case studies obtained from prior research. In comparison with the Pasternak foundation model degenerated from the proposed method, the outcomes produced using the proposed method align more closely with the measurement data. Further parameter studies show that skew angle between tunnels, depth of existing tunnel, and volume loss rate are significant factors affecting the tunnel behaviors due to tunneling underneath.

中文翻译：

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估算底层隧道开挖对现有隧道影响的简化方法


地下隧道的开挖必然会引起周围土体的自由位移，从而进一步显着影响上覆隧道的变形。在此基础上，提出了盾构隧道开挖上覆隧道变形的简化计算方法。首先，选择Loganathan公式来求解由于下伏隧道开挖引起的沿既有隧道的附加​​应力，然后将上覆隧道进一步简化为位于帕斯捷尔纳克基础上的无限欧拉-伯努利梁。介绍了侧向土体反应对既有隧道的影响，并采用能量法描述土体和隧道反应。利用最小势能原理求解新隧道开挖下伏引起的变分能量解，进一步得到隧道响应的显式解。通过与离心机测试和先前研究获得的现场案例研究的比较，证实了所提出方法的有效性。与从所提出的方法退化的帕斯捷尔纳克基础模型相比，使用所提出的方法产生的结果与测量数据更加一致。进一步的参数研究表明，隧道之间的倾斜角、现有隧道的深度和体积损失率是影响隧道开挖行为的重要因素。