To estimate the tunnel response induced by a new tunnel excavation underneath, theoretical solutions are proposed in this study. The overlying tunnel is idealized as an infinite Timoshenko beam resting on the Kerr foundation model, then the vertical force balance equation is established. The unloading stress can be expressed as Fourier cosine series and a theoretical solution can be derived. The effectiveness of the proposed method is verified by a centrifuge test and an actual field measurement, which are extracted from previous investigations. Calculation results from the proposed method show good accord to centrifuge test results and field-measured data. Meantime the predictions given by the proposed method are more accurate to estimate tunnel response compared with the previous method. Parametric analysis indicates that the volume loss ratio and the vertical clearance between two tunnels, are both significantly alleviate the tunnel response, but the effect of tunnel shear stiffness is slight. The theoretical solutions can be adopted to predict the overlying tunnel response induced by tunneling underneath in real projects.

中文翻译：

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评估新隧道开挖引起的隧道响应的简化方法

为了估计地下新隧道开挖引起的隧道响应，本研究提出了理论解决方案。将上覆隧道理想化为建立在Kerr基础模型上的无限Timoshenko梁，建立竖向力平衡方程。卸载应力可以表示为傅里叶余弦级数，并可以导出理论解。通过从先前的调查中提取的离心机测试和实际现场测量验证了所提出方法的有效性。该方法的计算结果与离心机试验结果和现场测量数据吻合良好。同时，与之前的方法相比，所提出的方法给出的预测能够更准确地估计隧道响应。参数分析表明，体积损失率和两隧道间的竖向净空均显着缓解了隧道响应，但隧道剪切刚度的影响较小。理论解决方案可用于预测实际工程中因地下隧道开挖而引起的上覆隧道响应。