An analytical model for predicting the vibrations from an underground railway tunnel embedded in an unsaturated half-space is proposed. The tunnel lining is modeled as an infinite Flügge cylindrical shell, and the unsaturated soil is modeled as a three-phase medium comprising solid grains and pores containing water and air. By using the transformation properties between the plane wave functions and the cylindrical wave functions, the model is coupled based on the boundary conditions. The developed model is validated by comparison with existing tunnel models, and the effect of saturation on the dynamic response of the tunnel–soil system is demonstrated through a case study.

提出了一种分析模型，该模型用于预测埋入非饱和半空间的地下铁路隧道的振动。隧道衬砌建模为无限的Flügge圆柱壳，非饱和土建模为三相介质，包括固体颗粒和包含水和空气的孔隙。通过使用平面波函数和圆柱波函数之间的转换特性，基于边界条件耦合模型。通过与现有隧道模型进行比较，验证了开发的模型，并通过案例研究证明了饱和度对隧道-土壤系统动力响应的影响。