Dynamic response of twin parallel tunnels in unsaturated soil under metro train loadings

The dynamic response of twin parallel tunnels in unsaturated soil under metro train loadings was investigated using analytical methods. In the analysis, the tunnel was simulated as a linear elastic thin cylindrical shell, while the surrounding soil was treated as an unsaturated porous medium containing two cylindrical cavities. The analytical generalized solutions were deduced by solving the governing equations for the coupled tunnel-soil system using the separation of variables method and the Helmholtz decomposition method combined with the Fourier transform technique. Mixed boundary conditions were applied to determine unknown coefficients in the general solutions, yielding closed-form analytical solutions for dynamic displacement fields, as well as pore water/air pressure fields of the tunnel linings and soil. The validity and correctness of the proposed method were confirmed by comparisons with existing theoretical solutions. The parameter sensitivity analysis revealed that the presence of pore fluids (water/air) significantly affects the dynamic response of tunnels and surrounding soil. Increasing the tunnel spacing can effectively reduce the dynamic coupling effect between parallel tunnels. The traditional elastic or saturated medium models, which don't consider the gas phase and the liquid phase, have a significant bias in the prediction of the dynamic interaction of the tunnel-soil system. The study reveals that variations in saturation degree significantly influence the displacement responses and pore pressure distributions of double-line parallel tunnels. Near-field displacement responses induced by saturated soils are substantially larger than those in unsaturated soils, whereas far-field displacements in saturated soils are smaller compared to unsaturated soils with higher saturation degrees. Moreover, a decrease in saturation degree leads to a rapid reduction in the bulk modulus of pore fluids, thereby amplifying the influence of the second tunnel on pore pressure. Analyzing the dynamic responses of double-line parallel tunnels under arbitrary saturation conditions facilitates more accurate prediction of metro train loading effects on soil behavior and provides critical guidance for tunnel design optimization.