Complex variable method for the ground surface settlement of twin parallel shield tunnels under the influence of seepage

• Considering the influence of groundwater seepage, the Slepcka index seepage model is derived based on the non-Darcy seepage assumption. • The coupling solutions between the complex variable method and stochastic medium theory are achieved to propose an analytical solution for the vertical displacement of surrounding rock caused by twin parallel shield tunnel excavation. • An analytical method for the ground surface settlement of twin parallel shield tunnels under the influence of seepage is established by the superposition principle. To investigate the ground surface settlement law of twin parallel shield tunnels under the action of groundwater seepage, in this study, twin equal circular tunnels were investigated, and groundwater seepage in the surrounding rock was assumed to follow the non-Darcy seepage law. The Slepcka index seepage model was presented, and the equations for the displacement of the surrounding rock under seepage in twin parallel shield tunnels were established on the basis of the seepage boundary conditions. A calculation method for the ground surface settlement of twin parallel shield tunnels under the influence of seepage was derived by using the stochastic medium theory and the complex variable method. Through the field monitoring results and numerical simulation results of actual engineering projects, the engineering applicability of the proposed method was validated. The results indicate that the theoretical calculation results are consistent with the field monitoring results and numerical simulation results. The root mean square error between the theoretical calculation results and the field monitoring results is 0.93, and the root mean square error between the theoretical calculation results and the numerical simulation results is only 0.28, which indicates the good engineering applicability of the proposed method. Therefore, this method can reveal not only the variation law of surface settlement under the influence of seepage but also the corresponding distribution law of pore water pressure, which can reliably guide the prediction and control of surface settlement deformation in similar tunnel engineering construction.