Prediction of tunnel lining forces and deformations using analytical and numerical solutions

Structural design of linings requires a reliable prognosis of lining forces and deformations. In engineering practice, both analytical and numerical solutions are popular to be employed to predict the system behavior. This paper employs the commonly accepted analytical solutions to calculate the lining forces and deformations for both shallow and deep tunnels, the results are compared to the numerical results for corresponding equivalent boundary conditions, initial conditions and identical material properties. Afterward, more sophisticated constitutive models for soil/structure elements in conjunction with more realistic construction aspects are taken into account. The comparison of the results of analytical and numerical solutions highlights the differences between these two well accepted methods as well as the effect of considering realistic features in numerical simulations. Moreover, the lining forces and deformations obtained from plain strain condition are compared to the 3D numerical results. The results show that the analytical bedding model is able to reasonably predict the lining behavior for both shallow and deep tunnels even if the soil is assumed to be an elastic material. In numerical solutions, lining forces and deformations depend to a large extent on the applied soil constitutive model and construction method. The face support pressure, backfill grouting and arching effect cannot be captured appropriately in plain strain condition, which leads to the discrepancy between the model responses obtained from 2D numerical/analytical solutions and realistic 3D simulations.