Comparison of Penzien and Wang analytical methods with the finite difference numerical method in seismic analyses of the Qazvin-Rasht (Kuhin) tunnel

Two analytical solutions for estimating the ovaling deformation and forces in circular tunnels are widely used in engineering practice, due to soil-structure interaction under seismic loading. This paper discusses the discrepancy between the two analytical and finite difference methods. A comparison of the two analytical methods shows that the calculated forces and displacements are identical for the condition of full-slip between the tunnel lining and ground. However, the calculated lining thrusts differ by an order of magnitude when considering no-slip between the tunnel lining and the ground. The analytical solutions are compared to numerical analyses of the no-slip condition using the finite difference method to validate which of the two methods provide the correct method. To achieve the goal, numerical modelling, field data of the Kuhin railway tunnel and Manjil earthquake characteristics are used. Numerical analysis results agree with one of the analytical solutions that provides a higher estimate of the thrust on the tunnel lining, thus highlighting the limitation of the other analytical solution.