numerical investigation of closed-form solutions for seismic design of a circular tunnel lining (by quasi-static method)

in this paper, four known analytical methods including wang (1993), penzien (2000), park et al. (2009), and bobet (2010) were evaluated based on seismic design of circular tunnel in tehran metro line 6. for this purpose, a quasi-static numerical method was applied in the framework of finite difference method (fdm) under the same assumptions. in both numerical and analytical methods, to consider the nonlinear behavior of soil, linear equivalent properties of soil derived from ground analysis were incorporated in eera software. obtained results shown that the park’s analytical solution under various conditions of interaction between the tunnel lining and soil provides very close results to the of numerical modeling. afterward, a comprehensive validation was performed to assess the impact of the rigidity of the surrounding ground and the maximum shear strain value. in this regard, several earthquake scenarios with different shear wave rates were used to achieve a wide range of flexibility ratio (f) and maximum shear strain. the results showed a significant difference between the results of penzine’s and bobet’s methods under the no-slip conditions and those of numerical analyses for a certain range of flexibility and shear strain ratios. in the final part of the paper, a quasi-static seismic numerical study was performed under realistic soil-structure interaction conditions to illustrate the importance of the actual interaction between the tunnel lining and surrounding soil. the results showed that the actual interaction conditions governing estimation of the axial force play a very important role. also, it was found that park’s solution, because of the ability to consider the slip at the interface provides results very close to those of the numerical modeling. in contrast, one of the serious limitations of the other analytical methods is their inability to simulate the slip interface between the tunnel lining and soil.