Numerical validation of analytical solutions and their use for equivalent-linear seismic analysis of circular tunnels

The first part of this paper presents an extensive validation of four analytical solutions for the seismic design of circular tunnels. The validation is performed with a quasi-static finite element (FE) model which conforms to the assumptions of the analytical solutions. Analyses are performed for a wide range of flexibility ratios, slippage conditions at soil-lining interface, assuming both drained and undrained behaviour. Based on the numerical predictions the relative merits of the considered analytical solutions are discussed and recommendations are given for their use in design. The second part of this paper explores the use of equivalent linear soil properties in analytical solutions as an approximate way of simulating nonlinearity. The results of equivalent linear site response analyses are used as an input for the analytical solutions. The comparison of the analytical predictions with nonlinear numerical analysis results is very satisfactory. The results of this study suggest that analytical solutions can be used for preliminary design using equivalent linear properties and the corresponding compatible strain as an approximate way of accounting for nonlinear soil response.