The great magnitude differences between the integral tunnel and its structure details make it impossible to numerically model and analyze the global and local seismic behavior of large-scale shield tunnels using a unified spatial scale, even with the help of supercomputers. The paper aims to present a combined equivalent & multi-scale simulation method, by which the tunnel's major mechanical properties under seismic loads can be represented by the equivalent model, and the seismic responses of the interested details can be studied efficiently by the coupled multi-scale model.
The nominal orthotropic material constants of the equivalent tunnel model are inversely determined by fitting the modal characteristics of the equivalent model with the corresponding segmental lining model. The critical sections are selected by comprehensive analyzing of the integral compression/extension and bending loads in the equivalent lining under the seismic shaking and the coupled multi-scale model containing the details of interest is solved by the mixed time explicit integration algorithm.
The combined equivalent & multi-scale simulation method is an effective and efficient way for seismic analyses of large-scale tunnels. The response of each flexible joint is related to its polar location on the lining ring, and the mixed time integration method can speed-up the calculation process for hybrid FE model with great differences in element sizes.
The orthotropic equivalent assumption is, to the best of the authors’ knowledge, for the first time, used in the 3D simulation of the shield tunnel lining, representing the rigidity discrepancies caused by the structural property.
The authors are grateful to the Shanghai Tunnel Engineering & Rail Transit Design and Research Institute for support and cooperation, and the Earthquake Administration of Shanghai Municipality for professional guidance in seismic analysis. This work is financially supported by the National High Technology Research and Development Program (863 Program) of China under the program 2012AA01AA307 and the Natural Science Foundation of China under the program 11272214.
Zhang, W., Jin, X. and Yang, Z. (2014), "Combined equivalent & multi-scale simulation method for 3-D seismic analysis of large-scale shield tunnel", Engineering Computations, Vol. 31 No. 3, pp. 584-620. https://doi.org/10.1108/EC-02-2012-0034Download as .RIS
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