Random Vibration Analysis of Urban Underground Tunnels Under Vertical Earthquake Excitations Based on Mass–Damper–Spring Model

Abstract

In this paper, the vertical seismic effects on tunnels are studied based on a classic mass–damper–spring model. An analytical discrete model of urban underground tunnels subjected to vertical earthquake excitations is proposed by considering the first vertical vibration mode. Taking a light rail project in Tianjin as an example, this study uses the proposed discrete model to analyze the displacements of tunnel and soil under vertical earthquake excitations. The soil displacement responses at different tunnel locations are analyzed with linear random vibration theory. The computational cost is greatly reduced using the proposed model. It can be seen that different from the case of horizontal earthquakes, the displacement responses under vertical earthquake excitations keep growing after seismic acceleration reaches its peak for a short duration, and then, they begin to decay. The soils at different positions around the tunnels have large relative displacement under vertical earthquake excitations. Moreover, a finite-element model is also established for displacement responses using ABAQUS. The comparison with the results of the finite-element model shows that the results of the proposed discrete model are available.

Keywords

Underground tunnel / Vertical seismic action / Mass–damper–spring model / Random vibration

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