Determination of the Racking Reduction Factor in a Horseshoe Shaped Tunnel Section Considering the Soil-Structure Interaction

Abstract

Effects of earthquakes on tunnels and underground structures can be investigated in two aspects: longitudinal tunnel behavior and Racking tunnel behavior. In this paper only the effects of the earthquake on tunnel section (racking behavior) is studied by modeling in plane-strain condition. Thus the obtained reduction factor is the tunnel racking reduction factor. In this paper, by performing a pushover analysis and using the proposed methods of Wang (Seismic design of tunnels: a state-of-the-art approach, Parsons Brinckerhoff Quade & Douglas, Inc., New York, 1993) and Hashash et al. (Tunn Undergr Space Technol 16:247–293, 2001) in determination of the tunnel racking deformation and proposing a trial and error pattern, the performance point of the tunnels in the earthquake is determined considering nonlinear behavior of the tunnel lining. In the next step, by using the pushover curve and applying the existing equations of calculating reduction factor in the structures and considering the soil-structure interaction, tunnel racking reduction factor (TRRF) are estimated. Finally, three nonlinear dynamic analyses consistent with the site are performed using finite element software. Comparison between the modified forces by using the reduction factor in the linear static analyses and the forces obtained by applying earthquake records in the nonlinear time history analyses, shows the good accuracy of the obtained reduction factors. The studies also show that implementing linear static analyses without tunnel racking reduction factor leads to very conservative results of lining force in tunnel. Since the TRRF values are sensitive to the soil type and overburden depth, the sensitivity analysis is performed for the overburden depths of 5 and 20 m and two soil types to achieve a more comprehensive result.