Mechanisms causing seismic damage of tunnels at different depths

https://doi.org/10.1016/j.tust.2011.09.001Get rights and content

Abstract

This study investigates the influence of the depth of a tunnel on its seismic damage. Dynamical finite element analysis based on a numerical model of rock mass and tunnel lining is carried out and the incident waves are modeled as harmonic S- and P-waves. The analysis reveals that seismically induced stress is strongly correlated with the depth and the wavelength of the incident wave: when the depth is one quarter of the wavelength, the amplification of the seismically induced stress is particularly pronounced. The amplification is caused by the reflection of waves from the free surface and the scattering effect of the tunnel. A case history of a seismically damaged tunnel is considered to confirm this amplification phenomenon. Damage potential to a tunnel is greatest when the tunnel is at a depth that is close to 0.25 times to the wavelength, so shallow tunnels in weak rock and deep tunnels in competent rocks are particularly vulnerable.

Highlights

► We model the responses of tunnels at various depths when they are subjected to seismic excitation. ► Seismically induced stress in lining is strongly correlated with depth and incident wavelength. ► Stress amplification is particularly pronounced at a depth of 0.25 times wavelength. ► Stress amplification is caused by reflection of wave from free surface and tunnel scattering effect. ► Shallow tunnels in weak rock and deep tunnels in competent rocks are particularly vulnerable.

Introduction

The relevant literature indicates that earthquakes can damage tunnels. Many instances of noticeable seismic tunnel damage were reported in Japan between 1923 and 2007, including 82 instances associated with the 1923 Kanto earthquake (Okamoto, 1973), 20 with the 1995 Kobe earthquake (Asakura and Sato, 1998), more than 50 with the 2005 Niigataken-Chuetu earthquake (Asakura et al., 2007) and six with the 2007 Niigataken Chuetu-Oki earthquake. In Taiwan, the old Sanyi railway tunnels were damaged in the 1935 Hsinchu-Taichung earthquake, and 49 tunnels were damaged in the 1999 Chi-Chi earthquake (Wang et al., 2001, Hwang and Lu, 2007). Seismic damage to tunnels has been reported in other countries, including the USA and Turkey (Brandl and Neugebauer, 2002, Hashash et al., 2001). Global databases of seismic damage to tunnels are available. For example, Dowding and Rozen (1978) collected 71 cases of seismic damage to tunnels, while Sharma and Judd (1991) collected 192 cases of damage to underground structures in 85 countries. These records reveal the need to investigate seismic damage to tunnels in rock.

The potential damage to a tunnel by an earthquake depends critically on its depth. Dowding and Rozen (1978) identified shallowness as one cause of seismic damage. Sharma and Judd (1991) pointed out that more tunnels at lower depths are damaged than are tunnels at large depths. The literature includes few numerical comparisons of tunnels at different depths. Fotiva et al. (2005) concluded that the maximum stress in the lining of a tunnel decreases as tunnel depth increases, based on three case histories of tunnels at different depths. The case histories collected in this present investigation (Section 4) reveal that in weak rock, shallow tunnels area damaged relatively more frequently. In contrast, in competent rock, deep tunnels are damaged more frequently. This finding has rarely been discussed or analyzed in the literature.

Although the mechanism by which depth influences damage has not been systematically examined, some related analyses have been performed. First, accelerations are high at lower depths (Okamoto, 1973, Hashash et al., 2001), and the amplitude of seismically induced stress decays with depth after it reaches a maximum close to the ground surface (Krammer, 1996, Madabhushi and Zeng, 2006, Chen and Han, 2009). Additionally, the geometry of a free surface may modify seismic waves. These factors may be important for tunnels at shallow depths, although the degree of their effect has not been explicitly studied. A systematic study of the effect of depth on possible damage to tunnels is highly desirable.

This study investigates the behaviors of tunnels at various depths when they are subjected to seismic excitation, to determine the effect of depth on seismically induced stress, including normalized axial stress, shear stress and flexural stress in the lining. The analysis aims to address the particular finding that tunnels at shallow depths in weak rock and those at large depths in competent rock are damaged relatively more frequently than others. In particular, both the tunnel depth and the wavelength of incident waves are correlated with seismically induced stress increments. Dynamical finite element analysis is used to model numerically the rock mass and tunnel linings, with the incident waves modeled as harmonic S- and P-waves. The effects of important factors, such as the damping ratio of the rock mass, the shape of the cross-section of the tunnel and the rigidity of the lining, are examined. Finally, the results of the analysis are compared to the damage to the San-I No. 1 tunnel in Taiwan during the 1999 Chi-Chi earthquake.

Section snippets

Setup of numerical model

Fig. 1 presents the configuration of the numerical model. The depth of a tunnel, H, is the vertical distance from the free surface to the center of the tunnel; H′ denotes the vertical distance from the bottom boundary to the center. An incident wave causes harmonic sinusoidal displacements along the bottom boundary. The upper boundary of the model is a free surface, while the left and right boundaries are set to “absorbent” boundaries, which are allowed to move to minimize the reflection of

Numerical results

Section 3.1 numerically analyzes the effect of depth on the seismically induced stress state in tunnels. Other factors that may affect the stress state are also considered. They include the effect of the damping ratio of the rock mass (Section 3.2), the shape of cross-section of the tunnel (Section 3.3) and the rigidity of the tunnel lining (Section 3.4). The damping of the rock mass is not considered in the analysis, except in Section 3.2.

Case study

The San-I No. 1 tunnel is one of the tunnels that were severely damaged in the Chi-Chi earthquake in 1999. The tunnel is located in central Taiwan and is 7260 m long. It passes through gravel, sandstone, an interlayer of sandstone and shale, and the active San-I Fault. Fig. 20 shows its location and the intensity of the earthquake in the vicinity. The tunnel is around 55 km from the epicenter of the Chi-Chi earthquake and 8 km away from the location of the surface rupture of the Chelungpu Fault,

Discussion

Both analytic solution and numerical simulation reveal that the seismic responses of a homogeneously semi-infinite stratum, owing to the free surface reflection from the ground surface, very greatly with depth. For an elastic ground without damping, the seismically induced increment in stress reaches its first peak value when H/λ is 0.25, at which the magnitude of stress is double the incident stress.

The presence of a tunnel inhibits the propagation of waves. The difference between the

Conclusion

Dynamic finite element analysis is employed to investigate the influence of depth on seismic damage to tunnels. The analysis reveals that the seismically induced stress state is strongly correlated with the depth as well as the wavelength of the incident wave: at a depth of 0.25 times the wavelength, the amplification of the stress state is particularly pronounced. The amplification is caused by the reflection of the wave from the free surface and the scattering effect of the tunnel, effects

Acknowledgements

The authors would like to acknowledge the contribution of Prof. Jian-Ye Ching in completion of the work. The authors also thank the National Science Council, Taiwan, for financially supporting this research under Contract Nos. 93-2211-E-002-008 and 99-2628-E-027-006.

References (18)

There are more references available in the full text version of this article.

Cited by (80)

View all citing articles on Scopus
View full text