Seismic vulnerability assessment of rectangular cut-and-cover subway tunnels

doi:10.1016/j.tust.2019.01.021

Tunnelling and Underground Space Technology

Volume 86, April 2019, Pages 247-261

https://doi.org/10.1016/j.tust.2019.01.021 Get rights and content

Highlights

•
We develop fragility curves of various types of metro box tunnels with respect to PGA, PGV, and PGV/V_s30.
•
The effect of site profile on the calculated fragility curve is shown to be significant.
•
The dependence on site characteristics is lowest when PGV/V_s30 is used.
•
The multi-box tunnels are more susceptible to earthquake damage than single box tunnels.

Abstract

This study develops fragility curves for rectangular cut-and-cover tunnels from nonlinear frame analyses. Fragility curves are generated for single, double, and triple boxes constructed for the subway system. A wide range of site profiles is used to evaluate the effect of soil characteristics on the calculated fragility curve. The fragility curves are developed for minor, moderate, and extensive damage states. The damage indices defined in a previous study as the ratio of the elastic moment demand to the yield moment at the critical section of the tunnel lining was used in the analyses. Fragility curves of the tunnels are generated in terms of surface peak ground acceleration (PGA), peak ground velocity (PGV), and PGV/V_s30 (V_s30 is the time-averaged shear-wave velocity to 30 m depth). The results highlight that the fragility curve is highly sensitive to the site profile, and that PGA based curves result in the largest scatter. The effect of the site profile is significantly reduced when PGV/V_s30 is used, where the fragility curves for all site profiles fall within a narrower band. This is because both the intensity of the ground motion and the soil stiffness is accounted for in the parameter PGV/V_s30. Considering the importance of site amplification characteristics, it is recommended that PGV/V_s30 be used instead of PGA and PGV in the generation of fragility curves of underground structures. Comparisons also demonstrate that multi-box tunnels are more vulnerable to earthquake damage compared with single box tunnels because the seismic demand is always larger.

Introduction

Underground structures such as subways, parking lots, conduits, and material storages are widely used for urban infrastructures. Such structures are known to be more resistant to seismically induced structural damage compared with above-ground structures (Dowding and Rozan, 1978, Hashash et al., 2001, Wang, 1993). However, recent large earthquakes have revealed that underground structures can suffer severe damages or even collapse during strong seismic excitations (Hashash et al., 2001, Pitilakis and Tsinidis, 2014). A number of studies documented the observed damage of tunnels in various earthquakes (Dowding and Rozan, 1978, Giannakou et al., 2005, Iida et al., 1996, Jiang et al., 2010, Kitagawa and Hiraishi, 2004, Li, 2012, Lu and Hwang, 2008, Nakamura et al., 1996, Owen and Scholl, 1981, Power et al., 1998, Sharma and Judd, 1991, Shen et al., 2014, Wang, 1985, Wang et al., 2009, Yamato et al., 1996, Yashiro et al., 2007, Yu et al., 2016, Yu et al., 2013). A review of seismic damage of mountain tunnels and possible failure mechanisms was systematically presented by Roy and Sarkar (2017). The observed damages reveal the need to assess the fragility levels of underground structures to minimize their potential vulnerability in future earthquakes.

The damage states need to be firstly defined to assess the seismic vulnerability of earthquakes. The seismic damage states of underground structures were defined from qualitative information and quantitative approaches. The qualitative observations (e.g. failure patterns of the tunnel lining, pavement, and soil/rock around the opening) were documented in several studies including ALA, 2001, Dowding and Rozan, 1978, HAZUS, 2004, and Werner et al. (2006). The quantitative approach was conducted based on the measure of cracking width and length for the rock tunnel lining (Corigliano et al., 2007), a global normalized cumulative rotation for deep tunnels (Andreotti and Carlo, 2014, Andreotti et al., 2013), and a moment ratio for shallow tunnels (Argyroudis and Pitilakis, 2012). More recently, Lee et al. (2016b) developed three damage states, which are minor/slight, moderate, and extensive for typical rectangular cut-and-cover metro tunnels. The proposed damage states were quantitatively determined based on the number of plastic hinges formed at the corners of the tunnel.

The seismic fragility curve represents the conditional probability of exceeding a predefined damage state as a function of a given intensity measured of ground motion. The fragility curve is a useful tool to assess the seismic vulnerability of buildings, lifelines, and infrastructures. Fragility curves have been commonly developed for above-ground structures such as buildings and bridges, whereas relatively few studies have been conducted on the seismic fragility analysis of underground structures.

In general, fragility curves of underground structures can be categorized into two groups: (1) empirical curves which are derived from damage experiences in past earthquake events and (2) numerical curves developed from numerical simulations. Empirical fragility curves for rock and cut-and-cover tunnels considering poor-to-average and good construction conditions were proposed by the American Lifelines Alliance (ALA, 2001). In HAZUS (2004), fragility curves of bored and cut-and-cover tunnels were empirically generated in terms of peak ground acceleration (PGA) and permanent ground displacement (PGD), in which the earthquake database was adopted partly from reports written by Dowding and Rozan (1978), and Owen and Scholl (1981). The limitation of empirical fragility curves is that it does not adequately take into account the specific factors including soil conditions and structural characteristics of the tunnel. In addition, the empirical fragility analysis requires a significant amount of damage database from the past earthquakes to be statistically meaningful.

Because of the limited damage data of underground structures, the numerical fragility analysis approach has been widely used to assess the seismic vulnerability of specific underground structures. A series of fragility curves were developed for bored circular tunnels. Fragility curves for deep rock tunnels were developed by Corigliano et al. (2007). A comprehensive study on fragility analysis of shallow bored tunnels in alluvial deposits was carried out by Argyroudis and Pitilakis (2012). The damage states and indices were assumed from empirical engineering judgments. Argyroudis et al., 2014, Argyroudis et al., 2017 adopted the damage states presented in Argyroudis and Pitilakis (2012) to produce fragility curves for two circular shallow metro tunnels considering the soil-tunnel interaction and the aging effects due to corrosion in the tunnel lining. Huang et al. (2017) proposed an analytical method to develop seismic fragility curves of rock mountain tunnels where Arias intensity was used as the intensity measure of the ground motion. Qiu et al. (2018) developed seismic fragility curves for a group of circular rock tunnels with different diameters, depths, and lining thicknesses based on pseudo-spectra acceleration at the fundamental period of the structure.

A suite of fragility curves was also developed for cut-and-cover underground box structures. Liu et al. (2016) developed fragility curves for the Daikai subway station by means of the incremental dynamic analysis where PGV was used as an intensity measure. Argyroudis and Pitilakis (2012) developed curves for a rectangular tunnel from pseudo-static analyses. The effect of soil variability was evaluated by using a series of idealized site profiles. Huh et al. (2017a) performed a pseudo-static analysis to derive seismic fragility curves of a two-cell reinforced concrete box tunnel. Using the same procedure, Huh et al. (2017b) also conducted a probabilistic fragility analysis of a two-story underground box structure. Previous studies on the seismic vulnerability of cut-and-cover box tunnels used a specific structure to derive the fragility curve. The effect of site profile on the fragility analysis was also not assessed except in the study of Argyroudis and Pitilakis (2012). Such site and structure-specific fragility curve cannot be routinely used in the seismic design.

The objective of this study is to derive seismic fragility curves for representative single-story cut-and-cover metro box tunnels in various soil conditions. The tunnels modeled are single, double, and triple box structures. Sixteen site profiles with different site thicknesses and soil types were selected. Three damage states proposed by Lee et al. (2016b) were adopted to construct fragility curves of the tunnels. A set of fragility curves were developed using PGA, PGV, and PGV/V_s30 as intensity measures. The derived fragility curves were compared with the published fragility curves from earlier studies. The effect of tunnel type and soil condition on seismic fragility curves are also examined in this paper.

Section snippets

Procedure for deriving fragility curves of tunnels

The seismic response analysis of tunnel structures can be performed by a dynamic or a pseudo-static approach. The pseudo-static analysis neglects the dynamic soil-tunnel interaction as well as the inertial effects. However, previous studies highlighted that the difference between two methods is not significant (Argyroudis and Pitilakis, 2012, Hashash et al., 2010b, Hwang and Lu, 2007, Zou et al., 2017). Thus, the pseudo-static procedure is widely applied in research and design practice (

Input ground motions

Earthquake ground excitation is a major source of uncertainty in the probabilistic analysis of structures. In this study, a series of input motions were selected to cover the variability of the intensity and frequency characteristics of the earthquake waves. Ground motions with a wide range of predominant frequencies and earthquake scenarios were selected, as summarized in Table 1. All ground motions were recorded at rock outcrops with V_s30 higher than 1500 m/s. The average of the normalized

1D site response analysis

In this study, sixteen site profiles classified as types B, C, and D according to Eurocode 8 (EC8, 2004) were used. Fig. 3 shows the shear wave velocity distributions of the selected site profiles. Four different soil depths (H) were used; H = 30 m, 50 m, 100 m, and 150 m. For each soil depth, there are two site profiles falling in a site class, therefore, they are denoted by an extra number 1 or 2 after the hyphen in legends, for instance, profiles C30-1 and C30-2 belong to site class C with

Structural modeling

The seismic response of tunnels can be categorized as ovaling (for circular tunnels) or racking (for rectangular tunnels) deformations, longitudinal bending, and axial compression or extension (Owen and Scholl, 1981). In this study, only the racking of the tunnels was investigated because it is the predominant mode of failure for rectangular tunnels. Three types of metro box tunnels, which are the single, double, and triple boxes, were modeled using nonlinear frame analysis program SAP2000 (

Seismic response and damage state of tunnels

The seismic responses of tunnels were calculated by imposing the soil displacements on the soil-tunnel model. The top-right and bottom-left corners of the tunnel frame were specified as critical sections for monitoring the variation of bending moment under the different seismic intensity levels and input ground motions. Fig. 11 shows examples of the bending moment distributions of the box tunnels. The displacement profile of C50 profile subjected to the 1999 Hector Mine earthquake (PGA = 0.3 g)

Development of fragility curves

Seismic fragility curves were developed for the three types of box tunnels based on the procedure presented in the previous sections. For each box tunnel, the fragility functions for three damage states were derived separately. The effects of the soil condition, tunnel type, and ground motion intensity measure on the probability of damage were also examined in this section.

Fig. 16 shows fragility curves of the single box for different site profiles with respect to PGA at the surface. The thin

Comparison of proposed fragility curves with existing curves

The fragility curves proposed in this study are compared with those presented in previous studies for cut-and-cover tunnels. It should be noted that we only compare mean curves based on PGA even though it is demonstrated that PGV/V_s30 is a more appropriate intensity measure, because published curves for cut-and-cover tunnels use PGA as the intensity measure. Fig. 20 shows the representative comparison between the fragility curves developed in this study and the existing empirical (ALA, 2001,

Conclusions

A series of pseudo-static analyses for developing seismic fragility curves of cut-and-cover box tunnels were performed. One-story tunnel structures with the single, double, and triple box which constructed for the urban metro in South Korea were selected for the case studies. Sixteen site profiles with a variation of the soil depth and average shear wave velocities (V_s30) classified as types B, C, and D according to EC8 were investigated. Induced displacements of soils were calculated through

Acknowledgment

This work was funded by the project titled “Development of performance-based seismic design technologies for advancement in design codes for port structures” (Ministry of Oceans and Fisheries of Korea) and Basic Science Research Program through the National Research Foundation of Korea (Ministry of Science, ICT and Future Planning, NRF-2015R1A2A2A01006129).

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