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

Tunnelling and Underground Space Technology 86 (2019) 247–261

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Seismic vulnerability assessment of rectangular cut-and-cover subway tunnels Duy-Duan Nguyena,c, Duhee Parkb, Sadiq Shamsherb, Van-Quang Nguyenb,c, Tae-Hyung Leea,

T ⁎

a

Department of Civil Engineering, Konkuk University, Seoul 05029, Republic of Korea Department of Civil and Environmental Engineering, Hanyang University, Seoul 04763, Republic of Korea c Department of Civil Engineering, Vinh University, Vinh 461010, Vietnam b

A R T I C LE I N FO

A B S T R A C T

Keywords: Cut-and-cover tunnel Seismic fragility curve Damage state Pseudo-static analysis Inelastic frame model

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/Vs30 (Vs30 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/Vs30 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/Vs30. Considering the importance of site amplification characteristics, it is recommended that PGV/Vs30 be used instead of PGA and PGV in the generation of fragility curves of underground structures. Comparisons also demonstrate that multibox tunnels are more vulnerable to earthquake damage compared with single box tunnels because the seismic demand is always larger.

1. 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, 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

Corresponding author. E-mail address: [email protected] (T.-H. Lee).

https://doi.org/10.1016/j.tust.2019.01.021 Received 2 August 2018; Received in revised form 21 January 2019; Accepted 24 January 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.

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fragility curves were developed using PGA, PGV, and PGV/Vs30 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.

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 and 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 pseudostatic analyses. The effect of soil variability was evaluated by using a series of idealized site profiles. Huh et al. (2017a) performed a pseudostatic 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-andcover 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

2. 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 (Anderson, 2008; Argyroudis et al., 2013, 2017; Argyroudis and Pitilakis, 2012; Debiasi et al., 2013; Hashash et al., 2010b; Iai, 2005; Katona, 2010; Liu and Shi, 2006; Lu and Hwang, 2017; MLTM, 2009; Park et al., 2009; Tsinidis et al., 2016b; Wang, 1993; Wood, 2004; Yoo et al., 2017; Zou et al., 2017). In this study, a series of pseudo-static analyses were carried out to develop the fragility curves of the tunnels. The procedure to construct the fragility curve is outlined in the following: (1) Perform 1D equivalent linear site response analyses for a set of ground motions. (2) Construct the structural system model considering the soil-tunnel interaction. (3) Impose horizontal free field displacements obtained from Step 1 on the structural model to obtain the associated bending moment demand (M) at the critical sections of the tunnel frames. (4) Define the damage states (DS) of the tunnel based on the damage index (DI) which is expressed as the ratio of the demand bending moment (M) to the yield moment (My) of the critical tunnel section. (5) Calculate the means and standard deviations of the damage indices for a given seismic intensity measures using the linear regression method (Tang and Ang, 2007). (6) Generate the fragility curve based on the two calculated parameters for each combination of a tunnel and a soil type. The pseudo-static procedure for deriving fragility curves of tunnels is depicted in Fig. 1. In this study, the fragility function was described by the lognormal cumulative distribution function, expressed by

P [DS |IM = X ] = Φ ⎛⎜ ⎝

ln X − μ ⎞ ⎟ β ⎠

(1)

where P[DS∣IM] is the conditional probability of exceeding a damage state (DS) at a given ground motion intensity measure (IM); Φ(−) is standard normal cumulative distribution function; X is the intensity measure of ground motion; μ and β are the median and standard deviation of lnX, respectively. The standard deviation β is calculated by combining of three uncertainties: (1) the capacity of the tunnel (βC), (2) the damage states definition (βDS), and (3) the ground motion demand (βD), expressed by

β=

2 βC2 + βDS + βD2

(2)

Based on the study of Salmon et al. (2003), the capacity uncertainty (βC) is set to 0.3. The uncertainty due to damage state definition (βDS) is set to 0.4 based on the recommendations of HAZUS (2004). The demand uncertainty due to earthquakes (βD) is calculated by the average standard deviation of the damage indices in the linear regression analysis. 248

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1D site response analysis

Soil layers

D.-D. Nguyen et al.

Estimate demand bending moments

Ground motions Perform pseudo-static analyses Damage Index (lnDI)

Probability of damage

Soil deformations 1.0 0.8 0.6 0.4 0.2 0.0 0.0

0.5

1.0

3 2 1

Define damage states based on DI = M/My

0 -1

0

0.2

0.4

0.6

0.8

1

-2 -3 -4

1.5

PGA (g) or PGV (m/s)

4

PGA (g) or PGV (m/s)

Plot DI versus intensity measure

Generate fragility curves

Fig. 1. Procedure of the pseudo-static analysis for deriving fragility curves of tunnels. Table 1 Selected ground motion records. No.

Earthquake event

Station

Year

Mag. (Mw)

Epic. distance (Km)

Pre. period (Tp)

PGA (g)

PGV (cm/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Cape Town, S. Africa Chichi, Taiwan Coyote, USA Duzce, Turkey El-Centro, USA Hector, USA Imperial Valley, USA Kobe, Japan Kocaeli, Turkey Landers, USA Loma Gilroy, USA Loma Gilroy, USA Mammoth Lakes, USA Nahanni, Canada Northridge, USA Northridge, USA Parkfield, USA San Fernando, USA Tabas, Iran Whittier Narrows, USA

Capetown CHY-101 San Juan Bautista Bolu Imperial Valley Distr. North Palm Spr. Elcentro array#1 Nishi-Akashi Arcelik Yermo Fire Gilroy array#2 Gilroy array#3 Long Valley Dam Nahanni-Station #3 Beverly Hills Canyon Country Parkfield-Cholame 5w Pacoima Dam Tabas Rancho Palos Verdes

1969 1999 1979 1999 1940 1999 1979 1995 1999 1992 1989 1989 1980 1985 1994 1994 1966 1971 1978 1987

6.3 7.6 5.7 7.1 6.9 7.1 6.5 6.9 7.4 7.3 6.9 6.9 6.3 6.8 6.7 6.7 6.1 6.6 7.8 6.0

11.6 15.3 17.2 12.4 6.0 48.0 26.5 0.6 17.0 23.6 19.9 11.6 15.5 16.0 26.8 43.4 9.9 1.81 2.05 21.2

0.12 0.54 0.42 0.32 0.46 0.22 0.32 0.45 0.16 0.34 0.24 0.40 0.16 0.06 0.18 0.44 0.38 0.24 0.12 0.16

0.384 0.183 0.124 0.727 0.400 0.265 0.169 0.509 0.218 0.244 0.170 0.357 0.430 0.148 0.217 0.098 0.357 0.209 0.899 0.186

21.9 39.3 7.6 56.4 37.8 28.5 11.6 37.3 17.7 25.7 14.2 28.6 23.5 6.1 9.8 8.9 21.5 18.9 55.0 4.6

2000

Average response spectrum EC8-Site A

3 2

Sv (mm/s)

Sa/PGA

4

1 0

1500 1000 500 0

0

1

2

3

4

0

1

Period (s)

2

3

4

Period (s)

Fig. 2. Response spectra of 20 ground motions.

3. Input ground motions

selected, as summarized in Table 1. All ground motions were recorded at rock outcrops with Vs30 higher than 1500 m/s. The average of the normalized acceleration spectra of the input ground motions is compared with EC8 Site class A design spectrum in Fig. 2a. The averaged spectrum is shown to compare well with the design spectrum. Fig. 2b plots the velocity spectra of all input ground motions as well as the average spectrum. Table 1 lists properties of the selected ground

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 249

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Vs (m/s)

Vs (m/s) 0

200

400

600

800

1000

0

0

200

400

600

800

1000

0 B30 C30-1 C30-2 D30

5

B50 C50 D50-1 D50-2

10

Depth (m)

Depth (m)

10 15

20

30

20

40

25

50

30

Vs (m/s) 0

200

400

600

Vs (m/s) 800

1000

0

400

600

0

0 B100 C100 D100-1 D100-2

20

40

60

800

1000

B150 C150-1 C150-2 D150

30

Depth (m)

Depth (m)

200

60

90

80

120

100

150

1

25

0.8

20

0.6 0.4 0.2 0 0.0001

Damping (%)

G/Gmax

Fig. 3. Selected site profiles.

20.5 kPa 61.4 kPa 122.9 kPa 204.8 kPa 0.001

0.01

0.1

1

Shear strain, Ȗ (%)

15 10

20.5 kPa 61.4 kPa 122.9 kPa 204.8 kPa

5 0 0.0001

0.001

0.01

0.1

1

Shear strain, Ȗ (%)

Fig. 4. Example of nonlinear curves for site profile C30-1.

4. 1D site response analysis

motions. All recorded ground acceleration time histories were provided by the Pacific Earthquake Engineering Research Center Strong Motion Database. For each ground motion, the PGA input was scaled from 0.1 g to 1.5 g, while PGV input was scaled from 0.1 m/s to 1.0 m/s to evaluate the influence of increment of seismic intensity.

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,

250

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Displacement (m)

Displacement (m) 0.02 0.04 0.06 0.08 0.1

0

Depth (m)

5

10 15 20 25

B30 30

0

CapeTown ChiChi Coyote Duzce ImperialValley ElCentro Hector Kobe Kocaeli Landers LomaGilroy LomaGilroy2 MammothLake Nahanni Northridge Northridge2 Parkfield SanFernando Tabas WhittierNarrows

0.4

0.4

20

30

D50-2 50

CapeTown ChiChi Coyote Duzce ImperialValley ElCentro Hector Kobe Kocaeli Landers LomaGilroy LomaGilroy2 MammothLake Nahanni Northridge Northridge2 Parkfield SanFernando Tabas WhittierNarrows

Displacement (m) 0.6

0

20

Depth (m)

0.3

40

40

60

80 D100-1 100

0

CapeTown ChiChi Coyote Duzce ImperialValley ElCentro Hector Kobe Kocaeli Landers LomaGilroy LomaGilroy2 MammothLake Nahanni Northridge Northridge2 Parkfield SanFernando Tabas WhittierNarrows

0.07

0.14

0.21

0

30

Depth (m)

0.2

0.2

10

Displacement (m) 0

0.1

0

Depth (m)

0

60

90

120 B150 150

CapeTown ChiChi Coyote Duzce ImperialValley ElCentro Hector Kobe Kocaeli Landers LomaGilroy LomaGilroy2 MammothLake Nahanni Northridge Northridge2 Parkfield SanFernando Tabas WhittierNarrows

Fig. 5. Peak horizontal displacements profiles at selected sites.

(a)

1000

400 C

C

C 6000

B

C 6000

(b)

B

1000

D D

400 C

C 6000

A

1000

1000

A D D

B

A

B

400 C

C 6000

B

1000 C

1000

1000

A B

D D

1000

A

1000

1000

B

A

1000

C 6000

B

A

1000

B

1000

1000

1000 C

500

A B

1000

B

A

1000

A B

A

1000

A

500 6000

H

14000

7000

Ground surface

C 6000

(c)

Fig. 6. Cross sections of cut-and-cover tunnels: (a) single box; (b) double box, (c) triple box.

was set to 18 KN/m3. The over-consolidation ratio (OCR) was assumed to be 1.0, the horizontal at-rest earth pressure factor (K0) was set to 0.5, plasticity index (PI) was set to zero (0), and the number of cycles of loading (N) and the excitation frequency (f) were defined as 10 and 1.0, respectively. For all profiles, the shear wave velocity of the bedrock was set to 1,500 m/s and was assumed to underlie the bottom of respective soil profiles. The input motions were imposed as rock outcrop motions.

for instance, profiles C30-1 and C30-2 belong to site class C with H = 30 m. The seismically induced horizontal displacements were calculated by the 1D equivalent linear site response analysis using DEEPSOIL v6.0 (Hashash et al., 2015). The shear modulus ratio G/Gmax and damping ratio D curves of Darendeli (2001) were used, as illustrated in Fig. 4. The sand soil type was assumed for all site profiles. The density of soil 251

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Fig. 7. Material model of concrete (a) and reinforcing bar (b) (Lee et al., 2016b).

3

C

1260

Racking ratio, R

Moment (KNm)

1300

1220 1180 1140 1100

0

16

32

48

64

2 This study Wang (1993) Penzien (2000), v=0.3 Penzien (2000), v=0.4 Anderson et al (2008)

1

0

Number of elements per frame member

0

3

6

9

12

15

Flexibility ratio, F

Fig. 8. Convergence test example with respect to the bending moment of the single box tunnel at location C (Lee et al., 2016b).

Fig. 10. R-F relation between the simplified model and existing results (Nguyen et al., 2019).

Ground surface Soil weight Shear force

Geostatic pressure

K K

K K

SS

H

V

Soil deformation

Shear force

SB

Bedrock

Fig. 9. Boundary conditions and loads to the box tunnel. Fig. 11. Bending moment of box tunnels (site profile: C50, input motion: Hector mine PGA = 0.3 g).

The peak horizontal displacements of site profiles due to ground motions were the maximum envelope displacements, as shown in Fig. 5. It should be noted that this approach is a conservative estimation.

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 (CSI, 2011). The cross-sectional dimensions of the box tunnels are shown in Fig. 6. The overburden depth of the tunnel and its ratio to the burial depth were fixed to 7.0 m and 1.2, respectively. Considering the narrow range of burial depth ratios for cut-and-

5. 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 252

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cross sections, as shown in Fig. 7. The nominal compressive strength and the elastic modulus of concrete are 27.5 MPa and 24.8 GPa, respectively. Meanwhile, the yield strength and the elastic modulus of reinforcement are 413 MPa and 200 GPa, respectively. The details of structural dimensions and modeling procedure of the tunnels are presented in Lee et al. (2016b). The flexibility ratio (F), which is defined as the relative stiffness of the soil and the tunnel, was calculated for the tunnels used in this study. F values of single, double, and triple box tunnels were calculated as ranged 0.16–2.62, 0.4–6.44, and 0.53–8.43, respectively. The stiffness of the tunnel was shown to decrease with an increase in the number of bays. Various sizes and shapes of tunnels were not considered because they were shown to have secondary influences on the seismic response (Nguyen et al., 2019). The mesh convergence analysis was performed to determine the number of elements. Fig. 8 shows an example of the converged bending moment in case of single box tunnel. Therefore, 64 elements per structural frame member were used for all analyses (Lee et al., 2016b). The boundary conditions, applied forces, and imposed soil displacements are depicted in Fig. 9. The pseudo-static analysis procedure in Iai (2005) was adopted in this study. The geostatic loads were firstly

Table 2 Definition of damage states and corresponding damage indices (DIs). Tunnel type

Damage state

Damage index (DI, M/ My) (Lee et al., 2016b)

Damage index (DI, M/ MRd) (Pitilakis, 2011)

Single box

None Minor/Slight Moderate Extensive None Minor/Slight Moderate Extensive

DI < 1.0 1.0 ≤ DI < 1.2 ≤ DI < 2.0 ≤ DI DI < 1.0 1.0 ≤ DI < 1.2 ≤ DI < 2.0 < DI

DI < 1.0 1.0 < DI ≤ 1.5 1.5 < DI ≤ 2.5 2.5 < DI < 3.5 N.A. N.A. N.A. N.A.

Double box Triple box

1.2 2.0

1.2 2.0

cover tunnels, the burial depth is expected to have a marginal influence on the damage pattern. However, a future study is warranted for quantification of the influence of the burial depth ratio. The structural members of tunnels (i.e. ceiling slab, wall, bottom slab, inner column) were modeled using frame elements. The optimal size of the member element was determined from a mesh convergence test. Nonlinear material models were applied for both concrete and reinforcing bar of the tunnel linings to evaluate the yielding moment of the structural 12

10

B30

10

y = 0.241e4.6624x

Damage Index

Damage Index

12

D30

8 6 4

8

y = 0.0328e2.8564x

6 4

2

2

0

0 0

0.2

0.4 0.6 PGA (g)

0.8

0

1

0.3

0.6

0.9 PGA (g)

1.2

1.5

1.8

(a) DI versus PGA 12

10 8

B30

10

y = 0.3154e4.1193x

Damage Index

Damage Index

12

D30

6 4

8

y = 0.1291e3.4353x

6

4 2

2

0

0 0

0.2

0.4 0.6 PGV (m/s)

0.8

0

1

0.2

0.4

0.6 PGV (m/s)

0.8

1

(b) DI versus PGV 12

10

y = 0.3154e535.51x

8

B30

10

Damage Index

Damage Index

12

D30

6 4 2

8 6

y = 0.1291e1374.1x

4 2

0

0 0

0.002

0.004 PGV/Vs30

0.006

0.008

0

0.0005 0.001 0.0015 0.002 0.0025 0.003 PGV/Vs30

(c) DI versus PGV/Vs30 Fig. 12. DI versus intensity measures for single box in H = 30 m profiles. 253

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12

10

B30

10

y = 0.3376e4.2325x

Damage Index

Damage Index

12

D30

8 6 4

8

y = 0.0934e2.3576x

6 4 2

2

0

0 0

0.2

0.4 0.6 PGA (g)

0.8

0

1

0.3

0.6

0.9 1.2 PGA (g)

1.5

1.8

(a) DI versus PGA 12

10

B30

10

y = 0.4354e4.3973x

Damage Index

Damage Index

12

D30

8 6 4

8

y = 0.2201e3.5264x

6

4 2

2

0

0 0

0.2

0.4 0.6 PGV (m/s)

0.8

0

1

0.2

0.4

0.6 PGV (m/s)

0.8

1

(b) DI versus PGV 12

10

y = 0.4354e571.65x

8

B30

10

Damage Index

Damage Index

12

D30

6 4

y = 0.2201e1410.5x

8 6 4

2

2

0

0 0

0.002

0.004 PGV/Vs30

0.006

0.008

0

0.0005 0.001 0.0015 0.002 0.0025 0.003 PGV/Vs30

(c) DI versus PGV/Vs30 Fig. 13. DI versus intensity measures for double box in H = 30 m profiles.

applied to the normal springs. Thereafter, the seismically induced soil displacements were imposed to the normal springs. Additionally, the shear stress, calculated as the product of the free field shear strain (γ) and the corresponding shear modulus of soil (G), was applied directly to the tunnel frame elements as described in detail in Lee et al., 2016b. To simulate the soil-tunnel interaction, a series of soil springs in the normal and the shear directions were attached to the nodes of the frame elements. The spring constants were calculated according to the seismic design code for the metropolitan subway of Korea (MLTM, 2009). The horizontal (KH) and vertical (KV) normal spring constants were defined as

h −3/4 KH = kh0 ⎛ ⎞ ⎝ 30 ⎠

(3)

b −3/4 KV = kh0 ⎛ ⎞ 30 ⎝ ⎠

(4)

K SS =

1 KH 4

(5)

K SB =

1 KV 4

(6)

In this study, the nonlinearity of soil is accounted for by calculating ED not from Vs, but from the equivalent linear shear modulus calculated from the respective site response analysis. The simplified soil spring model used in this study does not simulate the complex dynamic soil-structure interaction including slippage or gapping phenomena at the soil-tunnel interfaces or soil yielding around the tunnel. Nonlinear dynamic analysis is well recognized to provide most reliable estimate of the seismic tunnel response (Abuhajar et al., 2015; Cilingir and Madabhushi, 2011; Tsinidis, 2017; Tsinidis et al., 2016a, 2016b), but several studies reported that the difference between dynamic and pseudo-static analyses is not significant (e.g. Hashash et al., 2010a; Argyroudis and Pitilakis, 2012). Therefore, it was assumed that the pseudo-static analysis provides acceptable estimates for an engineering design and the accuracy of the pseudo-static approach was solely verified by comparison with pseudo-static analytical and numerical solutions. Fig. 10 shows the racking ratio (R) plotted against

( ) 1

where kh0 = 30 ED , h and b are the height and the width of the tunnel, respectively, ED is the elastic modulus of the surrounding soil. The shear springs for vertical (KSS) and horizontal (KSB) frames were defined as 254

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12

10

B30

10

y = 0.5029e3.7486x

Damage Index

Damage Index

12

D30

8 6 4

8

y = 0.1205e2.3267x

6 4 2

2

0

0 0

0.2

0.4 0.6 PGA (g)

0.8

0

1

0.3

0.6

0.9 PGA (g)

1.2

1.5

1.8

(a) DI versus PGA 12

B30

10

Damage Index

10

Damage Index

12

D30

8 6

y = 0.5135e4.5153x

4

y = 0.2938e3.6103x

8 6

4 2

2

0

0 0

0.2

0.4 0.6 PGV (m/s)

0.8

0

1

0.2

0.4

0.6 PGV (m/s)

0.8

1

(b) DI versus PGV 12

12

D30

B30

10

Damage Index

Damage Index

10 8

y = 0.5135e586.99x

6 4 2

y = 0.2938e1444.1x

8 6 4 2

0

0 0

0.002

0.004 PGV/Vs30

0.006

0.008

0

0.0005 0.001 0.0015 0.002 0.0025 0.003 PGV/Vs30

(c) DI versus PGV/Vs30 Fig. 14. DI versus intensity measures for triple box in H = 30 m profiles.

D30

2

y = 4.1193x - 1.1538

2 Extensive

1

Moderate Minor

0 0

0.2

0.4

0.6

0.8

-1

1

Damage Index (lnDI)

Damage Index (lnDI)

3

-2

B30 Extensive

1

Moderate

Minor

0 0

0.2

0.4

0.6

0.8

1

-1 -2

y = 3.4353x - 2.0471

-3

PGV (m/s)

PGV (m/s)

Fig. 15. Regression of damage index (ln(DI)) and IMs, and estimation of median values for damage states.

(Wang, 1993; Anderson, 2008).

the F calculated from the frame model (Nguyen et al., 2019), where R represents the ratio of the structural deformation to the free-field soil displacement. Fig. 10 reveals that R increases proportionally with an increase in F, showing that the tunnel response is larger for flexible structures. It is demonstrated that the beam-spring model fits agreeably with the analytical solution (Penzien, 2000) and numerical results

6. 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 bottom255

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1.0

Minor

0.8 0.6

Probability of damage

Probability of damage

1.0

Site class B

Site class D Site class C

0.4

individual average

0.2 0.0

Moderate

0.8

Site class D

0.6

Site class C

0.4

Site class B

0.2 0.0

0

0.3

0.6

0.9

1.2

1.5

0

0.3

0.6

0.9 PGA (g)

PGA (g)

1.2

1.5

Probability of damage

1.0

Extensive

0.8

Individual: Site class B

Site class D

0.6

Site class C

0.4 0.2

Site class B

Average: Site class B

Site class C

Site class C

Site class D

Site class D

0.0 0

0.3

0.6

0.9 PGA (g)

1.2

1.5

1.0

1.0

Minor

0.8

Site D

0.6

Probability of damage

Probability of damage

Fig. 16. Fragility curves in terms of PGA of the single tunnel.

Site C

0.4

Site B individual average

0.2 0.0 0

0.2

0.4

0.6

0.8

1

Moderate

0.8

Site D

0.6 0.4

Site B

0.2 0.0 0

0.2

0.4

PGV (m/s) Probability of damage

Site C

0.6 PGV (m/s)

0.8

1

1.0

Extensive

0.8 0.6

Site D

0.4

Individual: Site class B

Site C Site B

0.2

Average: Site class B

Site class C

Site class C

Site class D

Site class D

0.0 0

0.2

0.4

0.6 PGV (m/s)

0.8

1

Fig. 17. Fragility curves in terms of PGV the single tunnel.

was defined as the ratio of the elastic bending moment to the yield moment at the critical sections of the tunnel frames. Three damage states including minor/slight, moderate, and extensive and associated damage indices are described in Table 2. Figs. 12–14 show the relationship between DI of three box tunnels and selected ground motion intensity measures, which are PGA, PGV, and PGV/Vs30. The red1 lines represent linear regression functions for the given site profiles. It can be found that for a given ground motion intensity, DI of box tunnels is decreased from soft to stiff soils. This is attributed to the fact that the stiffer soil always yields a smaller horizontal deformation and therefore the corresponding demand of tunnels is less relative to tunnels in softer soil. Softer soil is shown to result in a

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) was imposed. The maximum bending moment of the single box is shown to be smaller than those of double and triple boxes. This is because multi-boxes have wider widths, which causes higher stresses, internal forces, and moments. As shown in Fig. 10, the tunnel response relative to the free field response increases with an increase in F. Because multi-box tunnels have higher F compared with the single box tunnel, the calculated forces and moments are larger. In this study, the authors used the damage states and damage indices (DIs) of cut-and-cover tunnels proposed by Lee et al. (2016b). DI

1 For interpretation of color in Figs. 12–14, the reader is referred to the web version of this article.

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1.0

Minor

0.8

Site B

0.6

Site C

0.4

Site D

individual average

0.2

Probability of damage

Probability of damage

1.0

Moderate

0.8

Site C

0.6

Site B

0.4

Site D

0.2 0.0

0.0 0

0.001

0.002

0.003

0.004

0.005

0

0.001

0.002

PGV/Vs30

0.003 PGV/Vs30

0.004

0.005

Probability of damage

1.0

Extensive

0.8 0.6

Individual: Site class B

Site C

Site B

0.4 Site D

0.2

Average: Site class B

Site class C

Site class C

Site class D

Site class D

0.0 0

0.001

0.002

0.003 PGV/Vs30

0.004

0.005

Fig. 18. Fragility curves in terms of PGV/Vs30 of the single tunnel.

et al., 2007; Liu et al., 2016). However, PGA is still the most frequently used intensity parameter to develop fragility curves of underground structures, including both the empirically (ALA, 2001; HAZUS, 2004) and numerically derived curves (Argyroudis and Pitilakis, 2012; Argyroudis et al., 2017; Huh et al., 2017a, 2017b; Kim et al., 2014; Lee et al., 2016a; Qiu et al., 2018; Salmon et al., 2003). In this study, we also generated fragility curves of tunnels using PGV/Vs30, which is an intensity measure to approximate the free-field shear strain. We used PGV/Vs30 because both the intensity of the ground motion and the soil stiffness is accounted for in the parameter. Fig. 18 shows fragility curves of the single box for all site profiles and the mean curves for three respective site classes. The effect of the site profile is significantly reduced when PGV/Vs30 is used, where the fragility curves for all site profiles fall within a relatively narrower band. This means that the variability of the fragility curve caused by the soil characteristics is reduced by including the soil parameter in the intensity measure. Comparisons highlight that PGV/Vs30 is a better seismic intensity parameter in developing the fragility curve of an underground structure than PGA and PGV. It should be noted that the probability of damage for a given PGV/ Vs30 is shown to be higher for stiffer site profiles, which is contrary to curves using PGA and PGV. Because PGV/Vs30 is an approximate estimate of shear strain, the seismic demand is always higher for stiffer soil if the ground deformation is identical. However, it does not mean that tunnels in stiffer soil are more vulnerable to earthquake-induced damage because stiffer soil is most likely to induce a lower PGV/Vs30 compared with softer soil when subjected to an identical level of excitation. As results in Figs. 16–18, fragility curves for different site profile depth are plotted in the thinner curves. It can be found that the effect of the profile depths on the fragility curves is noticeable. The variation of the curves in site class D is shown to be largest, followed by those in site C and D. In other words, the soft soil yields a larger scatter of fragility curves compared with stiffer soil. It is important to note that the scatter is reduced for PGV/Vs30 is used, as discussed in the previous paragraph. Additionally, Vs30 of site profiles also plays a vital role in resulting of fragility curves. Fig. 19 compares the mean fragility curves for three site classes and three types of box tunnels. For a given seismic intensity and site profile, single box tunnels are less vulnerable to damage than multi-box

higher level of scattering, highlighting that the uncertainty in the predicted damage level is higher for softer soil deposits. However, the level of scattering is demonstrated to be similar for all ground motion parameters. It also should be noted that the relationship between DI and intensity measures of the tunnels in all selected site profiles are generated, however, the authors provide herein some representative results for the sake of space. In this paper, the authors have applied the regression between the natural logarithm of DI (ln(DI)) and seismic intensity measures to calculate the median values and standard deviations due to ground motions. This method was also presented in Cornell et al. (2002), Argyroudis and Pitilakis (2012), and Qiu et al. (2018). Fig. 15 illustrates the examples of the relationship between the ln(DI) and PGV for the single box and the estimation of median values for damage states. This approach was applied to all tunnels and site profiles. 7. 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 lines represent curves calculated for respective site profiles, whereas the thick lines represent the mean curves. It can be observed that the probability of damage to the tunnel is negatively correlated with the stiffness of soil (Vs30). This is because smaller free-field shear strains and horizontal soil displacements are produced in a stiffer soil, thus the corresponding demands in the tunnel frame also decrease. Fig. 17 shows fragility curves of the single box in different site profiles with respect to PGV. Similar to the fragility curves in Fig. 16, the probability of failure of tunnels is larger for softer soil than that of stiffer soil. It is shown that the scatter of the PGV based fragility curves is less compared to the curves based on PGA, demonstrating that the curves are less sensitive to the propagated site profile when PGV is used. It is in line with the findings of previous studies that revealed that PGV is better correlated to the response of bored structures (Chen and Wei, 2013; Corigliano 257

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1.0

Minor

0.8

Probability of damage

Probability of damage

1.0

0.6 0.4 0.2

Moderate

0.8 0.6 0.4 0.2 0.0

0.0 0

0.3

0.6

0.9

1.2

0

1.5

0.3

0.6

0.9 PGA (g)

PGA (g)

1.2

1.5

Probability of damage

1.0

Extensive

0.8 0.6 0.4 0.2 0.0 0

0.3

0.6

0.9 PGA (g)

1.2

1.5

(a) 1.0

Minor

0.8

Probability of damage

Probability of damage

1.0

0.6 0.4 0.2 0.0 0

0.2

0.4

0.6

0.8

1

Moderate

0.8 0.6 0.4 0.2 0.0 0

PGV (m/s)

0.2

0.4

0.6 PGV (m/s)

0.8

1

Probability of damage

1.0

Extensive

0.8 0.6 0.4 0.2 0.0 0

0.2

0.4

0.6 PGV (m/s)

0.8

1

(b) Fig. 19. Comparison of fragility curves of different tunnels with various IMs: (a) PGA, (b) PGV, and (c) PGV/Vs30.

tunnels. This is because a larger bending moment is produced in multibox tunnels relative to single tunnels, as explained in the previous section. Consequently, the probability of damage for double and triple boxes is higher compared with the single box. Tables 3–5 present the mean and standard deviation values of fragility functions of box tunnels for different damage states with respect to PGA, PGV, and PGV/Vs30. It can be shown that the calculated standard deviations for PGV and PGV/ Vs30 are smaller than those for PGA. This is because of a larger scatter in DIs and PGA. The fragility curves developed in this study can be easily utilized for the seismic vulnerability assessment of box tunnels in the following three steps. The first step is determining Vs30 from site investigation and selecting the corresponding site class. The second step is calculating PGV at the free field surface from a site response analysis or an empirical procedure. The final step is determining the probability of exceedance of a damage state for a given type of box tunnel and PGV/Vs30

from the mean curves displayed in Fig. 19c.

8. 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/Vs30 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; HAZUS, 2004) and numerical curves of SYNER-G (Argyroudis and Kaynia, 2014) for the single box tunnel. The empirical fragility curves were developed based on the field observed data of cutand-cover tunnels. The numerical fragility curves of Argyroudis and Kaynia (2014) were proposed for a single box tunnel based on a set of 258

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1.0

Minor

0.8

Probability of damage

Probability of damage

1.0

0.6 0.4 0.2 0.0 0

0.001

0.002

0.003

0.004

0.005

Moderate

0.8 0.6 0.4 0.2 0.0 0

0.001

0.002

0.003 PGV/Vs30

PGV/Vs30

0.004

0.005

Probability of damage

1.0

Extensive

0.8 0.6 0.4 0.2 0.0 0

0.001

0.002

0.003 PGV/Vs30

0.004

0.005

(c) Single box: Site class B

Double box: Site class B

Triple box: Site class B

Site class C

Site class C

Site class C

Site class D

Site class D

Site class D

Fig. 19. (continued) Table 3 Fragility function parameters of the single box tunnel. Site profile

B

C

D

Damage state

Minor Moderate Extensive Minor Moderate Extensive Minor Moderate Extensive

PGA surface

Table 5 Fragility function parameters of the triple box tunnel.

PGV surface

PGV/Vs30

Site profile

µ (g)

β

µ (m/s)

β

µ

β

1.32 1.45 1.67 0.66 0.76 0.93 0.36 0.45 0.59

0.74 0.74 0.74 0.74 0.74 0.74 0.75 0.75 0.75

0.73 0.84 1.01 0.45 0.55 0.72 0.31 0.41 0.58

0.71 0.71 0.71 0.71 0.71 0.71 0.72 0.72 0.72

0.152% 0.176% 0.212% 0.180% 0.216% 0.283% 0.226% 0.302% 0.431%

0.71 0.71 0.71 0.71 0.71 0.71 0.72 0.72 0.72

B

C

D

B

C

D

Damage state

Minor Moderate Extensive Minor Moderate Extensive Minor Moderate Extensive

PGA surface

PGV surface

PGV/Vs30

µ (g)

β

µ (m/s)

β

µ

β

1.18 1.33 1.58 0.58 0.67 0.83 0.29 0.37 0.51

0.72 0.72 0.72 0.74 0.74 0.74 0.77 0.77 0.77

0.62 0.67 0.85 0.36 0.45 0.60 0.24 0.33 0.47

0.65 0.65 0.65 0.66 0.66 0.66 0.67 0.67 0.67

0.130% 0.151% 0.186% 0.152% 0.189% 0.248% 0.189% 0.260% 0.381%

0.65 0.65 0.65 0.66 0.66 0.66 0.67 0.67 0.67

Minor Moderate Extensive Minor Moderate Extensive Minor Moderate Extensive

PGA surface

PGV surface

PGV/Vs30

µ (g)

β

µ (m/s)

β

µ

β

1.07 1.21 1.43 0.51 0.61 0.77 0.25 0.33 0.48

0.71 0.71 0.71 0.73 0.73 0.73 0.76 0.76 0.76

0.55 0.64 0.79 0.31 0.40 0.55 0.21 0.29 0.43

0.66 0.66 0.66 0.65 0.65 0.65 0.66 0.66 0.66

0.106% 0.126% 0.160% 0.126% 0.162% 0.212% 0.151% 0.207% 0.308%

0.66 0.66 0.66 0.65 0.65 0.65 0.66 0.66 0.66

of Argyroudis and Kaynia (2014) is significantly larger at 16 × 10 m. The reinforced steel of the rectangular tunnel was not modeled in Argyroudis and Kaynia (2014), whereas it was modeled in the study of Lee et al. (2016b). The fragility curves of SYNER-G (Argyroudis and Kaynia, 2014) for site class C and D are shown to be almost identical, whereas the curves for site class B are greatly lower. This trend is different from our results, where the curves for all site classes demonstrate clear differences. For minor damage state, the probability of damage of SYNER-G (Argyroudis and Kaynia, 2014) are shown to be much higher than the calculated curves in this study. For moderate and extensive damage states, SYNERG site class C and D curves are very similar to the proposed site class C curve, and site class B curves are all in good agreement. The HAZUS and ALA curves are both similar. For minor damage state, both curves fall between proposed site class C and D curves. For moderate and extensive damage states, they are almost identical to the proposed site class C curve. The comparisons demonstrate that the proposed fragility curves are overall in good agreement with the empirical curves and also comparable with the numerical curves of SYNER-G except for the minor

Table 4 Fragility function parameters of the double box tunnel. Site profile

Damage state

assumed damage states and damage indices. The damage indices of Lee et al. (2016b), used in this study, and Argyroudis and Kaynia (2014) are compared in Table 2. The structure used in the simulations is also different. The tunnel of Lee et al. (2016b) is 7 × 7 m, whereas the tunnel

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1.0

Minor

0.8

Probability of damage

Probability of damage

1.0

0.6 0.4 0.2 0.0

Moderate

0.8 0.6 0.4 0.2 0.0

0

0.3

0.6

0.9

1.2

1.5

0

0.3

PGA (g)

0.6

0.9 PGA (g)

1.2

1.5

Probability of damage

1.0

Extensive

0.8

Empirical curves: HAZUS (2004) ALA (2001) good construction

0.6 0.4

This study: Site class B

Numerical curves: SYNER-G, Site class D

0.2

Site class C Site class D

SYNER-G, Site class C

0.0 0

0.3

0.6

0.9 PGA (g)

1.2

SYNER-G, Site class B

1.5

Fig. 20. Comparison of proposed and published fragility curves for single box tunnel. The curves of ALA (2001), HAZUS (2004), and SYNER-G (Argyroudis and Kaynia, 2014) for cut and cover tunnels are compared.

of Korea (Ministry of Science, ICT and Future Planning, NRF2015R1A2A2A01006129).

damage state. 9. Conclusions

References

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 (Vs30) classified as types B, C, and D according to EC8 were investigated. Induced displacements of soils were calculated through the 1D equivalent linear site response analyses in DEEPSOIL. Twenty acceleration time histories from worldwide earthquakes were utilized for considering uncertainties of the ground motions. Fragility curves for three types of box tunnels and three damage states were developed with respect to PGA, PGV, and PGV/Vs30. Based on the numerical results, the following conclusions are drawn.

Abuhajar, O., El Naggar, H., Newson, T., 2015. Experimental and numerical investigations of the effect of buried box culverts on earthquake excitation. Soil Dyn. Earthq. Eng. 79, 130–148. ALA, 2001. Seismic Fragility Formulations for Water Systems: Part 1-Guideline. American Society of Civil Engineers - FEMA. Anderson, D.G., 2008. Seismic Analysis and Design of Retaining Walls, Buried Structures, Slopes, and Embankments. Transportation Research Board. Andreotti, G., Carlo, G., 2014. Seismic vulnerability of deep tunnels: numerical modeling for a fully nonlinear dynamic analysis. 2ECEES (Second European Conference on Earthquake Engineering and Seismology), Istanbul, Turkey. Andreotti, G., Lai, C.G., Martinelli, M., 2013. Seismic Fragility Functions of Deep Tunnels: A New Cumulative Damage Model Based on Lumped Plasticity and Rotation Capacity. ICEGE Istanbul, Turkey. Argyroudis, S., Kaynia, A.M., 2014. Fragility functions of highway and railway infrastructure. In: Pitilakis, K., Crowley, H., Kaynia, A. (Eds.), SYNER-G: Typology Definition and Fragility Functions for Physical Elements at Seismic Risk. Springer, pp. 299–326. Argyroudis, S., Kaynia, A.M., Pitilakis, K., 2013. Development of fragility functions for geotechnical constructions: application to cantilever retaining walls. Soil Dyn. Earthq. Eng. 50, 106–116. Argyroudis, S., Pitilakis, K., 2012. Seismic fragility curves of shallow tunnels in alluvial deposits. Soil Dyn. Earthq. Eng. 35, 1–12. Argyroudis, S., Tsinidis, G., Gatti, F., Pitilakis, K., 2014. Seismic fragility curves of shallow tunnels considering SSI and aging effects. 2nd Eastern European Tunnelling Conference, Athens, Greece. Argyroudis, S., Tsinidis, G., Gatti, F., Pitilakis, K., 2017. Effects of SSI and lining corrosion on the seismic vulnerability of shallow circular tunnels. Soil Dyn. Earthq. Eng. 98, 244–256. Chen, Z., Wei, J., 2013. Correlation between ground motion parameters and lining damage indices for mountain tunnels. Nat. Hazards 65, 1683–1702. Cilingir, U., Madabhushi, S.G., 2011. A model study on the effects of input motion on the seismic behavior of tunnels. Soil Dyn. Earthq. Eng. 31, 452–462. Corigliano, M., Lai, C., Barla, G., 2007. Seismic vulnerability of rock tunnels using fragility curves. 11th ISRM Congress, Lisbon, Portugal. International Society for Rock Mechanics. Cornell, C.A., Jalayer, F., Hamburger, R.O., Foutch, D.A., 2002. Probabilistic basis for 2000 SAC federal emergency management agency steel moment frame guidelines. J. Struct. Eng. 128, 526–533. CSI, 2011. SAP2000 software, ver15. Berkeley, California, USA. Darendeli, M., 2001. Development of New Family of Normalized Modulus Reduction and Material Damping Curves. University of Texas, Austin, USA. Debiasi, E., Gajo, A., Zonta, D., 2013. On the seismic response of shallow-buried rectangular structures. Tunn. Undergr. Space Technol. 38, 99–113. Dowding, C.H., Rozan, A., 1978. Damage to rock tunnels from earthquake shaking. J. Soil Mech. Found. Div. 104, 175–191.

• The effect of site profile on the calculated fragility curve is shown to be significant and PGA based curves result has the largest scatter. • The effect of the site profile is significantly reduced when PGV/V s30

• •

is used. PGV/Vs30 is demonstrated to be the optimum seismic intensity parameter in developing the fragility curve of an underground structure. The multi-box tunnels are more vulnerable to earthquakes than the single box tunnel for a given intensity measure of an earthquake. The fragility curves proposed in this study can be readily applied for a seismic vulnerability assessment of shallow one-story box tunnels in different soil types with the site depth ≥30 m. A further study on the fragility analysis of different multi-story tunnels should be investigated to ensure completeness of fragility functions for cut-andcover box tunnels.

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 260

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