Seismic Vulnerability Assessment and Prioritization of Masonry Railway Tunnels: A Case Study

Abstract

Assessing seismic vulnerability and prioritizing railway tunnels for seismic rehabilitation are critical components of railway infrastructure management, especially in seismically active regions. This study focuses on a railway network in Northwest Iran, consisting of 103 old masonry rock tunnels. The vulnerability of these tunnels is evaluated under 12 active faults as seismic sources. Fragility curves derived from the HAZUS methodology estimate the probability of various damage states under seismic intensities, including peak ground acceleration (PGA) and peak ground displacement (PGD). The expected values of the damage states are computed as the damage index (DI) to measure the severity of damage. A normalized prioritization index (NPI) is proposed, considering seismic vulnerability and life cycle damages in tunnel prioritizing. Finally, a detailed prioritization is provided in four classes. The results indicate that 10% of the tunnels are classified as priority, 33% as second priority, 40% as third priority, and 17% as fourth priority. This prioritization is necessary when there are budget limitations and it is not possible to retrofit all tunnels simultaneously. The main contribution of this study is the development of an integrated, data-driven framework for prioritizing the seismic rehabilitation of aging masonry railway tunnels, combining fragility-based vulnerability assessment with life-cycle damage considerations in a high-risk and data-limited region. The framework outlined in this study enables decision-making organizations to efficiently prioritize the tunnels based on vulnerability, which helps to increase seismic resilience.

1. Introduction

Railway tunnels are vital transportation infrastructure components, facilitating efficient and reliable transit. However, the structural integrity of these tunnels, particularly those constructed using traditional masonry techniques, has often been compromised by seismic activities. This study investigates a railway network in Northwest Iran, which includes 103 masonry tunnels, each over 50 years old and manually constructed. The Northwest of Iran is a seismic-prone area with several powerful active faults, and there is a lack of research on the integrated vulnerability assessment of railway tunnels in this region.

Past earthquakes have consistently demonstrated the vulnerability of tunnels to various types of damage, including cracking, spalling, and collapse [1,2,3,4]. For example, in the 1995 Kobe earthquake, more than 30 tunnels sustained minor damage, and 10 tunnels needed significant repairs to ensure their safety [5]. During the 1999 Chichi earthquake in Taiwan, damage was reported in 50 tunnels, with 26 experiencing minor damage, 11 suffering moderate damage, and 13 being severely damaged [6]. In the 2008 Wenchuan earthquake with a moment magnitude of 7.8, inspections have revealed that 42 out of 52 tunnels have been damaged. Among these, 20 tunnels have experienced severe damage such as portal collapses, rock falls, and significant lining cracks, necessitating major repair [7]. The 2016 Kumamoto Earthquake in Japan, with a magnitude of 7.3, has caused various types of damage to the Tawarayama tunnel, including lining spalling and collapse, joint failures, groundwater leakage, and pavement deterioration [8]. However, there are numerous reports of tunnel damage caused by earthquakes [9,10,11,12,13], and it is vital to evaluate their seismic vulnerability and prioritize them for retrofitting, especially in old tunnels.

In recent years, there has been a growing body of research focusing on the seismic response of tunnels using a variety of experimental, numerical, and analytical approaches. Tsinidis et al. presented a comprehensive state-of-the-art review, including case studies of actual tunnel responses during earthquakes, shaking-table and centrifuge experiments, and modern numerical models, thereby highlighting current gaps and future research directions [14]. More recently, Wang et al. carried out shaking-table experiments and numerical analyses to investigate the seismic interaction mechanisms between adjacent horizontal parallel tunnels, revealing that tunnel spacing, burial depth, motion type, and soil characteristics significantly influence seismic behavior [15]. Zhao et al. developed three-dimensional numerical models to analyze the dynamic response of curved tunnels subjected to transverse SV-wave incidence, offering insights into deformation and internal force distributions under realistic conditions [16]. Complementing these studies, Lei et al. conducted shaking-table tests on overlapping tunnels simulating oblique intersecting configurations and evaluating structural responses under seismic loading. Collectively, these recent contributions underline the importance of accounting for complex tunnel geometries, soil–structure interactions, and multi-tunnel effects when assessing seismic vulnerability—strengthening the rationale for adopting an integrated prioritization framework as proposed in the present study [17]. In addition, recent studies have begun to address challenges unique to masonry structures. For instance, a study on the seismic retrofitting of a rubble masonry tunnel evaluated alternatives such as steel fiber shotcrete and inner concrete lining, offering insights into effective strengthening strategies for aging masonry tunnels. Meanwhile, post-earthquake investigations of tunnel performance during the February 2023 Kahramanmaraş earthquake sequence revealed that existing seismic risk models could be verified and refined based on real-world behavior, underscoring the need for reliable assessment frameworks, especially relevant to vulnerable or aged tunnels [18].

There are limited studies on old masonry tunnel modeling [19,20,21]. The existing technical literature is typically focused on modern reinforced concrete tunnel seismic vulnerability assessment [22,23,24,25,26]. Fragility curves serve as a main approach to represent the probability of a tunnel reaching or exceeding a specific damage state given a specific seismic intensity [27]. These curves have been developed using observational data from past earthquakes and analytical tunnel models [28]. Fragility curves provide a probabilistic assessment of tunnel performance under seismic loading and are widely used in vulnerability and risk assessment frameworks such as HAZUS [29]. Argyroudis and Pitilakis [30] proposed a numerical method for analyzing the seismic fragility of shallow tunnels located in alluvial deposits. Huang et al. [31] developed an analytical technique to create seismic fragility curves for rock tunnels by employing support vector machines (SVM), taking into account various uncertainties. Jamshidi Avanaki et al. [32] introduced a set of fragility curves for steel fiber-reinforced concrete used in segmental tunnels. Zhao et al. [33] developed fragility curves for circular tunnels by numerical modeling, taking into account factors such as the properties of the concrete, the dimensions of the tunnel lining, and the reinforcement ratio. Ansari et al. [34] assess the seismic vulnerability of circular tunnels in Jammu and Kashmir (India), utilizing fragility functions and microzonation to evaluate damage probabilities across different hazard zones.

Other methods based on finite element analysis (FEA) provide a more detailed approach by simulating the seismic response of tunnels specifically [35]. FEA divides the tunnel structure and surrounding ground into small, discrete elements governed by mathematical equations, offering insights into stress distributions, deformation, and potential failure points in tunnel structures. Several studies have applied FEA to different tunnel types, including circular and rectangular tunnels, shallow and deep tunnels, as well as tunnels in soft and rock soils, highlighting tunnel-specific behavior under seismic loading [36,37,38]. The simplified method for seismic analysis of long tunnels is a practical approach widely used by practitioners. This method generally models the tunnel as a beam supported by mass-spring systems connected to the ground, enabling analytical solutions for seismic response while significantly reducing computational effort compared to FEA [39]. Tunnel-specific applications of simplified methods have been reported in recent studies, demonstrating their effectiveness in predicting tunnel deformation and potential damage during earthquakes [40]. Recent advancements in artificial intelligence (AI) have also introduced new dimensions to seismic vulnerability assessment. Machine learning techniques, including deep learning [41], random forest [42], artificial neural networks [43,44], fuzzy seismic fragility analysis [45], and fuzzy multi-criteria decision-making analysis [46], are used to analyze large and complex datasets for predicting tunnel performance and damage.

As mentioned, the majority of the existing research has concentrated on modern tunnels constructed with reinforced concrete or advanced linings, whereas masonry tunnels—widely used in historical railway networks and still in service in many countries—have received far less attention in terms of seismic vulnerability assessment. Their age, material degradation, and construction techniques make them substantially more fragile than modern counterparts. Furthermore, unlike concrete tunnels, masonry tunnels often exhibit irregular geometries, discontinuities, and weaker interfaces, which exacerbate their susceptibility to seismic damage. This knowledge gap underlines the necessity of studies dedicated to the seismic response and prioritization of masonry tunnels, particularly within critical transportation networks, as pursued in the present research.

However, the mentioned studies have been limited to the seismic vulnerability of one tunnel, and there is no study in the literature that prioritizes tunnels of a large network for seismic retrofitting, especially old railway tunnels. This study aims to address the gaps in existing research by providing an integrated vulnerability assessment of old railway tunnels under seismic excitation and establishing a systematic prioritization framework for their retrofitting. The present study investigates the seismic vulnerability of aging railway network tunnels in northwest Iran, which is a highly seismic-prone area. In this area, there are 103 tunnels, all over 50 years old. Five major active faults and seven micro faults are seismic sources threatening the tunnels. In this study, the term “micro faults” refers to smaller-scale faults that are typically less significant than major faults but can affect seismic activity. The seismic intensities, including peak ground acceleration (PGA) and peak ground displacement (PGD) at each tunnel location, have been calculated based on the seismic scenarios of each fault. The damage index (DI) of the tunnels has been obtained using the fragility curves provided in the HAZUS [29] methodology. Then, a normalized prioritization index (NPI) has been proposed to classify the tunnels for retrofitting. NPI not only takes into account seismic damage but also evaluates damage from the tunnel’s lifecycle based on visual inspections. Finally, based on the NPI criteria, the tunnels are prioritized for seismic rehabilitation into four categories. The findings of this study can significantly improve the safety of railway infrastructure in seismic regions when there are budget limitations for rehabilitation.

The study’s remaining sections are organized as follows. Section 2 introduces the network topology of the study area and tunnel locations. Section 3 presents the topology of faults, seismicity characteristics of faults, and seismic intensity measures in the location of each tunnel. Section 4 describes the vulnerability analysis of tunnels. Section 5 develops the procedure for prioritizing tunnels, and Section 6 is the conclusion of this research.

2. Network Topology and Tunnel Location Identification

The railway network examined in this research, located in the northwest region of Iran, is marked on the Google Earth map and displayed in Figure 1. As shown in Figure 1, the railway network that is investigated in this research starts from Zanjan station and finally ends at Jolfa and Razi stations in East and West Azerbaijan provinces. Figure 2 provides a close-up view of tunnel locations and the railway line. Figure 3 provides examples of railway tunnels within the study area.

In the first step, the geographic coordinates (longitude and latitude) of the tunnels need to be extracted. These coordinates will then be used in the next steps to calculate the distance of each tunnel from the faults. The parameters of the tunnels in the network, including the number and type of tunnels, have been obtained from the Railway Organization of the Islamic Republic of Iran. The location of each tunnel has been manually extracted on the Google Earth map with high accuracy. The study area contains 83 tunnels and 20 galleries (in total 103 cases). In railways, galleries are used to prevent rocks and debris from falling onto the trains and tracks. These protective structures, often designed as semi-open tunnels or reinforced shelters, safeguard the railway infrastructure from natural hazards such as rockfalls and landslides. By providing a barrier between the mountain and the railway line, these galleries enhance safety for trains and passengers while also extending the lifespan of the railway tracks and related infrastructure.

3. Identification of Active Faults in the Region and Calculation of Intensity Measures

Earthquakes are primarily caused by the movement of faults in the Earth’s crust. Faults are fractures or zones of weakness where blocks of rock can move relative to each other. Over time, tectonic forces accumulate tension along these faults. When this stress surpasses the rock’s strength, the energy is released as seismic waves. This sudden release of energy causes the ground to shake, resulting in an earthquake. The location where the fault initially ruptures is known as the focal point, and the point on the Earth’s surface directly above it is the epicenter. Faults are categorized into three main types based on geometry and displacement: normal faults (extension of the crust), reverse faults (compression of the crust), and strike-slip faults (lateral movement).

In this research, faults are modeled by multi-segment lines on the ground surface. The main active faults that affect the tunnels have been determined based on the studies of the Seismography Center of the Geophysics Institute of Tehran University. Five active faults, including Tabriz, Maku, Ahar, Bozqush, and Takhte Solaiman, are the main faults that will affect the tunnels. Due to their significant length and potential to generate high-magnitude seismic events, the maximum ground acceleration (PGA) caused by these faults has been investigated in the vulnerability analysis of the tunnels. To consider the effects of micro-faults on the vulnerability of tunnels, the GIS layer of the fault map has been received from the Geological Organization of Iran, and seven effective micro-faults have been identified in the region. Due to their short length and limited seismic energy release, micro-faults may not generate significant ground acceleration at the regional scale. However, if these micro-faults are located in proximity to tunnels, the resulting ground displacement can pose a serious risk of structural damage [47,48]. For this reason, the maximum ground displacement (PGD) may be more important than acceleration in assessing tunnel damage influenced by micro-faults. Figure 4 shows the location of the tunnels, main faults, and micro-faults near the tunnels.

3.1. Determining Seismicity Parameters of Faults

Determining the seismicity characteristics of faults in a region is an important parameter in estimating seismic vulnerability. To analyze the seismic vulnerability, it is necessary to collect the required data from the seismic sources. Seismicity parameters of faults, such as the geometry of faults, length of faults, faulting mechanism, maximum magnitude, etc., are crucial for understanding earthquake potential hazards and vulnerability assessments.

3.1.1. Determination of Fault Length and Faulting Mechanism

Fault length and faulting mechanism are the most important influencing parameters in predicting the seismic power of faults. In this section, the length of the faults and their mechanism of faulting are extracted from the data taken from the Geological Organization of Iran and the Seismography Center of the Institute of Geophysics of Tehran University and are shown in

Table 1. The length of the faults and their faulting mechanism.

Number	Fault Name	Length (km)	Faulting Mechanism
1	Tabriz	240	Strike-Slip (right-lateral)
2	Bozqush	102	Reverse
3	Maku	100	Strike-Slip (right-lateral)
4	Takhte Solaiman (Tekab)	70	Strike-Slip (right-lateral) and Thrust
5	Ahar	65	Strike-Slip (right-lateral)
6	Chahar Sotun	32	Reverse (thrust)
7	Buket	25	Reverse (thrust)
8	Hessar Talkhuk	23	Reverse (thrust)
9	Shiramin	21	Reverse (thrust)
10	Talesh Kandi	21	Reverse (thrust)
11	Khanyordi	19	Strike-Slip (left-lateral)
12	Mahkuh	17	Reverse

.

In Table 1, the faults are classified into strike-slip and reverse types. A fault that mostly moves horizontally along the fault line with little to no vertical displacement is known as a strike-slip fault. These faults are characterized by lateral motion, which can be either right-lateral or left-lateral. When compressional forces push the hanging wall upward to the footwall, typically at angles greater than 45 degrees, a reverse fault is formed. A specific type of reverse fault with a shallow dip of less than 45 degrees is called a thrust fault. Both types result from compressional stresses and are significant in mountain regions, capable of generating powerful earthquakes due to the substantial energy released when these faults slip.

3.1.2. Determination of the Maximum Magnitude of the Fault

In this research, the maximum magnitude that the fault has the potential to create has been used to evaluate the damage of tunnels because this is the worst-case seismic scenario in network vulnerability assessment. Several relations are provided to calculate the maximum magnitude of a fault [49]. In this study, four relationships are employed to determine the maximum moment magnitude of faults ($M_{max}$) according to Equations (1) to (4). These relationships have been respectively proposed by Wells and Coppersmith [50], Nowroozi [51], Ghassemi [52], and Thingbaijam et al. [53]. The detailed formulations are presented in the following.

$$\begin{array}{cc}\mathrm{S}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{k}\mathrm{e}-\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}& M_w=1.21 Log\left(L\right)+5.16\\ \mathrm{R}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{e}& M_w=1.22 Log\left(L\right)+5\\ \mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}& M_w=1.32 Log\left(L\right)+4.86\end{array}$$

(1)

$$\begin{array}{cc}All& M_w=0.86 Log\left(L\right)+5.36\end{array}$$

(2)

$$\begin{array}{cc}\mathrm{S}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{k}\mathrm{e}-\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}& M_w=0.81 Log\left(L\right)+5.66\\ \mathrm{T}\mathrm{h}\mathrm{r}\mathrm{u}\mathrm{s}\mathrm{t}& M_w=0.97 Log\left(L\right)+5.29\end{array}$$

(3)

$$\begin{array}{cc}\mathrm{S}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{k}\mathrm{e}-\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}& M_w=1.47 Log\left(L\right)+4.32\\ \mathrm{R}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{e}& M_w=1.63 Log\left(L\right)+4.38\\ \mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}& M_w=2.06 Log\left(L\right)+3.55\end{array}$$

(4)

where (L) represents the fault length in kilometers. In this research, to reduce uncertainty, all the above 4 relationships have been used to calculate the maximum magnitude of faults, and their average is considered as the maximum possible magnitude of each fault listed in

Table 2. The maximum magnitude of each fault.

Number	Fault Name	$\mathbf{Maximum} \mathbf{Magnitude} \mathbf{of} \mathbf{Faults} \left({\mathit{M}}_{\mathit{m}\mathit{a}\mathit{x}}\right)$
1	Tabriz	7.7
2	Bozqush	7.2
3	Maku	7.2
4	Takhte Solaiman (Tekab)	7
5	Ahar	7
6	Chahar Sotun	6.7
7	Buket	6.6
8	Hessar Talkhuk	6.6
9	Shiramin	6.5
10	Talesh Kandi	6.5
11	Khanyordi	6.5
12	Mahkuh	6.4

.

3.1.3. Calculation of the Peak Ground Acceleration and Peak Ground Displacement

Attenuation relationships are employed to calculate the seismic intensity measure, including PGA and PGD. In this research, the attenuation relationship developed by Darzi et al. [54] has been used to calculate the PGA at the location of each tunnel. This attenuation relationship, developed using seismic data from Iranian earthquakes, is highly accurate in determining seismic intensity. The general form of this attenuation relationship is presented in the following Equation (5):

$${Log}_{10}\left(y\right)=f_M+f_R+f_{site}+f_{SoF}+\mathsf{\epsilon }$$

(5)

where

$$f_M=c_1+m_1{M}_w+m_2{M}_w^2$$

(5a)

$$f_R=r_1{Log}_{10}\left(\sqrt{R^2+h^2}\right)$$

(5b)

$$f_{site}=S_{II}II+S_{III}III$$

(5c)

$$f_{SoF}=f_{RV}RV+f_{SS}SS$$

(5d)

In Equation (5), y is the seismic intensity measure including PGA (cm/s²), PGV (m/s), and spectral acceleration SA (cm/s²) in different periods and $f_M$ is magnitude function, $f_R$ is distance function, $f_{site}$ is a function of soil type and $f_{SoF}$ is a function of the faulting mechanism of faults.

In Equation (5a), $M_w$ is the moment magnitude, and $c_1$, $m_1$ and $m_2$ are regression coefficients. In Equation (5b), R is the closest distance of the structure (in this study, the tunnel) from the fault, $r_1$ and h are linear regression coefficients. In Equation (5c), II = 1, III = 0 for type soil II (${375<V}_{s30}<750$) and III = 1, II = 0 for type soil III ${(375<V}_{s30})$ which $V_{s30}$ is the shear wave velocity in m/s and $S_{II}$, $S_{III}$ are regression coefficients. In Equation (5d), parameters $RV$ = 1 and SS = 0 for thrust-reverse fault and $RV$ = 0 and SS = 1 for strike-slip fault, and for other faults, both parameters are equal to zero, also $f_{RV}$ and $f_{SS}$ are regression parameters. All the regression parameters in Equations (5a) to (5b) are provided in Darzi et al. [54].

To calculate the peak ground displacement (PGD) at each tunnel’s location, the attenuation relationship developed by Alavi et al. [55] is used. This attenuation relationship is according to Equation (6):

$$\begin{gathered} Ln\left(PGD\right)\left(cm\right)=-8+M_w \\ +{\displaystyle \frac{4M_w-4Ln\left(R_{ClstD}\right)}{6+\frac{Ln\left(R_{ClstD}\right)}{-8+Ln\left(R_{ClstD}\right)+M_w^2/Ln\left(R_{ClstD}\right)}+\frac{M_{w}Ln\left(R_{ClstD}\right)\left(M_w-9\right)\left(2M_w-Ln\left(R_{ClstD}\right)\right)}{3-{Ln\left(R_{ClstD}\right)}^2-\mathit{sin}\left(\gamma \right)+V_{s30 }{M}_w\left(3M_w-15\right)}}} \end{gathered}$$

(6)

where $M_w$ is the moment magnitude, $R_{ClstD}$ is the closest distance from the structure to the fault, $V_{s30}$ is the shear wave velocity at a depth of 30 (m) of the earth and $\mathit{sin}\left(\gamma \right)$ is the function of the faulting mechanism as follows:

$$\mathit{sin}\left(\gamma \right)=\left\{\begin{array}{c}0.25 \mathrm{strike}-\mathrm{slip}\\ -1 Normal\\ 1 \mathrm{Reverse}\end{array}\right.$$

Since this attenuation relationship is based on a comprehensive database of Iranian earthquakes and provides highly accurate ground displacement estimates, other attenuation relationships are not employed in this study.

4. Tunnel Vulnerability Assessment

Historical earthquakes have demonstrated that tunnels are vulnerable to seismic events. Significant damage can occur due to ground shaking, fault rupture, or soil-structure interaction. For instance, Figure 5 illustrates examples of tunnel damage from various past earthquakes, highlighting the range and severity of impacts that seismic events can have on tunnel structures.

The PGD and PGA at the location of each tunnel have been calculated based on Equations (5) and (6) for the earthquake caused by each of the 12 faults. As an example, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 show the PGD and PGA at the location of each tunnel under the Tabriz fault and Shiramin fault earthquake, respectively.

In this research, the approach for analyzing tunnel vulnerability is based on fragility curves. The fragility curve shows the probability of exceeding a damage state (DS) for various levels of seismic intensity. The fragility curve is usually expressed based on the lognormal distribution according to Equation (7):

$$P_{DS\ge {DS}_k|IM}=\mathsf{\Phi }\left({\displaystyle \frac{\mathit{ln}\left(IM\right)-\mathit{ln}\left({\mathsf{\Theta }}_k\right)}{{\beta }_k}}\right)$$

(7)

where $P_{DS\ge {DS}_k|IM}$ is the probability of exceeding the k-th damage state, Φ is the cumulative standard normal probability function, IM is the seismic intensity measure including PGA and PGD, ${\mathsf{\Theta }}_k$ and ${\beta }_k$ are the median and standard deviation of the k-th damage state. Considering that the tunnels in the study network are rock-type, the fragility parameters of these tunnels should be extracted from the technical instructions. An identical fragility curve, which is derived from the HAZUS [29] and SYNER-G [56] methodologies, is used to analyze the vulnerability of all tunnels. Generating a specific fragility curve for each tunnel using analytical methods, such as incremental dynamic analysis (IDA), would be more beneficial. This process requires rock mechanics tests to determine the properties of the tunnel lining, such as compressive strength, modulus of elasticity, and other required parameters. However, due to the large number of old masonry tunnels (103 in total) and the limited availability of geotechnical data, tunnel-specific fragility development is out of the scope of this study.

In the HAZUS technical guide, rock railway tunnels are divided into two general categories: Bored/Drilled for tunnels and Cut/Cover for galleries, which are indicated by the abbreviations HTU1 and HTU2, respectively.

Table 3. Damage states of railway rock tunnels [29].

Damage State	Damage Description
None Damage (k = 0)	---
Slight/Minor (k = 1)	Minor cracking of the tunnel liner (damage requires no more than cosmetic repair) and some rock falling, or slight settlement of the ground at a tunnel portal
Moderate (k = 2)	Moderate cracking of the tunnel liner and rock falling
Extensive/Complete (k = 3)	Major ground settlement at a tunnel portal and extensive cracking of the tunnel liner/Major cracking of the tunnel liner, which may include possible collapse

shows the damage states defined in HAZUS for rock tunnels. Also,

Table 4. PGD fragility parameters for rock railway tunnels [29].

Classification	Damage State	Θ	β
Bored/Drilled (HTU1) & Cut/Cover (HTU2)	Slight/Minor	6.0	0.7
	Moderate	12.0	0.5
	Extensive/Complete	60.0	0.5

shows the values of PGD fragility parameters, including median and standard deviation for rock railway tunnels, provided by HAZUS.

The European collaborative research project SYNER-G has provided PGA fragility parameters for rock railway tunnels. For PGA, SYNER-G is employed because it defines fragility for three damage states (slight, moderate, and extensive), whereas HAZUS provides only two (slight and moderate). This combined approach allows a more realistic evaluation of both displacement- and acceleration-induced vulnerabilities of rock tunnels. In addition, SYNER-G accounts for tunnel condition over its life cycle damage, considering both poor-to-average and good conditions. The damage states described in SYNER-G are similar to those presented in Table 3.

Table 5. Fragility parameters for damage caused by PGA in railway rock tunnels [56].

Typology	Damage State	Θ (g)	β
Rock tunnels with poor-to-average conditions	Slight/Minor	0.35	0.4
	Moderate	0.55	0.4
	Extensive/Complete	1.1	0.5
Rock tunnels with good conditions	Slight/Minor	0.61	0.4
	Moderate	0.82	0.4
	Extensive/Complete	NA *	-
Alluvial (Soil) and Cut and Cover Tunnels with poor to average conditions	Slight/Minor	0.3	0.4
	Moderate	0.45	0.4
	Extensive/Complete	0.95	0.5
Alluvial (Soil) and Cut and Cover Tunnels with good conditions	Slight/Minor	0.5	0.4
	Moderate	0.7	0.4
	Extensive/Complete	NA *	-

* Not Available.

lists these parameters, including the standard deviation and median of the log-normal distribution, for rock railway tunnels. Given that the tunnels under study have a long lifespan (over 50 years), the SYNER-G fragility curves in poor condition have been used for the PGA parameter. Figure 12, Figure 13 and Figure 14 show two cases of fragility curves of tunnels and galleries for PGA and PGD parameters.

Damage Index and Vulnerability Curve

The probability that a tunnel will be in the k-th damage state ($P_{{DS}_k}$) is calculated based on the exceedance probability of the damage state obtained from Equation (7). Damage state probability is computed in accordance with Equation (8), and Figure 15 shows the concept of damage state probability for a specific seismic intensity.

$$P_{{DS}_0|IM}=1-P_{DS\ge {DS}_1|IM}$$

$$P_{{DS}_k|IM}=P_{DS\ge {DS}_k|IM}-P_{DS\ge {DS}_{k+1}|IM} , k=1, 2$$

(8)

$$P_{{DS}_3|IM}=P_{DS\ge {DS}_3|IM}$$

By mapping the damage states in the interval [0, 3], the expected values of the damage state are calculated as the damage index according to the following equation [25,57,58]:

$$DI= \sum _{k=0}^{3}k\ast P_{{Ds}_k|IM}$$

(9)

Table 6. Relationship between DS and DI.

PGD and PGA
Damage State	Damage Index
Slight/Minor	$0<DI<1$
Moderate	$1<DI<2$
Extensive/Complete	$2<DI<3$

shows the relation between the damage state (DS) and the damage index (DI). By calculating the DI for various values of seismic intensity, a diagram called the vulnerability curve is obtained, which is shown in Figure 16 and Figure 17.

The damage index at the location of each tunnel caused by 12 faults is calculated separately for the seismic intensity measure parameters, i.e., PGD and PGA. As an example, Figure 18 and Figure 19 show the damage index of tunnels for the earthquake resulting from the Tabriz fault. Also, Figure 20 and Figure 21 illustrate the damage index of tunnels under the Shiramin fault earthquake. As shown in Figure 18, Figure 19, Figure 20 and Figure 21, the Tabriz fault is large and affects almost all the tunnels in the region, while the Shiramin fault is small and affects only seven tunnels near it. According to Figure 18 and Figure 20, the damage index of tunnels is generally less than one (i.e., 0 < DI < 1), indicating that with high probability they do not sustain severe damage under PGD and their performance will be preserved. However, due to the uncertainties associated with fragility parameters and seismic input, this result should be considered as an expected result rather than an absolute outcome. Figure 19 and Figure 21 show that PGA is the most important parameter in the vulnerability of tunnels, and the probability of severe damage under the PGA is very high in some tunnels. Therefore, the vulnerability of tunnels under PGA must be evaluated, and the tunnels with the higher probability of damage should be given higher priority for seismic rehabilitation.

5. Tunnels Prioritization

Due to budget limitations, it is not possible to rehabilitate all tunnels simultaneously. It is assumed that all tunnels have equal importance in terms of transportation, and prioritization is only based on their vulnerability, so that the tunnels with high vulnerability are given high priority for rehabilitation. An axis in the network may be more important in terms of transportation. Determining the network’s importance weighting requires transportation data, such as the number of travels, and expert opinions, which necessitate further research. To prioritize tunnels, Equation (10) is proposed, which considers life cycle damages in addition to seismic vulnerability.

$${\left(\mathrm{N}\mathrm{P}\mathrm{I}\right)}_i=100\times {\displaystyle \frac{{(Seismic Vulnerability Index)}_i+{(Visual Inspection Weight)}_i}{({Seismic Vulnerability Index)}_{max}+{(Visual Inspection Weight)}_{max}}}$$

(10)

where ${\left(\mathrm{N}\mathrm{P}\mathrm{I}\right)}_i$ is the normalized prioritization index for the i-th tunnel, and the seismic vulnerability index (SVI) is the sum of the tunnel damage index caused by all faults, according to Equation (11):

$${(Seismic Vulnerability Index)}_i=\sum _{j=1}^N{\left(DI\right)}_{ij}$$

(11)

where j denotes the fault counter and N represents the total number of faults (in this study, N = 12), and ${\left(DI\right)}_{ij}$ is determined according to Equation (9). Some tunnels have been damaged and cracked over time, so the impact of these damages is taken into account in terms of visual inspection weight (VIW) in Equation (10). Based on the visual inspection of the tunnels, the damages are categorized into three levels: high, medium, and low as defined in

Table 7. Tunnel lifetime damages categorization.

Damage Level	Damage Description
High	Forming large gaps in the expansion joints, Significant ground settlement in the tunnel portal, High instability of the trench at the entrance-exit of the tunnel, Major horizontal cracks in the roof and sidewall of the tunnel, severe breakage and detachment of the lining, and water seepage from the crack, Falling rock cover of the tunnel
Medium	Minor vertical crack in the sidewall, Protrusion of the rock lining, defects of the drainage system, cracking of the tunnel portal and head-wall
Low	Slight cracks in the lining, Slight water leakage from the cover and floor, laxity of the rock lining

, according to engineering judgment. Figure 22 shows examples of tunnel lifetime damages in the study area. To quantify the damage, each damage level listed in Table 7 is given a corresponding weight as outlined in

Table 8. Damage level weighing.

Damage level	Non	Low	Medium	High
Visual Inspection Weight (VIW)	0	1	2	3

. In Equation (10), $({Seismic Vulnerability Index)}_{max}$ is the maximum value of the damage index summation, which is equal to 14.127 for the tunnel $i=16$ and ${(Visual Inspection Weight)}_{max}$ is the maximum weight obtained from visual inspection, which is equal to 3 (i.e., Equation (10) is normalized to 17.127). The prioritization criteria for classifying tunnels are defined based on the opinions of transportation managers, as shown in

Table 9. Tunnel prioritization criteria based on NPI.

NPI	<60	60–70	70–80	80–100
Prioritization	Fourth Priority	Third Priority	Second Priority	First Priority

.

Finally, the tunnels are prioritized into four classes, which are shown in

Table 10. Prioritization of tunnels.

Prioritization		Tunnel ID	Location		SVI	VIW	NPI
Main Class	Sub Class		Longitude	Latitude
First Priority	1-1	27G *	$47.3888725$°	$37.33695$°	14.008	2	93.46
	1-2	33	$47.2862134$°	$37.3399329$°	12.067	3	87.97
	1-3	79	$44.7109415$°	$38.4767273$°	11.448	3	86.36
	1-4	92	$44.6659554$°	$38.4556661$°	11.224	3	83.05
	1-5	16G	$47.5229574$°	$37.3712808$°	14.127 **	0	82.48
	1-6	15G	$47.5284559$°	$37.3745134$°	14.117	0	82.42
	1-7	20G	$47.455641$°	$37.3580349$°	14.110	0	82.38
	1-8	97	$44.6428761$°	$38.4640936$°	11.085	3	82.23
	1-9	26G	$47.3909989$°	$37.3383236$°	14.012	0	81.81
	1-10	9G	$47.6177549$°	$37.4046646$°	13.858	0	80.91
Second Priority	2-1	46G	$46.925463$°	$37.3450689$°	10.522	3	78.95
	2-2	36	$47.2540745$°	$37.3573404$°	13.519	0	78.92
	2-3	78	$44.7087854$°	$38.4890092$°	11.414	2	78.32
	2-4	103	$44.5288089$°	$38.4581489$°	10.326	3	77.80
	2-5	72G	$44.7760481$°	$38.4747849$°	11.885	1	75.23
	2-6	3	$47.8121811$°	$37.3500978$°	10.731	2	74.33
	2-7	69	$44.7934602$°	$38.4728638$°	11.717	1	74.25
	2-8	70	$44.7871955$°	$38.4743938$°	11.702	1	74.16
	2-9	74	$44.7502806$°	$38.4781241$°	11.598	1	73.57
	2-10	17	$47.5125891$°	$37.3664136$°	12.55	0	73.30
	2-11	1	$47.8230224$°	$37.3349528$°	10.547	2	73.26
	2-12	18	$47.4747827$°	$37.359906$°	12.534	0	73.18
	2-13	19	$47.4575947$°	$37.3578464$°	12.513	0	73.06
	2-14	21	$47.4489004$°	$37.3579147$°	12.495	0	72.95
	2-15	22	$47.4385313$°	$37.3540995$°	12.488	0	72.91
	2-16	14	$47.570567$°	$37.3882992$°	12.473	0	72.83
	2-17	23	$47.4213621$°	$37.3474904$°	12.469	0	72.80
	2-18	81	$44.7122991$°	$38.4669846$°	11.466	1	72.78
	2-19	24	$47.4131818$°	$37.3454633$°	12.453	0	72.71
	2-20	25	$47.3687134$°	$37.3334281$°	12.436	0	72.61
	2-21	13	$47.5843369$°	$37.3962094$°	12.409	0	72.45
	2-22	28	$47.3880809$°	$37.3324979$°	12.406	0	72.43
	2-23	29	$47.3687134$°	$37.3334281$°	12.343	0	72.07
	2-24	12	$47.5843369$°	$37.3962094$°	12.336	0	72.02
	2-25	11	$47.6007783$°	$37.4020909$°	12.311	0	71.88
	2-26	10	$47.6127676$°	$37.4045944$°	12.284	0	71.72
	2-27	8	$47.6231588$°	$37.404382$°	12.251	0	71.53
	2-28	67	$44.8184487$°	$38.3393055$°	11.228	1	71.39
	2-29	7	$47.6354766$°	$37.4022436$°	12.216	0	71.32
	2-30	30	$47.3259049$°	$37.3262241$°	12.201	0	71.24
	2-31	93	$44.6576581$°	$38.4584875$°	11.175	1	71.09
	2-32	31	$47.3038634$°	$37.3308712$°	12.125	0	70.79
	2-33	32	$47.2932418$°	$37.3379031$°	12.090	0	70.59
	2-34	34	$47.2777637$°	$37.3423696$°	12.037	0	70.28
Third Priority	3-1	35	$47.2627236$°	$37.3528734$°	11.972	0	69.90
	3-2	37	$47.2471531$°	$37.3607276$°	11.894	0	69.44
	3-3	38	$47.2440027$°	$37.3645507$°	11.872	0	69.32
	3-4	39	$47.230884$°	$37.3707979$°	11.793	0	68.86
	3-5	68	$44.7933504$°	$38.4663065$°	11.732	0	68.50
	3-6	101	$44.5882652$°	$38.4707001$°	10.731	1	68.49
	3-7	40	$47.216297$°	$37.3715659$°	11.710	0	68.37
	3-8	71	$44.7839813$°	$38.4750096$°	11.694	0	68.28
	3-9	73	$44.7585971$°	$38.4787578$°	11.622	0	68.86
	3-10	75	$44.742485$°	$38.4730574$°	11.581	0	67.62
	3-11	41	$47.1929316$°	$37.3756389$°	11.555	0	67.46
	3-12	76	$44.7218687$°	$38.4772168$°	11.494	0	67.11
Third Priority	3-13	82	$44.7137614$°	$38.4615824$°	11.477	0	67.01
	3-14	83	$44.7114959$°	$38.4584653$°	11.467	0	66.95
	3-15	80	$44.712759$°	$38.4756436$°	11.458	0	66.90
	3-16	77	$44.7145862$°	$38.4817574$°	11.456	0	66.88
	3-17	84	$44.7074516$°	$38.454875$°	11.447	0	66.83
	3-18	42	$47.1736966$°	$37.3749494$°	11.422	0	66.69
	3-19	85	$44.6935974$°	$38.4470138$°	11.373	0	66.40
	3-20	43	$47.1655401$°	$37.3752478$°	11.362	0	66.34
	3-21	86	$44.6887589$°	$38.4472039$°	11.346	0	66.25
	3-22	87	$44.6869354$°	$38.4473107$°	11.337	0	66.19
	3-23	50G	$46.7311721$°	$37.2957757$°	8.327	3	66.13
	3-24	88	$44.6833984$°	$38.4484213$°	11.318	0	66.08
	3-25	89	$44.6809867$°	$38.4495845$°	11.306	0	66.01
	3-26	90	$44.6773082$°	$38.4514458$°	11.287	0	65.90
	3-27	91	$44.6727701$°	$38.4531041$°	11.262	0	65.76
	3-28	6	$47.7756459$°	$37.3953886$°	11.166	0	65.20
	3-29	94	$44.6547987$°	$38.4598328$°	11.159	0	65.15
	3-30	95	$44.6528074$°	$38.4608566$°	11.146	0	65.08
	3-31	44	$47.1336416$°	$37.3776746$°	11.101	0	64.82
	3-32	96	$44.6453734$°	$38.4626368$°	11.085	0	64.72
	3-33	98	$44.6371453$°	$38.4653644$°	11.048	0	64.51
	3-34	99	$44.6307438$°	$38.4652606$°	11.006	0	64.26
	3-35	5	$47.7925656$°	$37.3771549$°	10.988	0	64.20
	3-36	100	$44.620597$°	$38.4688926$°	10.937	0	63.86
	3-37	65	$45.8272093$°	$37.702687$°	8.754	2	62.74
	3-38	4	$47.8135096$°	$37.3601098$°	10.736	0	62.68
	3-39	2	$47.8198049$°	$37.3458431$°	10.625	0	62.04
	3-40	55G	$46.6101971$°	$37.2829517$°	7.368	3	60.54
	3-41	102	$44.5339999$°	$38.4564628$°	10.358	0	60.48
Fourth Priority	4-1	54G	$46.7162409$°	$37.3073254$°	8.237	2	59.77
	4-2	64	$45.8012469$°	$37.5968033$°	8.168	2	59.37
	4-3	63	$45.7943015$°	$37.5915815$°	8.097	2	58.96
	4-4	57G	$46.5419076$°	$37.2948915$°	7.083	3	58.87
	4-5	59	$45.8233305$°	$37.5333576$°	7.945	2	58.05
	4-6	60	$45.8090345$°	$37.5431999$°	7.914	2	57.89
	4-7	61	$45.8067872$°	$37.5453676$°	7.891	2	57.75
	4-8	62	$45.7969424$°	$37.5562349$°	7.862	2	57.58
	4-9	45	$47.0175084$°	$37.3825017$°	9.823	0	57.35
	4-10	49G	$46.7708927$°	$37.3224207$°	8.781	1	57.11
	4-11	51G	$46.7270463$°	$37.2969702$°	8.295	1	54.27
	4-12	52G	$46.7255171$°	$37.2968576$°	8.281	1	54.19
	4-13	47G	$46.8126698$°	$37.3218622$°	9.200	0	53.72
	4-14	48G	$46.8041758$	$37.3222357$°	9.113	0	53.21
	4-15	56G	$46.5778717$°	$37.2882203$°	7.214	1	47.96
	4-16	53G	$46.7147613$°	$37.2988823$°	8.195	0	47.85
	4-17	58	$46.5119735$°	$37.3028089$°	5.184	1	36.11
	4-18	66	$45.6120502$°	$38.8015829$°	4.781	0	27.91

* G denotes gallery, ** Maximum Seismic Vulnerability Index (SVI).

. The results reveal that 10 tunnels are assigned the first priority, 34 tunnels the second priority, 41 tunnels the third priority, and 18 tunnels the fourth priority. Therefore, most tunnels are classified as second and third priority. In Table 10, each of the four main classes is divided into subclasses that provide more precise prioritization. As mentioned, tunnel 16 has the maximum vulnerability index among all tunnels, but it is ranked in priority 1–5, which indicates the effect of visual inspection weight impacts on prioritization. However, Table 10 offers a detailed prioritization for the tunnels in the study area, considering both seismic vulnerability and lifetime damage. This enables decision-making organizations to effectively plan rehabilitation efforts, which play a crucial role in seismic risk reduction.

6. Conclusions

This study aims to assist railway network managers in prioritizing the rehabilitation of tunnels under budget constraints. This research provided an integrated assessment of the seismic vulnerability of masonry railway tunnels in Northwest Iran, highlighting the critical need for prioritization in rehabilitation efforts. The vulnerability of 103 old masonry rock tunnels was examined under the impact of 12 active faults using fragility curves derived from the HAZUS and SYNER-G methodologies. This approach enabled a systematic estimation of the probability of various damage states under different seismic intensities. The expected values of damage states were utilized as a damage index (DI), providing a measure of the severity of potential damage. It was found that tunnels under PGA are more vulnerable than PGD; therefore, the damage caused by PGA was taken into account. A normalized prioritization index (NPI) was proposed, integrating seismic vulnerability and life cycle damages to effectively prioritize tunnels for rehabilitation. Four main classes were defined to prioritize. The results indicated that 10 tunnels were placed in the first class, 34 tunnels in the second class, 41 tunnels in the third class, and 18 tunnels in the last class. For each main class, a sub-classification was provided, which is essential for resource allocation in budget limitations.

It is hoped that this study will be useful in reducing seismic risk and helping railway transportation network managers. Future research can enhance the proposed framework by incorporating probabilistic seismic hazard models to account for the variability and uncertainties in seismic scenarios across different return periods and ground motion characteristics, such as magnitude. Moreover, developing tunnel-specific fragility curves using incremental dynamic analysis (IDA) can provide a more accurate representation of the seismic response of each tunnel, allowing for more precise damage estimation tailored to the structural and geotechnical characteristics of individual tunnels. Additionally, future studies could consider the effects of material degradation over time, inelastic behavior of lining shell elements, the influence of surrounding rock properties, and the presence of groundwater on the performance and vulnerability of each tunnel. Incorporating these parameters into the seismic assessment can improve the reliability of prioritization results. Expanding the framework to a multi-hazard context and integrating tunnel importance weighting in transportation networks or economic impact analysis would also make the rehabilitation strategy more comprehensive and practical for decision-makers. Furthermore, the methodology could be applied to other types of infrastructure, and the results could be validated using post-earthquake damage data to ensure robustness and generalizability.