The three vertices of the risk triangle are hazard, vulnerability, and exposure to assess the seismic risk of any region or specific structural element (Ansari et al. 2022a). The seismic hazard indicates the earthquake-induced devastation of any area or system. The seismic vulnerability depicts the probability of a region, or any structural constituent of infrastructure projects being damaged during a ground motion with the maximum peak ground acceleration for a defined set of epicentral distance and earthquake magnitude of a specific event (Ansari et al. 2022; Zhang et al. 2022). The exposure represents the socioeconomic value of the region or structure at risk and the projected catastrophic index. The semi-Quantitative Seismic Risk Assessment (SQ-SRA) approach is employed to check the serviceability of any system or part of the system in terms of performance risk (Eskesen et al. 2004; You et al. 2005; Shen et al. 2014; Zhang et al. 2015; Grasso and Soldo 2017; Berge-Thierry et al. 2020; Gómez-Soberón et al. 2022). Each category of risk can be defined as a limit, above which the risk is deemed unacceptable and below which additional risk reduction is not necessary (Eskesen et al. 2004). For different damage states, fragility functions are proposed to understand the level of vulnerability of the structural segment. The risk reduction process involves both active and passive steps. Active steps involve avoiding or reducing hazards, while passive steps involve choosing particular mitigation methods (Zhang et al. 2015). The risk matrices are formed based on the hazard and vulnerability data set. The Seismic Fragility Curves (SFC) are used to represent the vulnerability of structure in both pre and post-seismic stages. These curves establish the conditional probability of a tunnel reaching or exceeding a specified damage state (\({DS}_{i}\)) for the intensity measure (\(IM\)) of earthquake motion. SFC can be evaluated using the following Eq. (1) (Argyroudis and Pitilakis, 2012; Andreotti and Lai, 2019; Nguyen at al., 2019; Zhong et al., 2020; Fabozzi et al. 2022). As per Eq. (1), the fragility functions are represented by SFC with a lognormal distribution, assuming that all database uncertainty can be stated just by median uncertainty (Tsindis et al., 2020).
$$P\left[DS\ge {DS}_{i}| IM\right] = \varnothing \left(ln IM - ln {IM}_{{DS}_{i}}/{\beta }_{total}, {DS}_{i}\right)$$
1
where \(DS\) is the type of damage state in the tunnel lining, \(\varnothing\) is the standard normal cumulative distribution function, \({IM}_{{DS}_{i}}\)is the median threshold value of the seismic intensity measure (\(IM\)) responsible to form a specific type of damage (\({DS}_{i}\)) and product of \({\beta }_{total}\) and \({DS}_{i}\) give the total lognormal standard deviation describing the total variability associated with each damage state. \({IM}_{{DS}_{i}}\) and \({\beta }_{total} , {DS}_{i}\) are the two major parts of seismic fragility curves. For the determination of total lognormal standard deviations, the capacity of tunnel support (\({\beta }_{C}\)), seismic demand (\({\beta }_{D}\)), and the estimation of damage state thresholds (\({\beta }_{DS}\)) are regarded as the primary sources of uncertainty. The seismic damages can be grouped into five categories, none (\({DS}_{0}\)); minor (\({DS}_{1}\)); moderate (\({DS}_{2}\)), extensive (\({DS}_{3}\)), and collapse (\({DS}_{4}\)). Damage patterns for the tunnel portal and lining are enlisted in Table 6.
Table 6 Risk assessment chart for railway track serviceability
In the present study, the serviceability of all phases of the USBRL track was predicted as outcomes of risk assessment considering the SQ-SRA method. The Probabilistic Seismic Hazard Analysis (PSHA) technique, which considers both spatial and temporal uncertainty, was utilised to define the seismic hazard (Cornell, 1968). the central part of Udhampur, the bedrock level PGA is estimated as 0.34 g (Ansari et al. 2022c). The Reasi and Ramban have shown the maximum PGA of 0.4 g due to the combined seismic influence of MBT, MCT, and RT.
The probability of experiencing extensive damage to the North Portal of Tunnel T2 is 0.92 for PGA of 0.6 g, as shown in Fig. 8a. The highly jointed and weathered dolomite rock mass at the South Portal of Tunnel T5 indicates the 85% risk of extensive damage, which corresponds to 0.8 g as bedrock PGA produced at RT. The near-site shear zone and strong seismicity characteristics of MCT enhance the risk of both portals of the Tunnel T13 suffering moderate damage. For the Tunnel T40/41, the chance of extensive damage gradually increases when PGA > 0.5 g (Fig. 8b). Due to landslide-prone zones, the chances of extensive damage (\({DS}_{3}\)) of tunnel portals is very high for the tunnels in P2 among all three major phases. For the Tunnel T44/45, minor damage is twice as likely to occur for the same level of seismic intensity as moderate damage.
As illustrated in Fig. 8c, there is a considerable decline in the damage probability from\(P\left[DS\ge {DS}_{1}| \text{P}\text{G}\text{A} =0.7 \text{g} \right] = 0.89\) to \(P\left[DS\ge {DS}_{2}| \text{P}\text{G}\text{A} =0.7 \text{g} \right] = 0.32\), respectively at the North Portal of Tunnel T80. The vicinity of Tunnel T78 in Phase 33 is extremely vulnerable to slope failure, and debris flow indicates an equal probability of moderate and extensive damages. The Tunnel T80 is around 22.5 km from MCT and MBT, where PGA is anticipated to be more than 0.7 g. From the perspective of structural safety for T80, the tilting of the hazard scenario towards greater PGA and the proximity of the Himalayan thrusts are not looking good. The damage contribution of Tunnel T77D and Tunnel T78 under Phase P33 increases the likelihood of a portal collapse by 50%. The probability of minor damage (\({DS}_{1}\)), moderate damage (\({DS}_{2}\)), and extensive damage (\({DS}_{3}\)) are propounded in Table 7.
Table 7 Serviceability prediction for all phases of the USBRL project during post-seismic scenarios.
Phases
|
Tunnels
|
Probability of Exceedance
|
Probability of
Damage State
|
Remarks
|
DS2
|
DS3
|
DS1
|
DS2
|
DS3
|
P1
|
P11
|
T23
|
0.56
|
0.35
|
0.44
|
0.21
|
0.35
|
Accessible
|
T25
|
0.88
|
0.14
|
0.12
|
0.74
|
0.14
|
T1
|
0.72
|
0.21
|
0.28
|
0.51
|
0.21
|
P12
|
T2
|
0.94
|
0.92
|
0.06
|
0.02
|
0.92
|
Inaccessible
|
T3
|
0.82
|
0.43
|
0.18
|
0.39
|
0.43
|
T5
|
0.74
|
0.72
|
0.26
|
0.02
|
0.72
|
P13
|
T6
|
0.92
|
0.45
|
0.08
|
0.47
|
0.45
|
Accessible
|
T10
|
0.16
|
0.13
|
0.84
|
0.03
|
0.13
|
T11
|
0.18
|
0.17
|
0.82
|
0.01
|
0.17
|
P2
|
P21
|
T12
|
0.15
|
0.12
|
0.85
|
0.03
|
0.12
|
Accessible with moderate repair
|
T13
|
0.89
|
0.27
|
0.11
|
0.62
|
0.27
|
T14
|
0.75
|
0.44
|
0.25
|
0.31
|
0.44
|
P22
|
T15
|
0.92
|
0.73
|
0.08
|
0.19
|
0.73
|
Inaccessible
|
T40/41
|
0.81
|
0.79
|
0.19
|
0.02
|
0.79
|
T42/43
|
0.79
|
0.78
|
0.21
|
0.01
|
0.78
|
P23
|
T44/45
|
0.93
|
0.92
|
0.07
|
0.01
|
0.92
|
Inaccessible
|
T46
|
0.68
|
0.52
|
0.32
|
0.16
|
0.52
|
P3
|
P31
|
T47
|
0.83
|
0.43
|
0.17
|
0.4
|
0.43
|
Accessible
|
T48
|
0.76
|
0.16
|
0.24
|
0.6
|
0.16
|
P32
|
T49
|
0.77
|
0.54
|
0.23
|
0.23
|
0.54
|
Inaccessible
|
T50
|
0.65
|
0.63
|
0.35
|
0.02
|
0.63
|
T74R
|
0.62
|
0.59
|
0.38
|
0.03
|
0.59
|
P33
|
T77D
|
0.87
|
0.77
|
0.13
|
0.1
|
0.77
|
Inaccessible
|
T78
|
0.92
|
0.78
|
0.08
|
0.14
|
0.78
|
T80
|
0.83
|
0.71
|
0.17
|
0.12
|
0.71
|
The risk matrix of the SQ-SRA is shown in Fig. 9 for each subphase of Phases 2 and 3. The Tunnel T14 of Phase P21 is the most susceptible tunnel, with a 0.44 probability of extensive damage. The highest PGA of 0.83 g is anticipated at a distance of approximately 15 km from RT for this tunnel. The other two tunnels (T12 and T13) under Phase P21 predicted a comparably lower likelihood of damage, which led to this phase's predisposition towards accessibility (Fig. 9a). Because RT and JT are so near to Tunnels T1 and T2, any seismic activity in this area would undoubtedly have an impact on Phase P1. The combined damage contribution of these three tunnels enables Phase P21 to be accessed with very minor repairs. Tunnel T44/45 has a very high prospect of suffering significant damages since it is situated in a landslide-prone location. There is a strong enough risk that both portals will malfunction. If there is a damage probability greater than 95%, portal collapse, as well as lining cracks, may also occur. The Phase P23 route is inaccessible because of issues with slope instability, weathered rock mass, and a high chance of serious damage close to portal sections. Tunnel T42/43 is the hazard-dominating tunnel having \(P\left[DS\ge {DS}_{3}| \text{P}\text{G}\text{A} =0.5 \text{g} \right] = 0.77\) for North Portal and \(P\left[DS\ge {DS}_{3}| \text{P}\text{G}\text{A} =0.5 \text{g} \right] = 0.73\) for South Portal. During the excavation phase, the Tunnels T49, T50, and T74R experienced problems such as chimney formation at a collapsed tunnel face, debris flow, and portal deformation. According to the risk matrix, all three tunnels have a probability of extensive damage of more than 70% (Fig. 9b). Phase 2 is more vulnerable to damage and inaccessible during post-seismic situations as a result of these serious geological issues.
The SQ-SRA method conveyed that there are three categories of serviceability for the USBRL track: accessible (A), inaccessible (B), and accessible with moderate repair (C). The percentage of these three classes, A, B, and C, are shown on the route from Udhampur to Quazigund as 33, 56, and 11, respectively. Figure 10 illustrates the serviceability of railway tracks as a result of the seismic risk assessment of the USBRL project. Udhampur, Chak Rakhwal, Katra, and Reasi are the major railway stations on the track of Phase P1. Phases P11 (Udhampur to Katra) and P13 (Reasi onwards) were discovered to be serviceable (Fig. 10a). Phase P1 displays functional activity with minor (\({DS}_{1}\)) damage as the main type. Water leaking along the tunnel lining and minor rockfalls close to portal regions are possible, but this phase may be operated normally. The Tunnels along the route of Phase P2 exhibit moderate (\({DS}_{2}\)) damages and these damages can result in cracks that are 3–30 mm broad and 5–10 m long. The risk matrices highlighted the damage probabilities which indicate that P2 is accessible but repairing is required to mitigate the moderate damages. Subsection 2 is located near MT and is the most challenging phase due to critical geological influences and any repair cost may affect the overall project budget.
The active thrusts in the vicinity of Sangaldan, Arpinchala, Banihal, and Quazigund are MCT, MBT, and BT. The last subsection of the USBRL project is the Quazingund to Baramulla (QZ-BR) segment, including the Sadura, Anantnag, Awantipora, Pampore, Srinagar, Budgam, Mazhom, Pattan, Hamre, and Baramulla railway stations of Kashmir Valley (Fig. 10b). The worst-affected part was found to be Phase 3, which contains two subphases that exhibit a lack of serviceability. Phases P1 and 2 appear to be operable, however, Phase 3 is completely inaccessible (Fig. 10b). It appears that entering P3 from P2 is no longer feasible. The tunnels along the Phase 3 have shown the extensive damage (\({DS}_{3}\)) of linign and collapse (\({DS}_{4}\)) of the portals. Additionally, cracks longer than 20 m can be seen in key areas. Collapse (\({DS}_{4}\)) is the worst kind of damage, as it renders the functionality of the track non-operational without considerable rehabilitation, leading to project failure. At portals, there may be significant landslides and deep sliding, as well as significant spalling and cracking