Probabilistic Seismic Multi-hazard Risk and Restoration Modeling for Resilience-informed Decision Making in Railway Networks

Figures & data

Figure 1. The step-by-step graphical framework of the current study.

Figure 2. The physical network of Iran railway network (The Railways of Islamic Republic of Iran, 2005).

Figure 3. Satellite and aerial picture of the Tehran-Sari railway.

Table 1. The Tehran-Sari railway properties.

	Origin(Tehran, Tehran Province)	Destination(Sari, Mazandaran Province)
X-Coordinate	51.398014	53.050823
Y-Coordinate	35.658143	36.556579

Figure 4. Left: DoAb Bridge; Right: Veresk Bridge. both bridges are located on the map in Figure 3.

Table 2. The Tehran-Sari railway properties of the two studied bridges (Ahamri et al., 2016).

Name	X	Y	Number of spans (N)	Skew angle ($\alpha$)	Span width (W)	Bridge length (L)	Maximum span length (Lmax)
Veresk	52.99	35.90	1	0	5	86	66
DoAb	53.04	36.02	7	10	5	140	20

Figure 5. Seismic area sources of studied region using available data (Karimiparidari, 2014).

Table 3. Seismic parameters of the employed seismic sources in the current study (Karimiparidari, 2014).

ID	Name	Mmax	Mobs	$\beta$	$\lambda (4.5)$
5	AL6	7.4$\pm$0.51	7.8$\pm$0.5	1.62$\pm$0.10	0.10
6	ND1	7.3$\pm$0.51	6.6$\pm$0.5	1.98$\pm$0.14	0.12
7	ND5	6.3$\pm$0.72	6.5$\pm$0.5	2.06$\pm$0.21	1.00
10	KA5	6.8$\pm$0.41	6.4$\pm$0.4	2.12$\pm$0.15	0.21
19	AL10	6.4$\pm$0.51	5.6$\pm$0.5	1.91$\pm$0.11	0.08
20	KA1	6.9$\pm$0.13	7.1$\pm$0.1	2.2.$\pm$0.15	0.05
21	SK3	6.9$\pm$0.51	6.4$\pm$0.5	2.00$\pm$0.19	0.18
22	SK1	6.5$\pm$0.22	5.5$\pm$0.2	2.00$\pm$0.17	0.12
38	KA4	6.6$\pm$0.51	5.9$\pm$0.5	2.27$\pm$0.13	0.19
39	SK4	6.4$\pm$0.13	4.8$\pm$0.1	2.00$\pm$0.20	0.12
86	KD1	7.5$\pm$0.50	7.5$\pm$0.5	2.28$\pm$0.14	0.35
87	KD4	7.1$\pm$0.50	7.0$\pm$0.5	2.12$\pm$0.13	0.31
88	AL5	7.0$\pm$0.57	7.1$\pm$0.4	2.18$\pm$0.21	0.03
89	AL4	7.0$\pm$0.44	6.8$\pm$0.3	2.42$\pm$0.19	0.73
90	AL7	7.2$\pm$0.70	7.5$\pm$0.7	1.75$\pm$0.12	0.06
91	SK2	5.8$\pm$0.12	5.2$\pm$0.1	2.00$\pm$0.18	0.06
92	AL8	7.3$\pm$0.51	7.6$\pm$0.5	1.62$\pm$0.10	0.10
98	AL9	5.5$\pm$0.13	4.2$\pm$0.1	1.62$\pm$0.10	0.03
99	AL15	7.1$\pm$0.51	7.5$\pm$0.5	1.62$\pm$0.10	0.03
100	AL13	6.5$\pm$0.13	6.2$\pm$0.1	1.62$\pm$0.10	0.02
101	AL14	6.9$\pm$0.08	-	1.62$\pm$0.10	0.02
102	AL12	7.4$\pm$0.16	7.4$\pm$0.1	1.94$\pm$0.22	0.06
104	KA3	6.8$\pm$0.16	6.5$\pm$0.1	2.31$\pm$0.22	0.14
105	KA2	7.1$\pm$0.07	-	2.20$\pm$0.15	0.02
96	AL3	6.7$\pm$0.50	6.5$\pm$0.5	1.72$\pm$0.11	0.06

Figure 6. The final seismic hazard map analyzed using R-CRISIS.

Table 4. The applied attenuation models and assigned weights.

Assigned weight	Model name
0.30	Ambraseys et al. (2005)
0.21	Akkar and Bommer (2010)
0.14	Ghasemi et al. (2009)
0.13	Amiri et al. (2009)
0.09	Tavakoli and Pezeshk (2007)
0.08	Akyol and Karagöz (2009)
0.05	Norouzi (2005)

Table 5. Summary of the attenuation models used in this study.

Attenuation Model	Equation
(Ambraseys et al., 2005)	$logy=a_1+a_2{M}_w+\left(a_3+a_4{M}_w\right)log\sqrt{d^2+a_5^2}+a_6{S}_s+a_7{S}_A+a_8{F}_N+a_9{F}_T+a_{10}{F}_0$
(Akkar & Bommer, 2010)	$log\left(PSA\right)=b_1+b_{2}M+b_3{M}^2+\left(b_4+b_{5}M\right)log\sqrt{R_{jb}^2+b_6^2}+b_7{S}_s+b_8{S}_A+b_9{F}_N+b_{10}{F}_R+\epsilon \sigma$
(Ghasemi et al., 2009)	${log}_{10}Sa\left(T\right)=a_1+a_{2}M+a_3{log}_{10}\times \left(R+a_4{10}^{\left(a_{5}M\right)}\right)+a_6{S}_1+a_7{S}_2$
(Amiri et al., 2009)	$lny=C_1+C_2{M}_s+C_{3}ln\left[R+C_{4}exp\left[M_s\right]\right]+C_{5}R$
(Tavakoli & Pezeshk, 2007)	$ln(Y)=f_1(M_w)+f_2(r_{rup})+f_3(M_w,r_{rup})$
Akyol and Karagöz (2009)	$logy=1.330095+0.640047\left(M-6\right)-1.65663logr+0.14963S+0.27P$
(Norouzi, 2005)	$ln(PGH)=8.235+1.244\left(M_w-6\right)-1.087\ast Ln(sqrt\left(EP{D}^2+{10}^2\right))$

Figure 7. Liquefaction susceptibility map of the current studied region (Komakpanah & Farajzadeh, 1996).

Figure 8. Liquefaction-induced deformation map of the Tehran-Sari railway and two mentioned bridges (30 m DEM is used).

Figure 9. Landslide susceptibility map of the current studied region (Geological Survey of Iran, 2001).

Figure 10. Landslide-induced displacement map of the Tehran-Sari railway, and Veresk and DoAb bridges.

Figure 11. Fragility curves of railway tracks (FEMA, 2012).

Figure 12. Ground shaking standard fragility curves for conventionally designed major bridges (FEMA, 2012).

Table 6. Damage state definition of railway tracks (FEMA, 2012).

Damage State	Definition
DS1 (None)	None damage
DS2 (Slight/Minor)	Defined by minor (localized) derailment due to slight differential settlement of embankment or offset of the ground.
DS3 (Moderate)	Defined by considerable derailment due to differential settlement or offset of the ground. Rail repair is required.
DS4 (Extensive/Complete)	Defined by major differential settlement of the ground resulting in potential derailment over extended length.

Table 7. Damage states definition of railway bridges (FEMA, 2012).

Damage State	Definition
DS1 (None)	None damage
DS2 (slight/minor)	Defined by minor cracking and spalling to the abutment, cracks in shear keys at abutments, minor spalling and cracks at hinges, minor spalling at the column (damage requires no more than cosmetic repair) or minor cracking to the deck.
DS3 (Moderate)	Defined by any column experiencing moderate (shear cracks) cracking and spalling (column structurally still sound), moderate movement of the abutment (<2”), extensive cracking and spalling of shear keys, any connection having cracked shear keys or bent bolts, keeper bar failure without unseating, rocker bearing failure or moderate settlement of the approach.
DS4 (Extensive)	Defined by any column degrading without collapse – shear failure – (column structurally unsafe), significant residual movement at connections, or major settlement approach, vertical offset of the abutment, differential settlement at connections, shear key failure at abutments.
DS5 (Complete)	Defined by any column collapsing and connection losing all bearing support, which may lead to imminent deck collapse, tilting of substructure due to foundation failure.

Table 8. Standard fragility curves properties of railway tracks (FEMA, 2012).

Damage State	PGD Median (in)	PGD Dispersion ($\beta$)
DS1 (None)	-	-
DS2 (Slight/Minor)	12	0.7
DS3 (Moderate)	24	0.7
DS4 (Extensive/Complete)	60	0.7

Table 9. Standard fragility curves properties of railway bridges (FEMA, 2012).

Damage State	$PGD$ median ($in$) due to Ground Failure	PGD Dispersion ($\beta$)	$Sa$ (1.0 sec in $g$’s) due to Ground Shaking	Ground Shaking Dispersion ($\beta$)
DS1 (None)	-	-	-	-
DS2 (Slight)	3.9	0.2	0.4	0.6
DS3 (Moderate)	3.9	0.2	0.5	0.6
DS4 (Extensive)	3.9	0.2	0.7	0.6
DS5 (Complete)	13.8	0.2	0.9	0.6

Table 10. Modified properties used in fragility analyses of bridges.

Bridge	Number of spans (N)	$K_{skew}$	$K_{3D}$	New median
				DS2	DS3	DS4	DS5
Veresk	1	1.00	1.00	0.40	0.50	0.70	0.90
DoAb	7	0.99	1.04	0.4	0.52	0.72	0.93

Table 11. Intensity measures used for bridges risk assessment (obtained from seismic hazard analysis results).

Name	PGA	PGD(in)	b(1s)	b(0.3s)	Soil type 1	PSA 0.3s	PSA 1s
Veresk	0.30	31.03	1.12	2.50	1	0.75	0.34
DoAb	0.35	54.55	1.12	2.50	1	0.88	0.39

Table 12. Estimated shake-only, PGD-only and combined probability of exceeding of various damage states for bridge components of Tehran-Sari railway network.

Bridge	$P\left[ds\ge DS|S_{a1}\right]$				$P\left[ds\ge DS|PGD\right]$				$P_{COMB}\left[ds\ge DS\right]$
	DS2	DS3	DS4	DS5	DS2	DS3	DS4	DS5	DS2	DS3	DS4	DS5
Veresk	0.38	0.25	0.11	0.05	1.00	1.00	1.00	1.00	0.57	0.48	0.38	0.33
DoAb	0.48	0.32	0.15	0.07	1.00	1.00	1.00	1.00	0.64	0.52	0.41	0.35

Figure 13. Expected damage state map for the Tehran-Sari railway. The figure shows extensive damages are expected mostly in plain sector where the probability of liquefaction and the shake intensity measure are high.

Table 13. Combined exceeding probability of various damage states obtained from estimated damage probabilities subject to shaking, liquefaction and landslide.

Bridge	$P_{COMB}\left[ds=DS(i)\right]$
	DS1	DS2	DS3	DS4	DS5
Veresk	0.43	0.09	0.10	0.04	0.33
DoAb	0.36	0.11	0.12	0.05	0.35

Figure 14. Functionality percentage of the railway tracks obtained based on HAZUS discrete restoration functions. The reported minimum and maximum values show the lowest and highest functionality for various segments and the mean value reports the functionality of the entire railway track.

Figure 15. System level restoration curve for Tehran-Sari railway network providing functionality percentage of the systems days following a design basis earthquake scenario.

Table 14. Discrete restoration curves used for functionality analysis 1 day, 3 days, 7 days, 30 days and 90 days following seismic event (FEMA, 2012).

Classification	Damage state	Functional Percentage
		1 day	3 days	7 days	30 days	90 days
Railway Tracks	Slight	90	100	100	100	100
	Moderate	22	46	90	100	100
	Extensive	14	18	28	87	100
	Complete	6	8	10	22	70

Figure 16. Estimated economic loss map for the Tehran-Sari railway.

Table 15. Damage ratios and replacement values for railway track and railway bridge (FEMA, 2012).

	Damage State	Best Estimate Damage Ratio	Range of Damage Ratios	Replacement Value (thousand $\mathrm{\$}$)
Rail Track	slight	0.05	0.01 to 0.15	$1,{500}^{\ast }$
	moderate	0.20	0.15 to 0.40
	extensive/complete	0.70	0.40 to 1.00
Rail Bridge	slight	0.12	0.01 to 0.15	5,000
	moderate	0.19	0.15 to 0.40
	extensive	0.40	0.40 to 0.80
	complete	1.00	0.80 to 1.00

*Value based on 1 km length.

Figure A17. User interface of the seismic risk assessment model of Iran railway tracks.

Figure A18. User interface of the seismic risk assessment model of Iran railway bridges.

Ahamri, N., Mahdavinejad, M., & M, F. (2016). Interaction of natural landscape and modern heritage in case of Veresk, Iran. eQscientific Herald of the Voronezh State University of Architecture & Civil Engineering, 32(4), 70–91.

 Google Scholar

Karimiparidari, S. (2014). Seismic hazard analysis in Iran (475 years return period). International Institute of Earthquake Engineering and Seismology (IIEES).

 Google Scholar

Ambraseys, N., Douglas, J., Sarma, S., & Smit, P. (2005). Equations for the estimation of strong ground motions from shallow crustal earthquakes using data from Europe and the Middle East: Horizontal peak ground acceleration and spectral acceleration. Bulletin of Earthquake Engineering, 3(1), 1–53. https://doi.org/10.1007/s10518-005-0183-0

 Web of Science ®Google Scholar

Akkar, S., & Bommer, J. (2010). Empirical equations for the prediction of PGA, PGV, and spectral accelerations in Europe, the Mediterranean region, and the Middle East. Seismological Research Letters, 81(2), 195–206. https://doi.org/10.1785/gssrl.81.2.195

 Web of Science ®Google Scholar

Ghasemi, H., Zare, M., Fukushima, Y., & Koketsu, K. (2009). An empirical spectral ground- motion model for Iran. Journal of Seismology, 13(4), 499–515. https://doi.org/10.1007/s10950-008-9143-x

 Web of Science ®Google Scholar

Amiri, G. G., Khorasani, M., Hessabi, R. M., & Amrei, S. R. (2009). Ground-motion prediction equations of spectral ordinates and arias intensity for Iran. Journal of Earthquake Engineering, 14(1), 1–29. https://doi.org/10.1080/13632460902988984

 Web of Science ®Google Scholar

Tavakoli, B., & Pezeshk, S. (2007). A new approach to estimate a mixed model–based ground motion prediction equation. Earthquake Spectra, 23(3), 665–684.

 Web of Science ®Google Scholar

Akyol, N., & Karagöz, Ö. (2009). Empirical attenuation relationships for western Anatolia, Turkey. Turkish Journal of Earth Sciences, 18(3), 351–382.

 Web of Science ®Google Scholar

Norouzi, A. (2005). Attenuation relations for peak horizontal and vertical accelerations of earthquake ground motion in Iran: A preliminary analysis.

 Google Scholar

Komakpanah, A., & Farajzadeh, M. (1996). Liquefaction susceptibility and opportunity macrozonation of Iran. Proceedings of the Fifth International Conference on Seismic Zonation. Nice, France, October 17-19, 1651–1658.

 Google Scholar

FEMA. (2012). Multi-hazard loss estimation methodology: Earthquake model. Department of Homeland Security, FEMA, Washington, DC, 235–260.

 Google Scholar