Seismic Vulnerability of Tunnels in Jammu and Kashmir for Post Seismic Functionality

Abstract

In the last few decades, Jammu and Kashmir has faced many moderate to large earthquake events that caused catastrophic damage to the physical infrastructure and significant socioeconomic loss. The growing number of infrastructure projects, as well as previous historical records of severe earthquakes in this area demand the study of the seismic vulnerability of tunnel. In this paper, an attempt has been made to develop the seismic fragility curves for circular tunnels located in four distinct zones classified based on seismic microzonation results of the Jammu Region (JR). The damage probabilities of shallow tunnels in these zones decrease fiercely as lining thickness increases. Furthermore, increasing PGA by 0.2 g increases the exceedance probabilities for minor, moderate, and extensive damage exposed to 82%, 89%, and 93%, respectively for shallow tunnels. The fragility functions proposed for Jammu and Kashmir were employed to assess seismic risk for tunnels under Udhampur Srinagar Baramulla Rail Link (USBRL) project. Most of the tunnels in Phase 3 showed more than 50% of damage probability for the region specific defined seismic environment.

Appendix

Example 1: Ovaling deformation of a circular tunnel at shallow depth using formulations of Bobet approach (Bobet 2010).

Moment Magnitude, Mw		7.5
Source-to-site distance	km	15.00
Peak ground particle acceleration at surface, amax	g	0.50
Stiff soil, ρm	kg/m3	1600.00
Shear wave velocity, Cm	m/s	200.00
Poisson's ratio, νm		0.30
Mean diameter, d	m	6.0
Mean radius, r	m	3.0
Lining thickness	m	0.30
Young's modulus of lining, El	GPa	35,355.25
Poisson's ratio of lining, νl		0.15

• 1. Maximum Thrust (T_max) for full slip condition

  $${\mathrm{T}}_{\mathrm{max}}=-\frac{12\left(1-{\upnu }_{\mathrm{m}}\right) }{3\left(5-{6\upnu }_{\mathrm{m}}\right)+\left(1-{\upnu }_{\mathrm{m}}\right)\mathrm{F{^{\prime}}}}{\mathrm{G}}_{\mathrm{m}}\mathrm{r}{\Upsilon }_{\mathrm{max}}\mathrm{Sin}2\uptheta =120.76\mathrm{ kN}$$

• 2. Maximum Thrust (T_max) for no slip condition

  $${\mathrm{T}}_{\mathrm{max}}=-\left(1-{\mathrm{C}}_{2}\right){\mathrm{G}}_{\mathrm{m}}\mathrm{r}{\Upsilon }_{\mathrm{max}}\mathrm{Sin}2\uptheta =1176.32\mathrm{ kN}$$

• 3. Maximum Bending Moment (M_max) for full slip condition

  $${\mathrm{M}}_{\mathrm{max}}={\mathrm{T}}_{\mathrm{max }}.\mathrm{r}=362.28\mathrm{ kN}.\mathrm{m}$$

• 4. Maximum Bending Moment (M_max) for no slip condition

  $${\mathrm{M}}_{\mathrm{max}}=-\frac{1}{2}(1+{\mathrm{C}}_{1}+{\mathrm{C}}_{2}){\mathrm{G}}_{\mathrm{m}}{\mathrm{r}}^{2}{\Upsilon }_{\mathrm{max}}\mathrm{Sin}2\uptheta =304.64\mathrm{ kN}.\mathrm{m}$$

Example 2: Ovaling deformation of a circular tunnel at deeper depth using formulations of Kouretzis et al. approach (Kouretzis et al. 2014).

Moment Magnitude, Mw		7.5
Source-to-site distance	km	17.00
Peak ground particle acceleration at surface, amax	g	0.70
Stiff soil, ρm	kg/m3	2500.00
Shear wave velocity, Cm	m/s	750.00
Poisson's ratio, νm		0.25
Mean diameter, d	m	6.0
Mean radius, r	m	3.0
Lining thickness	m	0.30
Young's modulus of lining, El	GPa	35,355.25
Poisson's ratio of lining, νl		0.15

• 1. Maximum Thrust (T_max) for full slip condition

  $${\mathrm{T}}_{\mathrm{max}}=\mp \left[{\mathrm{K}}_{3}+{\mathrm{K}}_{5}\right]{\upsigma }_{\mathrm{max}}\mathrm{r}/2=129.35\mathrm{ kN}$$

• 2. Maximum Thrust (T_max) for no slip condition

  $${\mathrm{T}}_{\mathrm{max}}=\mp \left[{\mathrm{K}}_{3}+{\mathrm{K}}_{4}\right]{\upsigma }_{\mathrm{max}}\mathrm{r}/2=289.56\mathrm{ kN}$$

• 3. Maximum Bending Moment (M_max) for full slip condition

  $${\mathrm{M}}_{\mathrm{max}}=\mp \left[\frac{\mathrm{C}\left(1-{2\upnu }_{\mathrm{m}}\right)}{6\mathrm{F}}{\mathrm{K}}_{3}+{\mathrm{K}}_{5}\right]{\upsigma }_{\mathrm{max}}{\mathrm{r}}^{2}/2=2732.45\mathrm{ kN}.\mathrm{m}$$

• 4. Maximum Bending Moment (M_max) for no slip condition

  $${\mathrm{M}}_{\mathrm{max}}=\mp \left[\frac{\mathrm{C}\left(1-{2\upnu }_{\mathrm{m}}\right)}{6\mathrm{F}}{\mathrm{K}}_{3}-\frac{{\mathrm{K}}_{4}}{2}-{\mathrm{K}}_{6}+1\right]{\upsigma }_{\mathrm{max}}{\mathrm{r}}^{2}/2=2354.92\mathrm{ kN}.\mathrm{m}$$