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Theoretical Investigation into the Thermo-Mechanical Behaviours of Tunnel Lining During RABT Fire Development

  • Research Article - Civil Engineering
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Abstract

Safety assessment of tunnel lining after fire is a compulsory work and should be performed based on thermo-mechanical analysis. In this paper, a theoretical method is presented to investigate the thermo-mechanical behaviours of tunnel lining during fire development. The RABT curve is considered in this model, which includes three stages, i.e. temperature rising, temperature holding and cooling. By employing the Laplace transform and series solving method for ordinary differential equations, solutions for the time-dependent temperature and thermo-mechanical stresses are obtained. The unsteady temperature and stress distributions of the tunnel lining are discussed. Based on the limit state analysis, the fire-induced damage of tunnel lining is evaluated. All of the results are presented and discussed in detail.

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Abbreviations

r, \(\uptheta \) :

Cylindrical coordinates

R :

Dimensionless radius

\(r_{a}\), \(r_{b}\) :

Inner and outer radii

\({{R}}_{a}\), \({{R}}_{\mathrm{b}}\) :

Dimensionless inner and outer radii

\(h_{2}\) :

Heat transfer coefficient on the outer surface

\(\hbox {H}_{2}\) :

Dimensionless heat transfer coefficient on the outer surface

T :

Temperature

\(\Theta \) :

Dimensionless temperature

\(\Theta _{a}\) :

Dimensionless maximum temperature of fire

t :

Time

\(\tau \) :

Dimensionless time

\(\tau _{1}\), \(\tau _{2}\), \(\tau _{3}\) :

Dimensionless time points at the end of the rising, holding and cooling stage

\({T}_{\mathrm{b}}\) :

Temperature of the surrounding medium

\(\Theta _{\mathrm{b}}\) :

Dimensionless temperature of the surrounding medium

\(q_{a}\), \(q_{b}\) :

Pressures on the inner and outer surface

\(Q_{a}\), \(Q_{b}\) :

Dimensionless pressures on the inner and outer surface

X(R,s):

The Laplace transformation of \(\Theta _{1}(R,\tau )\)

s :

The variable of frequency domain corresponding to time domain \(\tau \)

\(\upalpha \); \(\upkappa \); \(\uplambda \) :

Thermal expansion, thermal diffusion and heat conduction coefficients

A; K; \(\Lambda \) :

Dimensionless thermal expansion, thermal diffusion and heat conduction coefficients

\(\upmu \) :

The Poisson’s ratio

E; \(\rho \); c;:

Elastic modulus, density, specific heat capacity

Y; C :

Dimensionless elastic modulus, specific heat capacity

\(\Theta (R, \tau )\) :

Dimensionless temperature field of tunnel lining during fire

U(R,\(\tau \)):

Dimensionless displacement field

\(\Theta _{1}(t)\) :

Dimensionless temperature on the inner surface for the rising stage

\(\Theta _{2}(t)\) :

Dimensionless temperature on the inner surface for the holding stage

\(\Theta _{3}(t)\) :

Dimensionless temperature on the inner surface for the cooling stage

\(\Theta _{1}(R, \tau )\) :

Dimensionless temperature field of tunnel lining for the rising stage

\(\Theta _{2}(R, \tau )\) :

Dimensionless temperature field of tunnel lining for the holding stage

\(\Theta _{3}(R, \tau )\) :

Dimensionless temperature field of tunnel lining for the cooling stage

\(\Sigma _{{r}}(R,\tau ), \Sigma _{\uptheta }(R,\tau \)):

Dimensionless radial and circumferential stress fields

\(r_{{m}}\), \({E}_{{m}}\), \(\alpha _{{m}}\), \(\lambda _{{m}}\), \({T}_{{m}}\) :

Reference values of radius, elastic modulus, thermal expansion coefficients, thermal conductivity coefficients, temperature

RWS curve:

Specified by the Rijkswaterstatt, the Netherlands Ministry of Transport and one of the most widely used fire load curves for tunnels

RABT curve:

German requirement for tunnel fires

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Authors and Affiliations

  1. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Rujia Qiao, Zhushan Shao, Wei Wei & YuanYuan Zhang

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  1. Rujia Qiao
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  2. Zhushan Shao
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Correspondence to Rujia Qiao or Zhushan Shao.

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Qiao, R., Shao, Z., Wei, W. et al. Theoretical Investigation into the Thermo-Mechanical Behaviours of Tunnel Lining During RABT Fire Development. Arab J Sci Eng 44, 4807–4818 (2019). https://doi.org/10.1007/s13369-018-3555-x

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