Arabian Journal for Science and Engineering

, Volume 44, Issue 5, pp 4807–4818 | Cite as

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

  • Rujia QiaoEmail author
  • Zhushan ShaoEmail author
  • Wei Wei
  • YuanYuan Zhang
Research Article - Civil Engineering


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.


Tunnel Fire RABT curve Thermo-mechanical stress Safety evaluation 

List of symbols

r, \(\uptheta \)

Cylindrical coordinates


Dimensionless radius

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

Inner and outer radii

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

Dimensionless inner and outer radii


Heat transfer coefficient on the outer surface

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

Dimensionless heat transfer coefficient on the outer surface



\(\Theta \)

Dimensionless temperature

\(\Theta _{a}\)

Dimensionless maximum temperature of fire



\(\tau \)

Dimensionless time

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

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


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


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


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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Khoury, G.A.: Effect of fire on concrete and concrete structures. Prog. Struct. Eng. Mater 2, 429–447 (2000)CrossRefGoogle Scholar
  2. 2.
    Schrefler, B.A.; Brunello, P.; Gawin, D.; Majorana, C.E.; Pesavento, F.: Concrete at high temperature with application to tunnel fire. Comput. Mech. 29(1), 43–51 (2002)CrossRefzbMATHGoogle Scholar
  3. 3.
    Lai, J.X.; Wang, X.L.; Qiu, J.L.; Zhang, G.Z.; Chen, J.X.; Xie, Y.L.: A state-of-the-art review of sustainable energy based freeze proof technology for cold-region tunnels in China. Renew. Sust. Energy Rev. 82, 3554–3569 (2018)CrossRefGoogle Scholar
  4. 4.
    Ma, Q.; Guo, R.; Zhao, Z.; Lin, Z.; He, K.: Mechanical properties of concrete at high temperature—a review. Constr. Build. Mater. 93, 371–383 (2015)CrossRefGoogle Scholar
  5. 5.
    Fan, L.F.; Wu, Z.J.; Wan, Z.; Gao, J.W.: Experimental investigation of thermal effects on dynamic behavior of granite. Appl. Therm. Eng. 125, 94–103 (2017)CrossRefGoogle Scholar
  6. 6.
    Kodur, V.K.R.; Dwaikat, M.M.S.; Dwaikat, M.B.: High-temperature properties of concrete for fire resistance modeling of structures. ACI Mater. J. 105(5), 517–527 (2008)Google Scholar
  7. 7.
    Ahmad, S.; Sallam, Y.S.; Al-Hawas, M.A.: Effects of key factors on compressive and tensile strengths of concrete exposed to elevated temperatures. Arab. J. Sci. Eng. 39(6), 4507–4513 (2014)CrossRefGoogle Scholar
  8. 8.
    Du, S.; Zhang, Y.; Sun, Q.; Gong, W.; Geng, J.; Zhang, K.: Experimental study on color change and compression strength of concrete tunnel lining in a fire. Tunn. Undergr. Sp. Technol. 71, 106–114 (2018)CrossRefGoogle Scholar
  9. 9.
    Hertz, K.D.: Limits of spalling of fire-exposed concrete. Fire Saf. J. 38(2), 103–116 (2003)CrossRefGoogle Scholar
  10. 10.
    Witek, A.; Gawin, D.; Pesavento, F.; Schrefler, B.A.: Finite element analysis of various methods for protection of concrete structures against spalling during fire. Comput. Mech. 39(3), 271–292 (2007)CrossRefzbMATHGoogle Scholar
  11. 11.
    Zhang, H.L.; Davie, C.T.: A numerical investigation of the influence of pore pressures and thermally induced stresses for spalling of concrete exposed to elevated temperatures. Fire Saf. J. 59(59), 102–110 (2013)CrossRefGoogle Scholar
  12. 12.
    Zhang, Y.; Zeiml, M.; Pichler, C.; Lackner, R.: Model-based risk assessment of concrete spalling in tunnel linings under fire loading. Eng. Struct. 77, 207–215 (2014)CrossRefGoogle Scholar
  13. 13.
    Guergah, C.; Dimia, M.S.; Guenfoud, M.: Contribution to the numerical modelling of the spalling phenomenon: case of a reinforced concrete beams. Arab. J. Sci. Eng. 2, 1–13 (2017)Google Scholar
  14. 14.
    Poon, C.S.; Shui, Z.H.; Lam, L.: Compressive behavior of fiber reinforced high-performance concrete subjected to elevated temperatures. Cem. Concr. Res. 34(12), 2215–2222 (2004)CrossRefGoogle Scholar
  15. 15.
    Habel, K.H.; Charron, J.P.; Braike, S.B.; Hooton, D.H.D.; Gauvreau, P.G.; Massicotte, B.M.: Ultra-high performance fibre reinforced concrete mix design in central. Can. J. Civ. Eng. 35(2), 217–224 (2008)CrossRefGoogle Scholar
  16. 16.
    Wu, Z.J.; Fan, L.F.; Liu, Q.S.; Ma, G.W.: Micro-mechanical modeling of the macro-mechanical response and fracture behavior of rock using the numerical manifold method. Eng. Geol. 225, 49–60 (2017)CrossRefGoogle Scholar
  17. 17.
    Gencel, O.: Effect of elevated temperatures on mechanical properties of high-strength concrete containing varying proportions of hematite. Fire Mater. 36, 217–230 (2012)CrossRefGoogle Scholar
  18. 18.
    Ali, F.; Nadjai, A.; Choi, S.: Numerical and experimental investigation of the behavior of high strength concrete columns in fire. Eng. Struct. 32(5), 1236–1243 (2010)CrossRefGoogle Scholar
  19. 19.
    Choi, E.G.; Shin, Y.S.: The structural behavior and simplified thermal analysis of normal-strength and high-strength concrete beams under fire. Eng. Struct. 33(4), 1123–1132 (2011)CrossRefGoogle Scholar
  20. 20.
    Kalifa, P.; Chéné, G.; Gallé, C.: High-temperature behaviour of HPC with polypropylene fibres: from spalling to microstructure. Cem. Concr. Res. 31(10), 1487–1499 (2001)CrossRefGoogle Scholar
  21. 21.
    Maluk, C.; Bisby, L.; Terrasi, G.P.: Effects of polypropylene fibre type and dose on the propensity for heat-induced concrete spalling. Eng. Struct. 141, 584–595 (2017)CrossRefGoogle Scholar
  22. 22.
    Varona, F.B.; Baeza, F.J.; Bru, D.; Ivorra, S.: Influence of high temperature on the mechanical properties of hybrid fiber reinforced normal and high strength concrete. Constr. Build. Mater. 159, 73–82 (2018)CrossRefGoogle Scholar
  23. 23.
    Caner, A.; Zlatanic, S.; Munfah, N.: Structural fire performance of concrete and shotcrete tunnel liners. J. Struct. Eng. 131(12), 1920–1925 (2005)CrossRefGoogle Scholar
  24. 24.
    Caner, A.; Böncü, A.: Structural fire safety of circular concrete railroad tunnel linings. J. Struct. Eng. 135(9), 1081–1092 (2009)CrossRefGoogle Scholar
  25. 25.
    Feist, C.; Aschaber, M.; Hofstetter, G.: Numerical simulation of the load-carrying behavior of RC tunnel structures exposed to fire. Finite Elem. Anal. Des. 45(12), 958–965 (2009)CrossRefGoogle Scholar
  26. 26.
    Guo, J.; Jiang, S.; Zhang, Z.: Fire thermal stress and its damage to subsea immersed tunnel. Proc. Eng. 166, 296–306 (2016)CrossRefGoogle Scholar
  27. 27.
    Capua, D.D.; Mari, A.R.: Nonlinear analysis of reinforced concrete cross-sections exposed to fire. Fire Saf. J. 42(2), 139–149 (2007)CrossRefGoogle Scholar
  28. 28.
    Lai, H.P.; Wang, S.Y.; Xie, Y.L.: Experimental research on temperature field and structure performance under different lining water contents in road tunnel fire. Tunn. Undergr. Sp. Technol. 43, 327–335 (2014)CrossRefGoogle Scholar
  29. 29.
    Zeiml, M.; Lackner, R.; Pesavento, F.; Schrefler, B.A.: Thermo-hydro-chemical couplings considered in safety assessment of shallow tunnels subjected to fire load. Fire Saf. J. 43(2), 83–95 (2008)CrossRefGoogle Scholar
  30. 30.
    Pichler, C.; Lackner, R.; Mang, H.A.: Safety assessment of concrete tunnel linings under fire load. J. Struct. Eng. 132(6), 961–969 (2006)CrossRefGoogle Scholar
  31. 31.
    Gawin, D.; Majorana, C.E.; Schrefler, B.A.: Numerical analysis of hygro-thermal behaviour and damage of concrete at high temperature. Mech. Cohes Frict. Mat. 4(1), 37–74 (2015)CrossRefGoogle Scholar
  32. 32.
    Choi, S.W.; Lee, J.; Chang, S.H.: A holistic numerical approach to simulating the thermal and mechanical behavior of a tunnel lining subject to fire. Tunn. Undergr. Sp. Technol. 35(2), 122–134 (2013)CrossRefGoogle Scholar
  33. 33.
    Shao, Z.S.; Wang, T.J.: Three-dimensional solutions for the stress fields in functionally graded cylindrical panel with finite length and subjected to thermal/mechanical loads. Int. J. Solids Struct. 43(13), 3856–3874 (2006)CrossRefzbMATHGoogle Scholar
  34. 34.
    Yan, Z.G.: A Study on Mechanical Behaviors and Fire proof Methods of Tunnel Lining Structure during and after Fire Scenarios. Ph.D. Thesis, Tongji University, Shanghai (2007)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.School of Civil EngineeringXi’an University of Architecture and TechnologyXi’anChina

Personalised recommendations