### Application of Hyperstatic Reaction Method for Designing of Tunnel Permanent Lining, Part I: 2D Numerical Modelling

Rahim Hassani, Rouhollah Basirat

#### Abstract

The increase of bored tunnels in the entire world has raised the question how to design the tunnel structure in an efficient way. This paper proposes a numerical approach to the Hyperstatic Reaction Method (HRM) for analysing permanent tunnel linings. The permanent tunnel lining is known as main structure of tunnel maintenance during the time. The HRM is one of the analysis methods for tunnel lining in long term. In this paper, two dimensional numerical modelling is performed by considering hyperstatic reaction concepts. Loading is done after the calculation of long term loads, and ground reaction is simulated by springs. Designing is done for Manjil-Rudabar freeway project, Tunnel No. 2. The numerical analyses were performed for Operational Design Earthquake (ODE) and Maximum Design Earthquake (MDE) loading conditions. A new simplified approach is used for considering the effect of earthquake loading on the tunnel lining. Then, an interaction diagram between axial force and bending moment used for investigating the capacity of tunnel lining. The thickness of tunnel lining and armature are calculated for three sections based on induced forces in tunnel lining. These forces were different in every section according to the load combinations, rock mechanics properties, lining properties, and overburden.  The numerical results showed that the forces in tunnel lining for MDE condition is approximately 50% more than ODE condition in earthquake loading. This numerical processing presented that the HRM is a proper, fast, and practical method for designing and analysing the tunnel lining.

#### Keywords

Hyperstatic Method; Tunnel Lining; Numerical Modeling; Static Analysis; Dynamic Analysis

#### References

Limkatanyu, S., Kuntiyawichai, K., Spacone, E., Kwon, M.H. “Nonlinear winkler-based beam element with improved displacement shape functions”. KSCE J. Civil Eng. 17(1), 192–201, 2013.

Do, N.A., Dias, D., Oreste, P., Djeran-Maigre, I. “The behavior of the segmental tunnel lining studied by the hyperstatic reaction method”. Eur. J. Environmental Civil Eng. 18(4), 489–510, 2014.

Barpi, F., Barbero, M., Peila, D. Numerical modelling of ground tunnel support interaction using bedded-beam-spring model with Fuzzy parameters. Gospodarka Surowcami Mineralnymi 27, 71–87, 2011.

Orestre, P. “A numerical approach to the hyperstatic reaction method for the dimensioning of tunnel support”. Tunnelling and Underground Space Technology. 22(2), 185–205, 2007.

Oreste, P. “A probabilistic design approach for tunnel supports”, Computers and Geotechnics 32, 520–534, 2005.

Do, N. A., Dias, D., Oreste, P., and Maigre, D. I., “A new numerical approach to the hyperstatic reaction method for segmental tunnel lining”, International Journal of Numerical and analytical method in Geomechanics, DOI: 10.1002/nag.2277, 2014.

Kim, J. S, Kim, M. K, • Sam Dong Jung, S.D, “Two-dimensional numerical tunnel model using a Winkler-based beam element and its application into tunnel monitoring systems”. Cluster Computer, DOI: 10.1007/s10586-014-0418-4, 2015.

DAUB (German Committee for Underground Construction). Recommendation for static analysis of shield tunnelling machines. Tunnel, vol. 7, pp. 44–58, 2005.

Association Française des Tunnels et de l’Espace Souterrain, Consideration on the usual method of tunnel lining design, Tunnels & Ouvrages Souterrains, vol. 14, mars/avril, 1976.

US Army Corps of Engineering (USACE) Tunnels and shafts in rock. Engineering Manual 1110-2-2901, Washington (USA), 1997.

Panet, M. AFTES, Recommendation on the Convergence-Confinement Method, 2001.

Mashimo H, Ishimura T. “Evaluation of the load on a shield tunnel lining in gravel”. Tunnelling and Underground Space Technology; 18:233–241, 2003.

Hashash YMA, Hook JJ, Schmidt B, Yao JI. “Seismic design and analysis of underground structures”. Tunnelling and Underground Space Technology;16:247–93, 2001.

Park, K.-H., Tantayopin, K., Tontavanich, B., and Owatsiriwong, A. “Analytical solution for seismic-induced ovaling of circular tunnel lining under no-slip interface conditions: A revisit”, Tunnelling and Underground Space Technology, 24(2): p. 231-235, 2009.

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DOI: 10.28991/cej-2016-00000030

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