A new numerical approach to the hyperstatic reaction method for segmental tunnel linings Ngoc Anh Do 1,4 , Daniel Dias 2, * ,† , Pierpaolo Oreste 3 and Irini Djeran-Maigre 1 1 University of Lyon, INSA of Lyon, Laboratory LGCIE, Villeurbanne, France 2 Grenoble Alpes University, Laboratory LTHE, Grenoble, France 3 Politecnico di Torino, Department of Environmental, Land and Infrastructural Engineering, Torino, Italy 4 Hanoi University of Mining and Geology, Faculty of Civil Engineering, Department of Underground and Mining Construction, Hanoi, Vietnam SUMMARY This paper proposes a numerical approach to the hyperstatic reaction method (HRM) for the analysis of segmental tunnel linings. The influence of segmental joints has been considered directly using a fixity ratio that is determined on the basis of the rotational stiffness. The parameters necessary for the calculation are presented. A specific implementation has been developed using a FEM framework. This code is able to consider the three-dimensional (3D) effect of segment joints in successive rings on the tunnel lining behaviour. The present HRM allows one to take an arbitrary distribution of segment joints along the tunnel boundary into consideration. In addition, the rotational stiffness of segment joints has been simulated using nonlinear behaviour, as it is closer to the true behaviour of a joint than linear or bilinear behaviour. The numerical results of three hypotheses on ring interaction, which allow the 3D effect of a segmental tunnel lining to be taken into account, have been compared with data obtained from the shield-driven tunnel of the Bologna–Florence high-speed railway line project. The numerical results presented in the paper show that the proposed HRM can be used to effectively estimate the behaviour of a segmental tunnel lining. Copyright © 2014 John Wiley & Sons, Ltd. Received 1 April 2013; Revised 18 February 2014; Accepted 19 February 2014 KEY WORDS: segmental tunnel lining; numerical method; hyperstatic reaction method; 3D effect; lining response 1. INTRODUCTION The shield-driven tunnelling method is frequently adopted for the construction of urban underground tunnels in soft ground, because of its flexibility, cost effectiveness and its small impact on the ground surface. A segmental concrete lining, which generally comprises a sequence of rings placed side by side, is commonly used in most shield-driven tunnels [1]. These rings are divided into parts, which are called segments (see Figure 1). Segments are assembled to form a circle, multi-circle or other shapes. A single circular tunnel is the most useful shape as it generally fulfils the requirements of a construction process. One of the most important factors in the design of a segmental tunnel lining is the effects of the segmental joints on its overall behaviour. As reviewed in the work of the same authors [2], these effects have usually been considered through direct and indirect methods. In indirect methods, the segmental tunnel lining is taken into consideration using a continuous lining ring embedded in a continuous soil mass [2–7]. The effect of segmental joints is usually taken into account through the reduction factor, η, of the flexural rigidity of the lining. In direct methods, segmental joints are *Correspondence to: Dias Daniel, Grenoble Alpes University, Laboratory LTHE, Grenoble, France. † E-mail: daniel.dias@ujf-grenoble.fr Copyright © 2014 John Wiley & Sons, Ltd. INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. 2014; 38:1617–1632 Published online 2 April 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nag.2277