2D numerical investigation of segmental tunnel lining behavior Ngoc-Anh Do a , Daniel Dias b,⇑ , Pierpaolo Oreste c , Irini Djeran-Maigre a a University of Lyon, INSA of Lyon, Laboratory L.G.C.I.E., Villeurbanne, France b University of Joseph-Fourier, Laboratory L.T.H.E., Grenoble, France c Politecnico of Turin, Department of L.E.G.E., Italy article info Article history: Received 13 April 2012 Received in revised form 16 January 2013 Accepted 29 March 2013 Available online 4 May 2013 Keywords: Shield-driven tunnel Segmental lining Lining force Displacement Joint stiffness Numerical model abstract The application field of shield tunneling has extended in recent years. Most shield-driven tunnels are sup- ported by segmental concrete linings. Although many well documented experimental, numerical and analytical results exist in literature concerning the functioning of segmental tunnel linings, their behavior under the influence of joints is still not clear. This paper presents a numerical study that has been performed to investigate the factors that affect segmental tunnel lining behavior. Analyses have been carried out using a two-dimensional finite differ- ence element model. The longitudinal joint between segments in a ring has been simulated through dou- ble node connections, with six degrees of freedom, represented by six springs. The proposed model allows the effect of not only the rotational stiffness but also the radial stiffness and the axial stiffness of the longitudinal joints to be taken into consideration. The numerical results show a significant reduc- tion in the bending moment induced in the tunnel lining as the joint number increases. The tunnel behav- ior in terms of the bending moment considering the effect of joint distribution, when the lateral earth pressure factor K 0 is equal to 0.5, 1.5 and 2, is almost similar and differs when K 0 is equal to unity. It has been seen that the influence of joint rotational stiffness, the reduction in joint rotation stiffness under the negative bending moment, the lateral earth pressure factor and Young’s modulus of ground surround- ing the tunnel should not be neglected. On the other hand, the results have also shown an insignificant influence of the axial and radial stiffness of the joints on segmental tunnel lining behavior. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The shield-driven tunneling method is widely adopted for the construction of urban underground tunnels in soft ground due to its flexibility, cost effectiveness and the minimum impact on the ground surface. Concrete segmental linings, which are generally made up of a sequence of rings placed side-by-side (Gruebl, 2006), are commonly used in most shield-driven tunnels. These rings are divided into sectors that are called segments. These seg- ments are assembled to form a circle, multi-circle or another shape. A single circular tunnel can be considered the most useful shape as it fulfills the normal requirements of a construction process. Because of the geometry of the lining rings and joint distribu- tion, segmental linings show a fully three dimensional (3D) behav- ior, but it is often considered a two dimensional (2D) calculation scheme, in order to reduce the calculation times. This assumption permits the influence of the calculation parameters to be pointed out but it also results in some drawbacks. One of the most important factors in designing a segmental tun- nel lining is the influence of the segmental joints on its overall behavior. In structural analyses, a segmental joint can be consid- ered as an elastic pin and its stiffness characteristics are influenced by rotational stiffness K RO , axial stiffness K A , and radial stiffness K R . The K RO value is defined as the bending moment-per-unit length required to develop a unit rotation angle along the joints of the assembled segments. Similarly, axial stiffness, K A , and radial stiff- ness, K R , are defined as the axial force and the shear force-per-unit length required to develop a unit axial and radial displacement at a given joint, respectively. In the literature, the effects of segmental joints on tunnel lining behavior are usually considered in both indirect and direct meth- ods. As far as indirect methods are concerned, the tunnel structure is perceived as a rigid lining ring embedded on a continuous ground model (Muir Wood, 1975; Einstein and Schwartz, 1979; Duddeck and Erdmann, 1985; Takano, 2000). The effect of joints is usually taken into account through a reduced rigidity of the tun- nel structure. The ground–structure interaction is usually consid- ered by means of so-called bedded ring models, in which the ground reaction is taken into consideration by means of discrete springs according to Winkler’s theory (e.g. Schulze and Duddeck, 1964). These simplified analytical methods can neither take into 0886-7798/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tust.2013.03.008 ⇑ Corresponding author. Tel.: +33 476 635135; fax: +33 4 76 82 52 86. E-mail address: daniel.dias@ujf-grenoble.fr (D. Dias). Tunnelling and Underground Space Technology 37 (2013) 115–127 Contents lists available at SciVerse ScienceDirect Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust