Numerical analysis on the interaction of shotcrete liner with rock for yielding supports Hongming Tian a , Weizhong Chen a,b , Diansen Yang a,⇑ , Guojun Wu a , Xianjun Tan a a State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, China b Research Centre of Geotechnical and Structural Engineering, Shandong University, Jinan, Shandong 250061, China article info Article history: Received 20 July 2015 Received in revised form 11 January 2016 Accepted 22 January 2016 Keywords: Yielding supports Liner–rock interaction Highly deformable element Damage of the liner abstract The yielding supports have been successfully used in excavation in squeezing rock. For yielding supports the shotcrete liner is often divided into several segments, and the HDEs (highly deformable elements) are installed between the segments. Compared to the shotcrete, HDEs have a considerably lower compressive strength and a higher deformation ability. To study the influences of HDEs on the liner–rock interaction, a number of numerical analyses were conducted. In all of these numerical analyses, an interface model that can reflect the failure behaviour of the liner–rock interface was employed. According to the numerical results, after the installation of the HDEs, the compressive and shear failures of the liner decrease sharply; however, obvious shear failure on the liner–rock interface and tensile failure of the liner are observed, which may result in the liner failing to provide sufficient support load. In this condition, reinforcement of the TH profile steel sets, which can decrease the shear failure of the liner–rock interface and the tensile failure of the liner, is suggested instead of thickening the shotcrete liner. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction When tunnelling in squeezing rock masses, large deformations of rock masses are likely to occur, and attempts to stop these defor- mations using stiffer support have always failed (Kimura et al., 1987). In this condition, a yielding support that is able to deform with the rock is suggested to be used (Cantieni and Anagnostou, 2009). For the yielding support, the shotcrete liner is divided into several segments with gaps between them. The gaps are filled with HDEs (highly deformable elements), such as timber blocks, honey- comb sets, highly deformable concrete or foamed concrete (Schubert, 1996; Thut et al., 2006; Podjadtke, 2009; Tian et al., 2012). The compressive strength of the HDE is considerably lower than that of shotcrete, while the deformable ability of the HDE is much greater than that of shotcrete. After the installation of the HDEs, the deformation of the rock is supposed to be absorbed by the HDE to avoid damaging the liner. When the ground pressure decreases to a lower level with the deformation of the rock, the gaps of the liner will be closed, either by deformation of the HDEs or by filling them with shotcrete. Then, the liner will establish suf- ficient support resistance to the rock. Many studies have been conducted to investigate the character- istics of yielding supports. Cantieni and Anagnostou (2009) studied ground-yielding support behaviour by means of spatial numerical analyses that considered the stress history of the ground. Rodríguez and Díaz-Aguado (2013) analysed the characteristic curve of yielding steel ribs based on the convergence- confinement method. Gschwandtner and Galler (2012) studied the influence of the time-dependent behaviour of shotcrete on the characteristic curve of liner with yielding elements. These studies are based on the assumption that the deformation of rock mass has not caused damage to the shotcrete of the yielding sup- ports, and the failure of the liner is ignored. Previous studies showed that the interaction of the shotcrete liner with rock mass is dependent not only on the mechanical properties of the shotcrete and the rock mass, but also on the beha- viour of the interface between the shotcrete liner and the rock (Bae et al., 2004; Malmgren and Nordlund, 2008; Lee, 2010; Zhang, 2013). When HDEs are introduced to the shotcrete liner, the thrust transmission of the liner will decrease (Schubert, 1996), and the shear stress of the interface between the liner and the rock may increase. Although the effect of the HDEs on the bending moment and the axial thrust of the liner has been investigated (Barla et al., 2011), the effect of the HDEs on the failure behaviour of the liner– rock interface has rarely been studied. To improve the understanding of the interaction of shotcrete liner and rock for yielding supports, a numerical analysis was con- ducted. In the numerical analysis, a model that can describe the failure behaviour of the interface between liner and rock was http://dx.doi.org/10.1016/j.tust.2016.01.025 0886-7798/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: hmtian@whrsm.ac.cn (H. Tian), dsyang@whrsm.ac.cn (D. Yang). Tunnelling and Underground Space Technology 54 (2016) 20–28 Contents lists available at ScienceDirect Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust