Spatial characterization of joint planes and stability analysis of tunnel blocks Shuhong Wang a,⇑ , Pengpeng Ni b,⇑ , Mudan Guo a a Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, College of Resources and Civil Engineering, Northeastern University, Shenyang 110819, China b GeoEngineering Centre at Queen’s – RMC, Queen’s University, Kingston, ON K7L 3N6, Canada article info Article history: Received 20 June 2012 Received in revised form 15 April 2013 Accepted 19 July 2013 Available online 17 August 2013 Keywords: Statistical joint modelling Digital photogrammetry Block theory Tunnel Stability analysis Limit equilibrium abstract It has been gaining credence over the past several decades that the spatial characteristics of rock joints exert detrimental effect on the stability of tunnel structures. The deterministic joint spatial distribution around the tunnel was defined by digital photogrammetry technique, which statistically provides the basis for performing Monte-Carlo simulation of stochastic joints that are hidden inside the surrounding rock. The blocks generated by the intersection between structural planes and excavation surfaces were analyzed based on the block theory and limit equilibrium. The keyblocks were identified and the corresponding factors of safety were determined. All these analysis procedures were codified into the computer program GeoSMA-3D (Geotechnical Structure and Model Analysis). The developed software satisfied the fast analysis requirements of joint plane simulation, spatial block modelling, keyblock identification and failure process illustration. The case study was performed with reference to Dabeigou Tunnel on Duolun Second-class Highway in Duolun Town, Nei Mongol, China. Failure process illustration would be useful to facilitate the practical engineers to understand the basic mechanism and select the strengthening strategies. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The safety of the tunnel during excavation process is of para- mount importance. Some tunnels are not necessarily designed with the installation of the systematic support, where the acciden- tal falling of rock blocks is the primary problem. Therefore, the support strategies for specific location should be performed. Most of the support design guidelines for tunnel are based on the empir- ical formulations. Typically, either the rock/soil types or Rock Mass Rating (RMR) values will govern the design (Bieniawski, 1973; Barton et al., 1974; Hoek, 1994). However, both stress- and struc- ture-induced failures are always neglected in practice (Wang, 2000). In order to prevent the catastrophic tragedy due to the incorrect judging of keyblock, removability analysis should be con- ducted on the rock blocks based on a precise characterization of joints by block theory (Goodman and Shi, 1985). Block theory is powerful in terms of fast analyzing rock blocks around underground openings created by the intersection of the tunnel surface and joints in the rock mass. The stability of rock is controlled in a sense by the characteristics of blocks, i.e. the size, orientation, persistence and shapes of the discontinuities, especially the keyblock for a given excavation geometry. The removable blocks as well as the possible occurring boundary limit can be distinguished by limit equilibrium theory (Mauldon et al., 1997). Warburton (1981) proposed the assumptions of rigid block located in fixed body of rock to perform computational analysis of a single three-dimensional rock block. The rigid block is bounded by the intersections of flat discontinuities and excavation surfaces, which is the common situation in practice. However, the limitation of such methodology is that the block can only move in transla- tional direction. Neglecting the rotational deformation will lead to less accurate results. A block fracturing algorithm has been pro- posed by Lin et al. (1996), incorporating the tension cut-off concept into Mohr-Coulomb criterion where the newly formed discontinu- ities are introduced and are further treated in the same way as the original discontinuity planes. The spatial modelling of discontinuities, such as distribution in terms of orientation, spacing, persistence and shape, exerts signif- icant effects on the accurate estimation of keyblock (Hatzor and Goodman, 1992). Chan and Goodman (1987) adopted Baecher disc model (Baecher et al., 1977) to compute the average number and volume of removable blocks, where log-normal distributed circular joint diameters and fixed orientations of joint sets are assumed. Similarly, instead of log-normal distribution, bivariate normal dis- tribution of joint orientation has been proposed by Hoerger and Young (1990) to analyze block stability. Shapiro and Delport (1991) used Monte-Carlo methods and simulation to analyze 0886-7798/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tust.2013.07.017 ⇑ Corresponding authors. Tel.: +86 24 31883594 (S. Wang), tel.: +1 613 483 2561 (P. Ni). E-mail addresses: wangshuhong@mail.neu.edu.cn (S. Wang), pengpeng.ni@ce. queensu.ca (P. Ni). Tunnelling and Underground Space Technology 38 (2013) 357–367 Contents lists available at ScienceDirect Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust