Tunnel roof deflection in blocky rock masses as a function of joint spacing and friction – A parametric study using discontinuous deformation analysis (DDA) Michael Tsesarsky * , Yossef H. Hatzor Department of Geological and Environmental Sciences, Ben Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel Received 2 September 2004; received in revised form 15 February 2005; accepted 30 May 2005 Abstract The stability of underground openings excavated in a blocky rock mass was studied using the discontinuous deformation analysis (DDA) method. The focus of the research was a kinematical analysis of the rock deformation as a function of joint spacing and friction. Two different opening geometries were studied: (1) span B = h t ; (2) B = 1.5h t ; where the opening height was h t = 10 m for both configurations. Fifty individual simulations were performed for different values of joint spacing and friction angle. It was found that the extent of loosening above the excavation was predominantly controlled by the spacing of the joints, and only secondarily by the shear strength. The height of the loosening zone h r was found to be dependent upon the ratio between joint spac- ing and excavation span S j /B: (1) h r < 0.56B for S j /B 6 2/10; (2) stable arching within the rock mass for S j /B P 3/10. The results of this study provide explicit correlation between geometrical features of the rock mass, routinely collected during site investigation and excavation, and the expected extent of the loosening zone at the roof, which determines the required support. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Roof deflection; Discontinuities; Numeric analysis; DDA 1. Introduction Most rock masses are discontinuous over a wide range of scales, from macroscopic to microscopic. In sedimentary rocks the two major sources of discontinu- ities are bedding planes and joints, the intersection of which form the so-called ‘‘blocky’’ rock mass (Terzaghi, 1946). Excavation of an underground opening in a blocky rock mass disturbs the initial equilibrium, and the stres- ses in the rock mass tend to readjust until new equilib- rium is attained. During readjustment of internal stresses, and consequently rearrangement of load resist- ing forces, some displacements of rock blocks occurs. Joints and beddings are sources of weakness in the otherwise competent rock mass and therefore large dis- placements and rotations are only possible across these discontinuities. Failure occurs when the stresses can no longer readjust to form a stable, load resisting structure. This may occur either when the material strength is exceeded at some locations, or when movements of rock blocks preclude the development of a stable geometric configuration. Terzaghi (1946) in his rock load classification scheme estimated that for tunnels excavated in stratified rock the maximum expected over-break, if no support is in- stalled, is 0.25B to 0.5B, where B is the tunnel span. For tunnels excavated in moderately jointed rock the maximum expected over break is 0.25B. For tunnels 0886-7798/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2005.05.001 * Corresponding author. Present address: Faculty of Civil and Environmental Engineering, Technion, Israel Institute of Technology, Haifa 3200, Israel. Tel.: +972 4 8292462. E-mail address: michaelt@technion.ac.il (M. Tsesarsky). www.elsevier.com/locate/tust Tunnelling and Underground Space Technology xxx (2005) xxx–xxx Tunnelling and Underground Space Technology incorporating Trenchless Technology Research ARTICLE IN PRESS