INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech., 24, 201 } 213 (2000) TUNNEL REINFORCEMENT VIA TOPOLOGY OPTIMIZATION LUZHONG YIN, WEI YANG* AND TIANFU GUO FML, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China SUMMARY Anchoring is a fundamental method for supporting tunnels. It reinforces the original rock mass and reduces the deformation along the tunnel surface. The topological complexity of its layouts renders a design methodology di$cult. A numerical approach to reinforce the host ground becomes desirable. The present paper proposes a topology optimization method based on a two-phase cell model and "nite-element discretization of the host ground. The element consists of the original rock and the reinforcing material. The design issue involves the distribution of the reinforcing materials. The relative ratios of the two phases in various elements will be optimized to reduce the compliance of the tunnel. The method enables the computer-aided design for the support of underground structures. The capabili- ties of the method are demonstrated by the designs to support a deep tunnel under various in situ stresses. The results indicate that oriented reinforcement is needed along the direction of the largest absolute value of the principal stress. Copyright  2000 John Wiley & Sons, Ltd. KEY WORDS: tunnel reinforcement; topology optimization; two-phase cell; "nite elements; compliance 1. INTRODUCTION Supports for an excavation can be divided into two classes: passive support and active support, the latter emphasizes the use of ground itself. A fundamental form of active support is through rock bolts. The idea that the host ground and support structures share the full load, and the host ground takes a major share of the load stimulates the emergence of the active support methodo- logy. Lang and Bischo!  pioneered the designs of excavations that are based on the rock}bolt reinforcement of the rock mass. Bischo! and Smart introduced a concept in which the use of rock}bolt reinforcement creates a uniform additional pressure on rock that is equivalent to that taken by steel ribs. The U.S. Army discussed the design of rock bolts from a joint friction approach. Cording and Deere introduced the concept of &internal pressure' for the design of rock bolts to support a sliding critical wedge. A loosing zone theory based on the use of rock bolts is suggested by Dong et al. Nowadays designs of anchoring are still based on the past experiences or on the empirical recommendations. Fairhurst pointed out that a partial reinforcement is preferred over a uniform one to stabilize the ground more e$ciently. The ways of partial reinforcement are obviously * Correspondence to: Professor Wei Yang, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China. E-mail: yw-dem@mail.tsinghua-edu.cn Contract/grant sponsor: National Naval Science Foundation of China CCC 0363}9061/2000/020201}13$17.50 Received 18 June 1998 Copyright  2000 John Wiley & Sons, Ltd. Revised 1 February 1999; 21 April 1999