INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. (2013) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nag.2202 Layout design of rockbolts for natural ground reinforcement Junji Kato 1, * ,† , Keiichiro Ishii 2 , Kenjiro Terada 1 and Takashi Kyoya 2 1 International Research Institute of Dissaster Sceience, Tohoku University, Aramaki-Aoba 6-6-06, Aoba, Sendai, 980-8579, Japan 2 Mechanics of MaterialsLaboratory, Tohoku University, Aramaki-Aoba 6-6-06, Aoba, Sendai, 980-8579, Japan SUMMARY The present study addresses a layout design of rockbolts for reinforcing natural ground structures applying a special optimization method, called multiphase layout optimization. Rockbolts are used to tighten loosed natural ground, and the layout of rockbolts are determined without sufficient information about the physical properties of the ground materials. Because of this uncertainty, unexpected deformation often occurs at the excavation surface of natural ground. In that case, it is requested to determine an effective layout of the additional rockbolts promptly with respect to the actual deformation at the construction site. However, it is not easy to determine the optimal layout because of its complexity, and consequently, it has no choice but to determine the layout in an empirical way. This study introduces a numerical approach to determine an optimal layout of rockbolts with respect to arbitrarily possible deformation of natural ground. The objective is to maximize the stiffness of the over- all ground structure reinforced with rockbolts. For optimization, a gradient-based optimization scheme is applied because of its numerical efficiency. It was verified from a series of numerical examples that this method has great potential to improve the stiffness of the overall ground structure and shows a certain applicability to a practical design. Copyright © 2013 John Wiley & Sons, Ltd. Received 13 February 2013; Revised 28 April 2013; Accepted 29 April 2013 KEY WORDS: multiphase layout optimization; rockbolts; reinforcement; NATM; reinforced slopes 1. INTRODUCTION Rockbolt tunnel support has been widely employed in the New Austrian Tunneling Method (NATM), the representative construction method for building tunnels. The mechanism for reinforcing natural ground is to integrate the ground by the tensile strength of rockbolts cast into the ground and to increase the stiffness of the integral structure to prevent collapse of the natural ground. Although much experience has been accumulated with rockbolt tunnel support, the problem in designs is how to determine the layout of the rockbolts without sufficient information about the physi- cal properties of the ground material. For instance, with regard to the NATM, as it is difficult to obtain the material properties of natural ground that stands apart from the reclaimed surface, the usual method for determining the layout is to roughly classify the natural ground by using the insufficiently known physical properties of the ground materials and then to choose the most suitable layout pattern for the conditions from the standard layout patterns of tunnel support systems determined by past experience and performance. In the layout patterns, called ‘the standard layout patterns of tunnel support system’, the rockbolts are cast into natural ground with the same length, placed radially with equal spacing, and are said to present an effective layout against isotropic ground pressure. *Correspondence to: Junji Kato, International Research Institute of Dissaster Sceience, Tohoku University, Aramaki- Aoba 6-6-06, Aoba, Sendai, 980-8579, Japan. † E-mail: jkato@civil.tohoku.ac.jp Copyright © 2013 John Wiley & Sons, Ltd.