Tunnel reinforcement via topology optimization

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 difficult. 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 finite-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 capabilities 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 (C) 2000 John Wiley & Sons, Ltd.