Topology optimization for tunnel support in layered geological structures

Tunnel construction commonly proceeds in an environment of layered geological formation. Design for tunnel support relies on the tunnel location and the mismatch of di!erent layers. The present paper proposes a topology optimization method for the design of tunnel support. The design domain is discretized by "nite elements. An element is composed of the original rock (hard or soft) and the reinforcing material (rock reinforced by grouting or bolting). The design issue involves the distribution of reinforcements. We model the reinforced host ground by a power-weighted mixture law. The ratios of two phases in various elements are optimized to minimize the deformation of the tunnel. The method enables a computer-aided design for the supports of underground tunnels embedded within layered geological structures. The reinforced areas for the tunnel are displayed under the passive geological stress and the active external loading. Four kinds of rock formations are examined. They are homogeneous rock, hard}soft}hard (HSH) sandwich structure, two-layer structure with the soft rock at the top and the hard rock at the bottom (SH), and the one with the hard rock at the top and the soft rock at the bottom (HS). The simulation reveals the high e$ciency of tunnel support by optimizing its topologies.