Simultaneous pattern and size optimisation of rock bolts for underground excavations

Designing a rock bolt reinforcement system for underground excavation involves determining bolt pattern, spacing, and size. In this paper, a topology optimisation technique is presented and employed to simultaneously optimise these design variables. To improve rock bolt design, the proposed technique minimises a displacement based function around the opening after bolt installation. This optimisation technique is independent of the material model and can be easily applied to any material model for rock and bolts. It is also extremely flexible in that it can be applied to any mechanical analysis method. To illustrate the capabilities of this method, numerical examples with non-linear material models and discontinuities in the host rock are presented. It is shown that the complexity of systems optimised using this approach is only restricted by limitations of the method used to analyse mechanical system responses.