Using topology optimization in tunnel reinforcement design

In tunnel reinforcement design, having a suitable tool which is able to capture complex ground material and various tunnelling conditions is definitely significant. Since early stages of tunnelling engineering, empirical approaches using rock mass classification and accumulated experiences have been commonly used. Nevertheless, as developed from long-term accumulated knowledge in older projects, it is not always applicable to new ground conditions and also hardly guarantees a best design to be obtained. Analytical method is another tool to provide explicit calculations, however, its applications are limited to only some simple scenarios such as circular tunnel. It is also noted that these two approaches are only applicable to free-field conditions. Owing to the ability in modelling complex ground conditions with consideration of discontinuities or adjacent structures, numerical simulations has been constantly developing and applying in tunnel excavation design in the last decades. An appropriate incorporation of numerical analysis and optimisation techniques, if applicable, would provide a powerful tool for obtaining an optimal tunnel design. In spite of effectiveness of topology optimisation theory, which is proved to work effectively in a broad range of engineering disciplines, its applications in geotechnical engineering and specifically in tunnelling design is fairly humble. Some research works have already attempted to incorporate topology optimisaton techniques in tunnel reinforcement design and proposed some initial achievements in the area. However, simple assumptions on the material models and modeling techniques of geomaterials and reinforcement materials have essentially limited its applications and practicality in a complicated structure like underground excavations. This thesis explores the incorporation of topology optimisation methods in tunnel reinforcement design. The main focus of the study is to improve some critical shortcomings of the previous works on reinforcement optimisation and propose new optimisation algorithms in searching for the best distribution of reinforcement material. As the first step in this study, material nonlinearities are accounted for in optimization techniques to improve the linear elastic material model assumption of previous studies. Practical behaviours of material, hence, can be captured. The Bidirectional Evolutionary Structural Optimisation (BESO) method is extended to consider nonlinear material behaviour. An elastic perfectly-plastic Mohr-Coulomb model is utilised for both host ground and reinforced material. External work along the tunnel wall is considered as the objective function. Various in situ stress conditions with different horizontal stress ratios and different geostatic stress magnitudes are investigated through several examples. The outcomes show that the proposed approach is capable of improving tunnel reinforcement design. Also, significant difference in optimal reinforcement distribution for the cases of linear and nonlinear analysis results proves the importance of the influence of realistic nonlinear material properties on the final outcome. Another serious shortcoming of the previous studies is that reinforced areas were modelled as homogenised isotropic elements. Optimisation results, therefore, do not clearly show reinforcement distributions, leading to difficulties in explaining the final outcomes. In order to overcome this deficiency, a more advanced modelling technique in which reinforcements are explicitly modelled as truss elements embedded in rock mass media is employed. Corresponding optimization algorithm are proposed to seek for an optimised bolt layout. Also, a topology optimisation technique is employed to simultaneously optimise all bolt parameters including pattern for bolts, spacing between the bolts and size of the bolts. The external work along the opening is selected as the objective function with a constraint on volume of bolt. To demonstrate the capabilities of the methods, numerical examples of nonlinear material models are presented. Various tunnelling characters and geological conditions with presence of discontinuities in the host rock have been successfully investigated in numerous examples, showing the broad applicability and usefulness of the proposed approaches. In reality, minimisation of certain displacements such as heave issues or ground displacements in shallow tunnel is sometimes of concern. Extending optimization methods to capture these objective functions is crucial. A general displacement-based objective function is introduced with a constraint on a bolt volume. Sensitivity analysis is conducted and details on identification of necessary parameters are provided. Using the presented optimisation algorithm, an example on optimizing bolt layout to minimise a heave function is performed. It is shown that the displacement-based objective function can be effectively captured by the proposed optimisation technique. This study focuses on applying topology optimisation in tunnel reinforcement design to take advantage of both numerical analysis and optimisation methods. The presented techniques are applicable to any material models of host ground and reinforcements and provides clear and practical final outcomes. Using the proposed methods, all significant factors including geological conditions, construction sequences and tunnel characters can be taken into account to obtain an optimised reinforcement distribution. It is also demonstrated that various objective functions can be employed and usefully optimised by the methods. The obtained results proves that the optimisation techniques presented in this thesis are promising tools to reinforcement design of underground excavations.