Adaptive Discontinuity Layout Optimization

Discontinuity layout optimization (DLO) is a powerful tool for determination of collapse loads and mechanisms of structures, frequently employed to investigate the performance of masonry, geotechnical, and load-carrying structures. Nevertheless, in contrast to other numerical analysis methods, such as e.g. the finite element method, continuous refinement of the underlying discretization was found to not necessarily improve the obtained results. In contrary, the refined arrangement of discontinuities in DLO yields to so-called zic-zac failure mechanisms leading to artificially increasing failure loads in the course of refinement. As a remedy, error-estimation based and adaptive techniques are proposed in this research project. This extension of DLO towards adaptive DLO shall allow to (i) obtain results meeting a user-prescribed accuracy and (ii) minimize computational cost. For this purpose, error estimators standardly used in other numerical analysis methods will be reviewed and adapted to the special situation encountered in limit analysis, characterized by plastic-flow vectors serving as unknown quantities. Within error estimation, an improved solution may be found by appropriate smoothing techniques. Based on the estimated error, the underlying discontinuity layout (discretization in DLO) shall be adapted, aiming at a user-prescribed accuracy of the numerical results. The developed error estimation and adaptation procedure shall be implemented in the three-dimensional (3D) formulation of DLO, allowing application of the tool to three-dimensional geotechnical problems and, finally, to material systems characterized by matrix-inclusion morphologies. The benefits of the expected findings are twofold: on the one hand, the anticipated procedure shall provide insight into the quality of results obtained from limit analysis and ways to improve these results by adaptation of the underlying discretization. On the other hand, the planned 3D formulation of adaptive DLO shall make 3D simulation of material systems possible. Without elimination of inactive discontinuities within the proposed research project inactive discontinuities should be removed and employing uniform refinement of the discretization which not necessarily improves the results 3D simulation of material systems is not possible. With the anticipated adaptive analysis tool at hand, a wide range of possible research endeavors shall become possible, focusing on failure load and mechanisms of structures and material systems. As regards the latter, refined insight into the origin of strength properties, especially the amount of scatter and the beneficial effect of fillers and fibers are of growing interest.

Discontinuity layout optimization (DLO) is a recently presented numerical procedure for determining the limit load and failure mechanism of structures. By introducing a great amount (over millions) of potential discontinuities into the domain and automatically generating a set of activated discontinuities corresponding to the upper bound limit load, this method has a great advantage over other limit analysis methods, because of the wide search space provided by the DLO being directly related to the quality of the results.Within this project, two main achievements as regards the improvement and extension of the DLO were obtained as follows:1. The three-dimensional discontinuity layout optimization (3D DLO) was introduced.Despite of the great success of the two-dimensional DLO (2D DLO), the 3D DLO is not well studied and applied in the open literature, mainly due to its complexity and non-linear programming nature. Aiming at the elimination of unnecessary discontinuities in 3D DLO and adaptively searching the optimal solution for reducing the computing effort, a multi-slicing strategy and a corresponding grid search procedure was successfully implemented, paving the way for the analysis of large- scale engineering problems with 3D DLO.2. The combination of DLO with multi-field analysis techniques represents the second achievement as regards the extension of DLO within the project. Hereby, a realistic hydration model for shotcrete was combined with the convergence-confinement method, enabling the application of 2D DLO for the numerical assessment of the stability of shotcrete-supported shallow tunnels built with the New Austrian Tunnelling Method (NATM). Based on the numerical approach, the effect of tunnelling parameter (driving speed, excavation steps, ) and material properties (shotcrete, soil) on the stability of tunnels can be evaluated, finally enabling the optimization and safety improvement of the tunnel excavation process. The successfully established extension of the DLO to multi-field problems highlights the potential of the methods, being well-suited for the solution of practical engineering problems.