Mesoscale simulation based optimization of fibre distribution and orientation in UHPFRC beams

The high cost of a large number of uniformly distributed and randomly oriented high-strength steel fibres severely limits the applicability of ultra high performance fibre reinforced concrete (UHPFRC) to engineering structures. In this study, two types of mesoscale modelling based optimization algorithms are proposed and applied to optimize the fibre orientation and distribution in UHPFRC beams to reduce the total amount of steel fibres. The first algorithm heuristically distributes fibres in regions with high tensile stresses only with their orientations parallel to the principal tensile stresses, considering that the steel fibres contribute little to the compressive strength but significantly to the tensile and flexural strength of UHPFRC beams. The second method optimises the beams’ topology into strut-tie models using algorithms such as SIMP and BESO and then adds steel fibres oriented longitudinally in the tensile ties. The load-carrying capacity and failure process of the optimised beams are then simulated and assessed using a meso-scale finite element modelling approach recently developed by the authors. Based on the results of steel-bar reinforced UHPFRC beams under 3 or 4-point bending, it was found that the usage of steel fibres could be reduced by up to 60 %, and the amount of UHPC and cement could be reduced by up to 50 %, respectively, without sacrificing the load-carrying capacities of the beams compared with the beams with uniformly distributed and randomly oriented fibres.