Orientation of short steel fibres in concrete: measuring and modelling

This research focuses on a cementitious composite formed by mixing of concrete matrix with short steel fibres, SFRC. This composite is quite extensively employed in the construction industry, for example in floors resting on soil and even in some load-bearing structures, such as floor-slabs. The complexity of SFRC is the presence of the anisotropic behaviour occurring due to different alignments of short fibres. The examinations performed comprise two research branches: measuring of fibre orientations from the hardened concrete matrix and modelling of composite properties considering the orientation distribution of fibres. Two methods of measuring fibre orientations are developed: slicing method and X-ray micro-tomography. Parts extracted from the full-size floor-slabs are used as samples. The slicing with photometry approach is improved by DC-conductivity testing joined with image analysis. X-ray micro-tomography is performed on sufficiently large samples and the orientation of fibres is specified by the analysis of 3D voxel images of scanned fibres. The received measuring results proved that both DC-conductivity testing combined with photometry and X-ray micro-tomography have high accuracy and they can be applied in defining fibre orientations from real concrete samples reliably. The material model developed for one meso-volume element of SFRC is based on an orthotropic hyperelastic material model where the second-order terms of the strain energy function are employed resulting in orthotropic St. Venant-Kirchhoff model. The orthotropic meso-symmetry of the composite is modelled by the structural tensors based on the eigenvectors of the second-order alignment tensor, which represent the dominating alignment of fibres. The material model developed for SFRC consists of an isotropic part presenting the concrete and the orthotropic part including the influence of short steel fibres. The orientation distribution function of fibres is utilized to evaluate the orthotropic effect in the defined material symmetry directions. The advantage of the material model developed is that it uses the full orientation information of fibres and employs tensor quantities, which are independent of any reference frame. Finally, the implementation of the model is demonstrated by examples based on fibre orientations measured from test samples.