A stereological approach to estimation of fibre distribution in concrete

Abstract

Steel fibre reinforced concrete (SFRC) continues to gain popularity as a sustainable construction material with enhanced strength and durability properties. These mechanical properties are dependent on the distribution and orientation of steel fibres achieved during casting, the determination of which is challenging. Three-dimensional X-ray micro-CT scanning is currently the only technique that yields the true three-dimensional (3D) dispersion of fibres, but the technology is applicable only to small samples at laboratory settings. In this study, a mathematical framework is developed to utilize 2D probing, like X-ray projectional radiography, which is more practical for in situ nondestructive characterization of fibre dispersion in SFRC members. For the first time, fibres are treated as finite-sized inclusions, developing the appropriate mathematical formulations consistent with published research in the field of stereology and practically applying them to digitized X-ray projected images of SFRC and UHPFRC. Stereological principles were employed to establish the volume fraction of fibres (3D property) from their areal fraction in images. The method was developed and tested for both X-ray slices and projected images. Tests were performed on UHPFRC cores as well as SFRC dogbones with different nominal fibre dosages. It is shown that accurate estimation of fibre volume fraction and their spatial distribution can be robotically achieved from 2D imaging using the developed algorithms. The influence of parameters such as fibre geometry and thickness of structural members on the applicability of the stereological equations and accuracy of estimated results is investigated, with a comprehensive discussion of the stereology approach.