A stochastic mixing model for fibre distribution in fibrereinforced concrete and its implications (2026)

The spatial distribution of fibres can be effectively described using stochastic models. Under normal-consistency concrete conditions, fibre orientation may be assumed to be random; however, in the vicinity of the formwork, a certain degree of preferential alignment can be observed.
The most widely used method for determining material parameters is the three-point bending beam test. Owing to the small reference cross-sectional area, this test exhibits considerable scatter in the measured results. This variability is predominantly governed by the number and spatial position of fibres intersecting the fracture section. From a probabilistic viewpoint, this scatter is largely a statistical consequence of the limited fracture surface and the stochastic nature of fibre dispersion, rather than solely a material inconsistency. During evaluation, incorporating the fibre moment contribution leads to material parameters that are more representative of actual structural behaviour.
In real structural elements, the flexural load-bearing capacity of a cross-section is mainly governed by the same two factors, namely the number and position of fibres within the section. As the cross-sectional area increases, the relative statistical variability decreases, and the behaviour approaches the deterministic limit defined by the mean fibre distribution. Moreover, on site fibre dosage control can be performed by evaluating measured fibre counts against a confidence interval derived from a stochastic mixing model at a prescribed confidence level. To address these aspects, this paper introduces a novel stochastic mixing model for fibre distribution and demonstrates its applicability to material parameter evaluation, structural capacity assessment, and on-site quality control.