Stereological Principles of Spatial Modeling Applied to Steel Fiber-Reinforced Concrete in Tension

Abstract

Mechanical properties of steel fiber-reinforced concrete (SFRC) partly depend on the dispersion characteristics of the micro-reinforcement. The established theory of geometrical probability (integral geometry, stereology) offers a straightforward approach to spatial modeling of fibers reinforcing a leading crack in concrete. These theoretical principles are introduced, discussed, and applied to SFRC in tension, yielding general expressions for fiber contributions to stress transfer over the leading crack for the ultimate as well as the post-ultimate domain. This involves fiber anisotropy due to fiber reorientation resulting from filling the mold and compaction, and from slenderness of the specimens. The expressions could be elaborated using the same methodological approach for specific cases of fiber geometry and type as well as mechanics of stress transfer. Global three-dimensional information on actual fiber structures in experimental approaches should be obtained by quantitative image analysis. It is demonstrated by elaborating the necessary analytical framework that the sampling and data collection strategies are based on the same stereological principles. Finally, economic and reliable approaches are discussed based only on vertical sections or only on X-ray projections of vertical slices.