Overestimation of the interface thickness around convex-shaped grain by sectional analysis

Sectional analysis is commonly used to characterize qualitatively and quantitatively the interfacial transition zone (ITZ) of concrete, especially its thickness. However, the normal of the sectioning plane is in general not perpendicular to the normal of the aggregate surface due to the irregularity of the shape of the aggregates. Therefore, the sectional approach overestimates ITZ thickness. Calculating the degree of overestimation is key to obtain a precise measure of ITZ thickness and therefore the influence of the ITZ on the macro-properties of composites. However, the irregularity of the aggregates makes this a difficult task. In this contribution, some related theorems and results from geometrical probability were used to study the relationship between the statistical value of the apparent ITZ thickness and actual ITZ thickness. General solutions are derived for an arbitrary convex-shaped aggregate grain for both two- and three-dimensional cases.