Bridging the gap between structural levels in concrete technology – Principles of geometric averaging

Abstract

Research on cementitious materials can provide geometric data on structural topics of interest. Such structural data should be subjected to a process called “geometric averaging” to be coupled on the engineering level with properties like strength, stiffness or permeability. The prime purpose of this work is to demonstrate that the mathematics underlying the process of going from the materials structure to engineering properties is governed by simple stereology-based constants. Particularly, Cauchy concepts are referred to for expressions relating the length of a curved line in a plane or in space, alternatively of a curved surface in space, to extensions of total projections on lines, respectively planes, in random directions. The two parameters due to Cauchy, i.e., 2/π and 1/2 will be demonstrated dominantly governing the geometric averaging process. The stereological methodology to assess the geometric material parameters and the engineering application of the outcomes are also briefly touched upon in the paper.