Cauchy-based modelling in cementitious materials technology

Abstract

Cauchy paved the way for constructing models in concrete technology, and elsewhere. He determined the (non-flat) surface area in 3D by measuring random total projections. Analogously, he determined the length of a curved line in 2D by way of measuring the total projections. The paper will present the mathematical expressions, because in many branches of concrete technology, modelling is found based on such Cauchy concepts. These branches - fractography in compression, tension or shear, fibre reinforcement and permeability estimation - will briefly be mentioned to demonstrate this. It has been found that, for the discussed fields of engineering relevance, major model parameters for cementitious materials are similar to those developed by Cauchy in the 19th century. In the paper some previous investigations concerning fractography, fibre reinforcement and fracture roughness will be summarized but basically a new development on porosimetry will be presented. Particularly a new achievement of successful implementation of the methodology (also based on Cauchy) for optimizing permeability estimation will be discussed.