Title: History of a Mathematical Model for Strength Development of Portland Cement Concrete

Author(s): Sandor Popovics

Publication: Materials Journal

Volume: 95

Issue: 5

Appears on pages(s): 593-600

Keywords: compound composition; concretes; mathematical model; mortar; strength; portland cement;

DOI: 10.14359/401

Date: 9/1/1998

Abstract:
This paper is an organized summary of a dozen publications the writer produced on modeling the strength development of portland cement during the past forty years. It appears that this mathematical model performs better and within wider limits than other cement models for strengths. Since the earlier papers were published in various places, mostly abroad, it seems worthwhile to present a condensed summation of the development and capabilities of the exponential model. The most recent, most advanced form of the model is presented in the first part of the paper. The main features of this form are: it consists of two hardening components: C3S and everything else, mostly C2S; with the two components developing strength independently at different rates; C3A acts as a catalyst on the strength development of the two hardening components; the model needs only two experimental parameters with which the model is applicable to all portland cement types, a wide range of curing temperatures, and age between 1 day through 1 year or more; the process of strength development is divided into three stages: the zeroth stage which is the period immediately after mixing; the first stage when the hydration is controlled by the rates of chemical reactions; and, the second stage where the hydration is controlled by a diffusion mechanism. The steps leading to the present form of the model are illustrated in the second half of the paper, mostly for educational purposes but also because they provide insight into the roles of the cement compounds in strength development. The support of the model by comparison with experimental data is demonstrated by several examples.