HISTORY OF MATHEMATICAL-MODEL FOR STRENGTH DEVELOPMENT OF PORTLAND-CEMENT CONCRETE

This paper is a summary of a dozen publications the writer produced on modeling the strength development of portland cement during the past 40 years; It appears that this mathematical model performs better and within wirier limits than other cement models for strengths. Since the earlier papers were published in various places, mostly abroad, it se ems 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 There a re several main features of this form. First, it consists of two harde ning components: C3S and everything else, mostly C2S; with the two com ponents developing strength independently at different rates. Second, C(3)A acts as a catalyst on the strength development of the two harden ing components. Third, the model needs only two experimental parameter s with which the model is applicable to all portland cement types, a w ide range of curing temperatures, and age between 1 day through I year or more. Fourth, 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 con trolled by a diffusion mechanism. The steps leading to the present for m of the model are illustrated in the second half of the paper mostly for educational purposes but also because they provide insight into th e roles of the cement compounds in strength development. The support o f the model by comparison with experimental data is demonstrated by se veral examples.