Fitting Function for Flexural Strength of Cement Paste

Abstract

There are many analytical expressions for compressive strength as functions of porosity of cement-based materials but only a few such expressions exist for flexural strength of these materials. In the present paper a new functional candidate for fitting the data of flexural strength of hydrated Portland cement paste has been tested. The functional candidate has been initially derived for porous polymeric materials on the basis of the percolation theory. The parameters of this function have been optimized for the cement paste by using the Levenberg-Marquardt iterative fitting procedure. The optimized function has been capable of accurate reproducing all the measured flexural data. This fact has been confirmed by a high value of the correlation coefficient and rather low values of statistical uncertainties. It has been shown that this modified fitting function is well applicable to the pastes of ordinary Portland cements and probably to other cementitious materials, too.There are many analytical expressions for compressive strength as functions of porosity of cement-based materials but only a few such expressions exist for flexural strength of these materials. In the present paper a new functional candidate for fitting the data of flexural strength of hydrated Portland cement paste has been tested. The functional candidate has been initially derived for porous polymeric materials on the basis of the percolation theory. The parameters of this function have been optimized for the cement paste by using the Levenberg-Marquardt iterative fitting procedure. The optimized function has been capable of accurate reproducing all the measured flexural data. This fact has been confirmed by a high value of the correlation coefficient and rather low values of statistical uncertainties. It has been shown that this modified fitting function is well applicable to the pastes of ordinary Portland cements and probably to other cementitious materials, too.