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Uncertainty in Bogue-Calculated Phase Composition of Hydraulic Cements



Paul E. Stutzman


The Bogue calculations of cement composition are used for manufacturing process control and cement classification. While it is commonly understood that the Bogue calculations are estimates with potential intrinsic biases, the magnitudes of such biases are not known. Using biased formulas can adversely affect cement classification and relationships between performance and phase composition. The biases stem primarily from the compositional variation due to the phase solid solution, resulting in deviation of their bulk chemistry form that is assumed in the calculations, and bulk oxide measurement uncertainties. Uncertainties in Bogue estimates from these sources are quantified here through propagation-of-error analysis combining effects from bulk chemical analysis imprecision and variability in chemical compositions of the four principal clinker phases. As an illustration of the utility of the method, the uncertainties introduced by using different commonly assumed bulk chemical analysis methods by the reference chemical analyses and X-Ray fluorescence using pressed powders and fused glass are assessed relative to the new overall measurement uncertainties. While the quantifiable errors of the reference and the X-ray fluorescence methods are slightly different, the Bogue-calculated compositions based on data from the three methods are similar. When compared to earlier studies on the effects of bulk oxide measurement uncertainties, the uncertainties in the phases that are contributed by the Bogue formulation — 1σ values of about 9.6 % for alite and belite, and 2.2 % and 1.4 % for aluminate and ferrite — reflect a significant increase, attributable to the imprecision of the Bogue constants. These results suggest that cement phase fraction estimate uncertainties should be cited along with the phase estimates themselves.
Cement and Concrete Research


Stutzman, P. (2014), Uncertainty in Bogue-Calculated Phase Composition of Hydraulic Cements, Cement and Concrete Research, [online], (Accessed July 25, 2024)


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Created July 1, 2014, Updated November 10, 2018