New Approach to Determine the Activity Concentration Index in Cements, Fly Ashes, and Slags on the Basis of Their Chemical Composition

Abstract

The manufacture of Portland cement entails high energy and environmental costs, and various solutions have been implemented in recent years to mitigate this negative impact. These solutions include improvements in the manufacture of cement clinker or the use of supplementary cementitious materials (SCMs), such as fly ash (FA) or slag as a replacement for a portion of the clinker in cement. The incorporation of these SCMs in cement may increase its radiological content as they are naturally occurring radioactive materials (NORMs). The Activity Concentration Index (ACI) is a screening tool established in the European EURATOM Directive 2013/59 to determine the radiation protection suitability of a final construction material. The ACI is determined by the activity concentrations of ²²⁶Ra, ²³²Th and ⁴⁰K, usually determined by gamma spectrometry. The methodology of gamma spectrometry is accurate and appropriate, but this technique is not available in all laboratories. For this reason, and taking into account that there is a relationship between the chemical and radiological composition of these building materials, a new approach is proposed to determine the radiological content of these materials from a chemical analysis such as X-ray fluorescence (XRF). In this paper, principal component analysis (PCA) is used to establish the relationships between the chemical composition and radiological content of cements, FAs, and slags of different natures. Through PCA it was possible to group the cements based on two variables: CaO content and Fe₂O_3-Al₂O_3-TiO₂ content. A lower correlation was observed for the FAs and slags, as the sample scores were centered around the origin of the coordinates and showed greater dispersion than the cements. The clusters obtained in the HJ-Biplots allowed the determination, using multiple regression, of models relating the activity concentration of ²²⁶Ra, ²³²Th (²¹²Pb), and ⁴⁰K to the oxide percentages obtained for the three matrices studied. The models were validated using five cements, one FA and one slag with relative percentage deviations (RSD(%)) equal to or less than 30% for 89% of the activity concentrations and 100% of the ACI determined.

Keywords: HJ-Biplot; NORM; activity concentration index; cement; fly ash; slag.

Figure 1

Diagram of the statistical process applied to the activity concentrations and chemical compositions obtained by XRF.

Figure 2

Activity concentration ranges of the radionuclides belonging to the natural radioactive series of uranium (²³⁴Th, ²²⁶Ra, ²¹⁴Pb, ²¹⁴Bi, and ²¹⁰Pb) and thorium (²²⁸Ac, ²¹²Pb, and ²⁰⁸Tl) together with the ⁴⁰K, and chemical composition (in percentage of oxides) for the cements, FA and S analyzed in this study. The actinium (²³⁵U) series was not represented as all activity concentrations were below the lower limit of detection (LoD).

Figure 3

HJ–Biplot for the cements analyzed. The variables studied were CaO, SO₃, SiO₂, MnO, MgO, K₂O, Na₂O, TiO₂, Fe₂O₃, Al₂O₃, ²³⁴Th, ²²⁸Ac, ²²⁶Ra, ²¹⁴Bi, ²¹⁴Pb, ²¹²Pb, ²¹⁰Pb, ²⁰⁸Tl, and ⁴⁰K, represented as a vector. The scores of the cement samples were calculated from the weights of the studied variables. The cements were grouped into three sets according to their content: (a) CaO and SO₃; (b) Fe₂O₃, Al₂O₃, TiO₂, thorium series (²²⁸Ac, ²¹²Pb, and ²⁰⁸Tl) and uranium series (²³⁴Th, ²²⁶Ra, ²¹⁴Pb, and ²¹⁴Bi); and (c) Na₂O and ²¹⁰Pb. The correlations between the studied variables were established from the cosine of the angle they form between them. The groupings were established by means of confidence ellipses determined at a significance level α = 0.05.

Figure 4

HJ–Biplot for the analyzed FA. The variables studied were CaO, SO₃, SiO₂, MnO, MgO, K₂O, Na₂O, TiO₂, Fe₂O₃, Al₂O₃, radionuclides of the uranium and thorium series, and ⁴⁰K, represented as a vector. The 6 groups obtained are represented by their confidence ellipses and show high variability as they are distributed in the 4 quadrants. FA22 can be considered an outlier with respect to the other 5 sets of samples.

Figure 5

HJ–Biplot for the S analyzed. The variables studied were CaO, SiO₂, MgO, K₂O, Na₂O, TiO₂, Al₂O₃, radionuclides of the uranium and thorium series, and ⁴⁰K, represented as a vector. The KMO suitability index value obtained was 0.700. Most of the sample scores are centered on the origin of the coordinates, reflecting a lower correlation with the two factors found. Slags S9, which is strongly correlated with MgO, and S10, whose high uranium and thorium series radioisotope content distinguishes them from the rest of the samples analyzed, are the only exceptions.

Figure 6

Graphical representation of the activity concentration values of ²²⁶Ra, ²³²Th(²¹²Pb), and ⁴⁰K measured experimentally versus those estimated using the models obtained that relate the chemical composition of the cements to the activity concentration of the different radionuclides. The models explain more than 98% of the dispersion. The clusters depicted by the confidence ellipses in Figure 3 are shown in the same color at the represented points (dark blue for CAC, green for CEM I and white cements, and light blue for CEM I type cements with higher ²¹⁰Pb content). The comparison between the experimental and estimated values showed no significant differences, as the p-value for the paired t-test and Fisher’s F-test were higher than the significance value α 0.05. The values obtained in the validation of the method are included to check their agreement with the proposed model. The chemical composition and activity concentrations of the samples analyzed in validation are given in Tables S8 and S9 of the Supplementary Information.

Figure 7

Graphical representation of the experimentally measured ²²⁶Ra, ²³²Th(²¹²Pb), and ⁴⁰K activity concentration values versus those estimated by the obtained models relating the chemical composition of the ashes to the activity concentration of the different radionuclides. The models explain more than 95% of the dispersion. The clusters represented by the confidence ellipses in the HJ-Biplot in Figure 4 are shown in the same color as the plotted points. The comparison between experimental and estimated values showed no significant differences, as the p-values for the paired t-test and Fisher’s F-test were higher than the α significance value of 0.05. The results obtained in the validation of the method are included to check their agreement with the proposed model.

Figure 8

Graphical representation of the activity concentration values of ²²⁶Ra, ²³²Th(²¹²Pb), and ⁴⁰K measured experimentally versus those estimated using the models obtained that relate the chemical composition of the cements to the activity concentration of the different radionuclides. The models explain more than 73% of the dispersion. The clusters represented by the confidence ellipses in Figure 5 are shown with the same color at the represented points. Comparison between experimental and estimated values showed no significant differences, as the p-value for the paired t-test and Fisher’s F-test were above the α significance value of 0.05. The results obtained in the validation of the method are included for agreement with the proposed model.

Figure 9

Validation of activity concentrations for ²²⁶Ra, ²¹²Pb, and ⁴⁰K, and ACI experimentally determined by gamma spectrometry and those estimated by the proposed models. The validation criterion for satisfactory results was an RSD(%) value of less than or equal to 30%. Eighty-nine percent of the concentrations met the acceptance criterion. The ⁴⁰K was also accepted for the 2 samples with an activity concentration value below the limit of detection (LoD). The RSD(%) values obtained for the ACIs were all satisfactory at less than 16.1%.