Fly ash particle characterization for predicting concrete compressive strength

Construction and Building Materials 165 (2018) 560–571

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Fly ash particle characterization for predicting concrete compressive strength Taehwan Kim a, Jeffrey M. Davis c,1,⇑, M. Tyler Ley b, Shinhyu Kang b, Pouya Amrollahi b a

Center for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia Oklahoma State University, Department of Civil and Environmental Engineering, Stillwater, OK 74078, USA c PNDetector GmbH, Otto-Hahn-Ring 6, Munich, Germany b

h i g h l i g h t s
It was demonstrated that fly as particles can be grouped into compositionally distinct groups.
Fly ashes with similar bulk composition may produce different compressive strengths in concrete.
The compositional strength can be predicted using the particle group composition.
Linear modeling of the particle group composition has significant predictive power for concrete.
There are specific particle groups most strongly associated with early strength gain.

a r t i c l e

i n f o

Article history: Received 6 June 2017 Received in revised form 9 January 2018 Accepted 9 January 2018

Keywords: B. EDX C. Compressive Strength E. Modeling E. Concrete D. Fly Ash

a b s t r a c t A new classification approach is presented that uses individual fly ash particle measurements to provide improved and more in-depth information about the properties of the concrete. The technique uses machine guided X-ray microanalysis to measure the compositions of 2000 randomly selected particles from 20 different fly ashes. This paper details the methods used to acquire the particle composition data and the derivation of the representative groups of the fly ash particles or classification groups. This method is named the Particle Model. To investigate the utility of these groups, 12 fly ashes were used at a 20% mass replacement of the cement in a series of concrete mixtures, which were tested for compressive strength at various times over 180 d of curing. Seven of the nine particle compositions identified were found to influence the compressive strength of the concrete with a linear model R-squared value of 0.99. The Particle Model showed a statistically significant improvement over the Class C or F classification from ASTM C618 and EN450. This work aims to establish the Particle Model and show that the classification shows promise to be used as a method to predict the physical properties of concretes that contain fly ash. Ó 2018 Published by Elsevier Ltd.

1. Introduction Over 98% of the ready mix concrete companies in the United States have used fly ash as a replacement for cement in concrete because of the good performance and economic benefits [1–3]. Fly ash is a by-product of the combustion processes of pulverized coal and is composed of finely divided spherical particles with a diameter of 1 mm to 150 mm obtained from a dust-collection system [2,4] The major oxide components of fly ash are SiO2, Al2O3,

⇑ Corresponding author. E-mail address: [email protected] (J.M. Davis). This author is acting in a volunteer capacity in order to further the field of cement and concrete research. 1

https://doi.org/10.1016/j.conbuildmat.2018.01.059 0950-0618/Ó 2018 Published by Elsevier Ltd.

Fe2O3, and CaO with various minor oxides [1,2,5]. Applications for fly ash include: a low-cost adsorbent for cleaning flue gas, wastewater treatment, the raw material for synthesis of geopolymers and zeolites, a backfill material in mining, soil stabilization, and a supplementary cementitious material (SCM) in concrete [1,6,7]. Though the demand for fly ash as an SCM in concrete continues to increase, several challenges limit the consistency and the predictability [4,8–10]. Past studies of the reactivity of fly ash largely relied on bulk characterization methods, such as X-ray fluorescence (XRF), X-ray diffraction (XRD), and solution chemistry based on leaching tests [4,11–14]. Both ASTM C618 and EN 450 use bulk composition to classify fly ash as either Class C or F. While understanding a bulk property of a material is useful, it can only describe

T. Kim et al. / Construction and Building Materials 165 (2018) 560–571

the average of the system. Moreover, the individual fly ash particles do not have a homogeneous composition [12,15]. Rather, studies have shown that individual particles have a wide range of compositions, which, in turn, affect their performance in concrete. For example, the physical and chemical properties of a highcalcium fly ash were measured from a coal plant for approximately 2 years [16]. After analyzing one hundred and sixty fly ash paste samples, it was found that the bulk chemical compositions were fairly uniform. However, the 7 d compressive strengths of fly ash pastes varied widely. This highlights how bulk composition alone could not explain the change in the compressive strength and it suggests that a more fundamental understanding is needed in order to predict performance. Potential insights into the performance of fly ash can be gained from a thorough study of the individual particles. Others have tried to take a more fundamental approach to understanding fly ash [8,15,17–21]. Several studies have tried to find unique chemical groups by using scanning electron microscopy with electron dispersive spectrometry (SEM/EDS) to examine polished sections of thousands of fly ash particles [8,15,22]. While the early results were variable, more recent work suggested that the fly ashes investigated are mainly composed of four groups of glasses: a) silicate, b) calcium silicate, c) alumino-silicate with low to moderate calcium, and d) calcium-rich alumino-silicate [15]. Additional work attempted to better understand the reactivity of these glasses by synthesizing glasses that are similar in composition and then testing them [22]. The work found that the different glasses showed different levels of reactivity. Both studies revealed that Ca-rich aluminosilcate has the fastest reactivity and silicate is the slowest [15,22]. Other recent work used lab scale micro-computed tomography (mCT) and SEM/EDS along with synchrotron-based nano-computed tomography (nCT) and nano X-ray fluorescence (nXRF) to study individual fly ash particles [17,19,23]. The fly ash particles investigated consisted largely of a single constituent with only minor inclusions. This means that individual fly ash particles have an almost constant chemical consistency. Thus, if the chemical consistency and elemental composition of individual particles are well understood, then this could provide important insights into fly ash performance. These previous studies made two critical observations: a) certain glass compositions are associated with different levels of reactivity [15,22] and b) single fly ash particles have a nearly uniform chemical composition with only minor chemical inclusions [17,19,23]. Although literature has tended to discuss the glassy and crystalline materials within fly ash, these observations suggest that it may be possible to characterize the reactivity of individual particles based on their chemical composition. In addition, these observations provide an important opportunity to study the variance of elemental oxides contents of individual particles and determine improved ways to classify them. This is the focus of the work in this paper. The current classification system for fly ash based on ASTM C618 or EN450 is essentially a binary classification (i.e., an ash is either Class C or Class F) and so fly ash will fit within one of these categories. However, this work uses a large collection of data from individual particles and a rigorous data science approach to identify the unique groups of particles and classify them based on their performance in concrete. For this paper, the compressive strength of concrete will be used over the first 180 d. Additional work is underway to compare these results to other concrete properties but they are outside the scope of this work. It is not the goal of this paper to provide a comprehensive understanding of why each particle group causes certain properties in concrete, nor is it to comprehensively predict the compressive strength of concrete. Instead, this paper aims to provide an outline of the analytical procedures that were used to find these groups,

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introduce the groups, and show the usefulness of these groups to predict the compressive strength gain of concrete over time within the materials investigated. 2. Materials and methods 2.1. Materials Twenty different fly ashes were investigated with automated scanning electron microscopy with electron dispersive spectrometry (ASEM-EDS). Ten of the fly ashes were classified as Class C and ten were classified as Class F by ASTM C618 [24]. All of these fly ashes were produced in the United States from varying coal sources, boiler designs, and collection conditions. The bulk chemical composition for all fly ashes was analyzed using XRF as per ASTM D4326 [25] and the ASEM-EDS method as per a previous publication [23]. The results are shown in Table 1. All concrete mixtures used in the study used an ASTM C150 Type I [26] ordinary Portland cement (OPC) and the composition of cement is summarized in Table 2. Limestone and natural sands were used as a coarse aggregate and a fine aggregate, both of which were locally available in Oklahoma. The specific gravities of coarse and fine aggregates were both 2.6 and their absorptions were, respectively, 0.64% and 0.55%. All of the aggregate, both coarse and fine, were brought into the temperature controlled mixing facility at least a day before and their batch weights corrected for the moisture content. The aggregates and two-thirds of the mixing water are charged into the mixer and mixed for three minutes. Next, any clumped fine aggregate was removed from the walls of the mixer. Then the cement and fly ash were added, followed by the remaining mixing water. The mixer was turned on for three minutes. Once complete, the mixture rested for two minutes while removing the buildup of material along the walls. Mixing continued for another three minutes. Slump, unit weight, and air content were measured [27–29]. Twelve different fly ashes (C1, C2, C3, C4, C5, C6, C7, F1, F2, F3, F4, and F5) were investigated with concrete mixtures. These fly ashes were chosen as they showed a wide range of different particle compositions. A mixture without fly ash was also included for comparison. Each concrete mixture had a water to cement ratio of 0.45. The mixtures with fly ash used a 20% replacement rate by mass of cement. Chemical admixtures are not included to reduce the potential variables. Table 3 shows the mixture proportions for a cubic meter of concrete. Cylindrical samples (10.2 cm in diameter and 20.3 cm in height) were prepared, sealed, and cured at 23 °C and 100% RH for 24 h. The samples were then demolded and placed in the curing room at 100% relative humidity until testing [30]. 2.2. Automated scanning electron microscopy methods The ASEM method uses a SEM equipped with an image analysis operating system and an energy dispersive X-ray spectrometry (EDS) system. The instrument used was an Aspex Explorer PSEMEDS. One advantage of ASEM is the ability to rapidly measure the physical and chemical information of individual particles. This method investigates the composition, size, and shape of approximately 350 particles per hour with no intervention by the user [23]. The Instrument settings and consistency of results are presented in the Appendix A and is also discussed in previous publications [23]. One challenge with this method is that these particles are not flat and so they violate one of the assumptions of classical quantitative EDS analysis. However, EDS correction algorithms can account for geometric effects if the particles are a known shape

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Table 1 Bulk chemical composition by XRF and ASEM. Ash

Method

SiO2

Al2O3

Fe2O3

CaO

MgO

SO3

Na2O

K2O

TiO2

P2O5

SrO

LOI

C1 C1

XRF ASEM

39.10 39.40

20.40 23.60

6.20 4.30

21.20 19.60

5.30 7.10

1.40 1.10

1.60 3.10

0.70 0.90

1.30 0.90

1.60 0.80

0.34 0.24

0.20

C2 C2

XRF ASEM

36.20 37.20

19.90 20.50

6.70 5.30

24.00 23.90

5.20 5.20

1.40 0.80

1.70 3.80

0.50 0.90

1.40 0.90

1.40 0.90

0.40 0.70

0.20

C3 C3

XRF ASEM

38.70 34.00

18.80 18.30

5.80 5.70

23.10 21.70

5.60 6.20

1.20 1.40

1.80 4.00

0.60 1.30

1.40 0.80

1.50 1.30

0.40 0.70

0.40

C4 C4

XRF ASEM

34.50 38.00

20.40 21.40

5.70 7.40

26.50 22.10

4.70 3.90

1.70 0.20

1.80 3.70

0.40 1.70

1.50 0.60

1.50 0.40

0.50 0.50

0.10

C5 C5

XRF ASEM

36.20 30.20

19.60 20.70

5.80 6.00

24.00 26.60

6.00 8.30

1.00 1.50

1.80 3.60

0.40 0.60

0.60

1.70

0.20

C6 C6

XRF ASEM

38.10 35.10

21.00 23.30

5.50 3.00

15.50 15.00

3.70 4.00

2.90 2.00

7.90 13.40

0.80 0.60

1.30 1.10

0.70 1.70

0.70 0.90

0.40

C7 C7

XRF ASEM

38.30 32.20

19.90 21.60

6.10 4.60

23.10 22.20

5.20 5.40

1.10 1.80

1.50 7.30

0.60 0.80

1.40 0.80

1.10 2.80

0.40 0.70

0.60

C8 C8

XRF ASEM

40.00 42.50

20.90 22.00

5.90 4.40

21.50 18.00

5.00 8.40

0.90 0.70

1.60 4.10

0.70 1.00

0.60

1.30

0.10

C9 C9

XRF ASEM

36.00 32.00

22.40 25.10

5.50 5.70

24.00 24.90

4.80 5.30

1.20 0.90

1.70 3.60

0.50 0.50

0.90

1.00

0.20

C10 C10

XRF ASEM

35.90 37.70

18.00 17.30

6.70 5.10

25.80 24.30

6.10 6.70

1.80 1.20

1.80 5.10

0.40 0.90

1.20 0.90

0.80 0.20

0.50 0.50

0.20

F1 F1

XRF ASEM

56.70 57.10

20.30 22.90

5.62 4.56

10.00 8.80

2.90 2.10

0.50 0.40

0.50 0.40

1.40 2.90

1.10 0.50

0.10 0.10

0.30 0.40

0.20

F2 F2

XRF ASEM

52.00 54.00

16.40 20.50

4.40 3.90

18.70 14.30

2.90 3.30

0.90 0.50

0.80 1.20

0.90 1.30

1.00 0.60

0.30 0.10

0.20 0.40

1.20

F3 F3

XRF ASEM

56.60 56.90

24.30 24.70

6.00 5.60

6.40 6.00

1.80 1.60

0.40 0.30

1.20 2.80

1.00 1.40

0.50

0.30

0.04

F4 F4

XRF ASEM

51.80 46.40

18.10 22.00

4.60 3.40

16.50 17.80

4.00 5.60

0.70 0.50

1.00 2.80

0.70 0.80

0.40

0.20

0.10

F5 F5

XRF ASEM

53.20 53.10

27.50 25.90

8.40 9.00

1.50 3.10

1.00 0.30

1.00 1.20

0.40 1.30

2.40 4.30

0.80

0.10

1.00

F6 F6

XRF ASEM

53.90 55.30

27.60 26.00

6.30 6.00

2.00 2.30

1.05 0.75

0.30 0.32

0.39 0.93

2.45 7.10

1.57 0.92

0.33 0.08

0.11 0.20

3.02

F7 F7

XRF ASEM

47.70 49.90

24.90 26.00

14.70 8.20

3.70 3.80

0.90 0.50

0.70 1.20

0.70 4.40

1.70 4.40

1.30 0.80

0.30 0.50

0.10 0.20

2.20

F8 F8

XRF ASEM

56.90 58.00

22.60 24.10

4.60 3.20

7.30 5.50

2.30 1.80

0.30 0.10

1.70 3.80

1.20 2.20

0.30

1.00

0.10

F9 F9

XRF ASEM

53.50 51.20

19.20 23.80

6.30 5.50

13.20 11.80

3.10 3.10

0.60 0.50

0.60 1.30

1.10 1.70

1.10

0.20

0.10

F10 F10

XRF ASEM

57.70 61.80

24.50 27.70

4.10 1.80

8.10 5.30

2.00 1.10

0.30 0.20

0.20 0.10

0.90 1.60

0.20

0.10

0.00

such as being a sphere. The particle correction model developed by Armstrong and Love-Scott [31,32] and Armstrong-Buseck [33,34] makes corrections for k-ratios of 12 elements (Na, Mg, Al, Si, P, S, K, Ca, Ti, Fe, Sr, and Zr) by using CalcZAF [35,36]. Previous publications validate this approach [23] and Table 1 shows close agreement between the XRF and bulk ASEM data. The particles ranged from 0.2 mm to 50 mm. Fig. 1 shows the particle size distribution (PSD) from ASEM using 0.5 mm of bean size. Previous research by Aboustait et al. [23]. and Aichele et al. [37] analyzed glass beads, fly ashes, and soft latex particles using ASEM technique and acoustic attenuation spectroscopy and found both methods provide similar PSDs particle distribution despite the intrinsically different physics of both techniques. More detailed information regarding the procedure for the ASEM method is found in the Appendix A and elsewhere [23,37].

1.30

0.20 0.10

0.60 0.50 3.60

0.50 0.40 0.50

particles provides a representative sample of the fly ash [23]. To deal with this large data a Self Organizing Map (SOM) algorithm reduces the dimensionality and identifies statistically unique groups [38–40]. This process takes a small, random collection of particle compositions and fits them into a two-dimensional space. Once the space is defined, the remainder of the particles are classified based on that geometry. The result is a two-dimensional representation of the 12-dimensional space that still contains most of the information of the high dimensional space. This classification procedure is called the Particle Model. This information is used to find statistically unique compositional groups that correlate to the material properties of concrete. Thus each fly ash can be classified by contents of these groups. More details are given in the Results. 2.4. Linear modeling

2.3. Data processing The result of the ASEM and quantitative microanalysis is a matrix of 40 000 rows (one row for each of the 2000 fly ash particles from 20 different fly ashes). Past research has shown that 2000

The usefulness of the compositional groups found from SOM is tested by deriving a linear model for compressive strength of concrete at different times by using a number of particles in each compositional group. After finding the derived groups, simple linear

T. Kim et al. / Construction and Building Materials 165 (2018) 560–571 Table 2 Properties of Type I Portland cement used in the preparation of concrete. Element

Composition (%)

SiO2 Al2O3 MgO Fe2O3 CaO SO3 Na2O K2O TiO2 P2O5 SrO BaO

20.77 4.57 2.37 2.62 62.67 3.18 0.19 0.32 0.34 0.14 0.22 0.07

Phase C3S C2S C3A C4AF

Composition (%) 52.13 20.22 7.68 7.97

Table 3 Mix proportions for concrete specimens. Material

Cement Fly ash Coarse aggregate Fine aggregate Water w/cement ratio

Quantity (kg/m3) With Fly Ash

Without Fly Ash

290 72 1098 714 163 0.45

363 1104 721 163 0.45

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It should be noted that the derived linear model shows the usefulness of the unique compositional groups on the compressive strength. As mentioned in the introduction, it is not the goal of this paper to provide a rigorous model that predicts the compressive strength of concrete. The main purpose is to show the benefit of a classification that uses the chemical compositional groups of individual particles rather than the bulk chemistry of the current ASTM C618 classification. A need for a fly ash classification system that relates to performance is even recognized by ASTM C618 as it suggests that the current method should not be used to predict performance [24]. The performance of the Particle Model will be compared to the Class C or F classification method. A linear system was chosen due to its simplicity. With a linear model, compressive strength can be predicted as a linear combination of the number of days of hydration and the percentage of particles falling into a particular compositional group as shown in Eq. (1). A figure of merit must be used to compare different linear models. For this work, the coefficient of determination, also known as the R-squared value was used. Thus, the best model is the one with the highest R-squared value. Other methods can be used to determine the suitability and accuracy of the models, but this figure of merit provides a simple measure for comparing models. In addition to the R-squared value, the classical analysis of variance (ANOVA) [43] was used to determine the statistical significance of various model components. This feature is important when considering several compositional groups and determining which, if any, contribute to compressive strength. Choosing only the statistically significant groups allows us to refine the model to the essential components.

3. Results modeling was developed as shown in Eq. (1). Group N is the fraction of the particles in Group N derived from the data processing. The coefficients of the linear model were found and investigated with a series of quality metrics. This modeling is done using the free and open source R programming environment [41,42].

Compressive stregnth ¼ aðlnðDays of hydrationÞÞ þ bðGroup 1Þ þ cðGroup 2Þ þ    þ nðGroup NÞ

a) Class C fly ashes

ð1Þ

3.1. Modeling based on ASTM C618 Two linear models were derived from the data. The first model did not use the ASEM-EDS compositional data or any of the groups derived from it. Instead, this model used the current ASTM C618 Class C or F classification versus age of the cylinder. The results are shown in Fig. 1, where colored dots represent the measured data and the solid lines show the corresponding models. As shown in the Table A3 the range of compressive strength values at 28 d

b) Class F fly ashes

Fig. 1. Comparison of the particle size distribution: a) the C fly ashes and b) the F fly ashes investigated in concrete mixtures. Each fly ash is shown as a different color. The black line shows the results for all of the fly ashes (bin size: 0.5 mm).

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spans about 11 MPa. Considering that the standard deviation of each mixture varied within a very narrow range from 0.05 MPa to 1.36 MPa (see Table A3), the 11 MPa of strength difference between different mixtures would be a high variance in compressive strength values. A logarithmic model (i.e., taking the natural logarithm of the number of days transforms the data) was used to fit the data. Table 4 shows the results for the model. The ”Coefficient” column gives the estimate of the parameter. The slope for Days is approximately 7.887/ln(Days), meaning that the concrete gains approximately 7.887 MPa per ln(Day). The ”Pr(>|t|)” column is a measure of the statistical significance for each estimator. Values in this column close to 0 represent significant variables, while values greater than 0.1 represent generally non-significant values. If Type F ash is used at 20% replacement, then the model predicts a modest strength gain of 0.62 MPa, and if Type C ash is used, then the strength gain is approximately 4.65 MPa. The R-squared value for this model was 0.934, indicating that the fit for the data was relatively good, even though ASTM C618 classification is not recommended to be used to predict fly ash performance in concrete [24]. 3.2. Group centers Fig. 2 reveals the primary drawback to the ASTM C618 classification method. The difference between the C and F curves do not capture the differences in performance. For example, there are Type C ashes that have a very small strength gain (i.e., they act more like Type F ashes) and vice versa. The ASTM C618 classification seems to not account for some information that affects fly ash performance. Table 4 Type of fly ash model summary.

(Intercept) Type C Type F

Coefficient

Std. Error

t value

Pr(>|t|)

7.8867 4.6526 0.6228

0.1251 0.6483 0.6643

63.03 7.18 0.94

0.0000 0.0000 0.3493

Fig. 2. Predicted Compressive Strength Curves for the Fly Ash Type Model. This plot shows the predicted strength gain with time for the model that considers the time of hydration and the type of ash used. Since there are only three classes for the ash (i.e., ”C”, ”F” and ”Cement Only”), the model produces three possible curves, shown here in black, red and green. The original data are shown as points on the chart matching the colors of the line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The SOM can reveal the underlying structure among the variables of input data – 12 elemental oxides in this study – by reducing the large dimensionality to two dimensions without losing the information. To aid in this calculation, the user selects an assumed geometry and then fits the data to it. The rectangular geometry, for instance, is simply a rectangular grid. Each element of the grid shares a border with at least two other grid elements. In training the model, the algorithm is determining where these borders are and how large the distance is between the grid centers. It does so by randomly selecting a subset of the particles and then assigning them to the various grid elements. This process is performed numerous times, with the geometry updated each time. Once completed, each grid element will represent a cluster of compositionally distinct fly ash particles. Increasing the number of grids increases the number of clusters. Thus, a 2  2 rectangular or hexagonal grid will result in four clusters. The implementation of the SOM on the ASEM-EDS data is dependent on the choice of the model geometry. In this work, a choice was made to balance between simplicity and information content. Four different model geometries were tested to find the best choice for this study. These geometries were a) four rectangular nodes (Rec 2  2), b) 9 rectangular nodes (Rec 3  3), c) 4 hexagonal nodes (Hex 2  2), and d) 9 hexagonal nodes (Hex 3  3). The results are shown in Fig. 3. Fig. 3 shows the R-squared value for four different model geometries. The results show that an overly constrained model geometry, Rec 2  2 and Hec 2  2 with four or fewer groups, does not perform as well as the larger geometries with 9 groups, Rec 3  3 and Hex 3  3. In other words, it was determined that the four cluster models were too small to adequately describe the space, so the model size was increased to 3  3. The nature of the grid (i.e., rectangular vs. hexagonal) did not have a significant effect on the Rsquared value (see Fig. 3). Finally, it is important to note that the full data set has seven unique data points in the experiment, namely, the seven times that the cylinders were tested for compressive strength. Any model that contains, therefore, more than seven terms may overfit the data. Because of this, ANOVA will be used to simplify the derived model. The model geometry chosen is therefore not definitive but represents a balance between practicality, model robustness and the present state of knowledge of fly ash composition. Each time the analysis was performed the R-squared value was determined for each model and recorded. Since the SOM takes a random portion of the data to create the initial map, each time the model is run, the groups are slightly different. To achieve the best possible group centers, the SOM process was repeated 200 times, each group was modeled, and the grouping with the highest R-squared value was chosen for further study and analysis. Table 5

Fig. 3. Variation of the R-squared value SOM geometry. A plot showing how the quality of the model changes with changes in a variation of the SOM mapped geometry.

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shows the compositional groups and Table 6 shows the relative amount of the groups found in each fly ash. Each fly ash is made of the 9 different groups shown in Table 6. Although each group composition shown in the Table 5 contains all 12 elements each group has its distinct compositional feature. For example, fly ash particles belonging to Group 3 distinctively contain large contents of Al and Ca. Group 9 is fly ash particles that are mostly composed of silica phases and presumably crystalline quartz. Particles in Group 4 have exceptionally high contents of Na. These different groups will be discussed in more detail later in the paper. Table 6 shows the proportion of the 2000 analyzed particles for each fly ash that fall within each of the nine identified groups. It should be noted that the particle groups in Table 6 do not total to 100%. Since this study restricts itself to the correlation of particle composition to compressive strength over the first 180 d, it follows that some particle compositions may not contribute to this and are therefore excluded from the model. More details can be found in the Appendix C and more insights will be gained as additional testing is completed on other concrete properties. A Spectral angle analysis was used to generalize the results and provide a simplified method to classify and sort fly ash results with a spreadsheet program. This could be a useful approach in the future to implement the Particle Model as it does not require a detailed statistical analysis. The details of the spectral angle analysis are given in the Appendix C. The particle size distribution of the different compositional groups and the overall size distribution of all the fly ash investigated are plotted in Fig. 4. Fig. 4 shows that more than 60% of the particles in the identified groups are between 1 lm and 3 lm with the most common size being approximately 2 lm. Furthermore, all of these identified groups have less than 3% of the particles that are greater than 6 lm in size. This comparison shows that there is little difference between the particle size distribution of the different compositional groups and for all of the particles investigated. Because the results are similar, the importance of particle size was not investigated in this model. This will be discussed in more detail in Section 4.2.

Fig. 4. Comparison of the particle size distribution of the different particle groups. Each particle group is shown with a different line. The black line shows the results for all of the fly ashes combined (bean size: 0.5 mm).

3.3. Model simplification with ANOVA The initial model performance with all nine groups included is shown in Table 7. The full group model has an R-squared value of 0.969, which is significantly higher than the linear model using the Class C or F classification. Next, an ANOVA is used to determine the significance of the variables. This significance is tested by determining the t value of a coefficient. In this simplified case, the t value is simply the coefficient divided by the standard error (i.e., the ‘‘Coefficients” divided by ‘‘Std. Error”, as shown in Table 7). From the t value, the probability that subsequent analyses will yield a different coefficient can be estimated. If that probability is high, then the variable is not significant. Variable significance can also be estimated intuitively from the value of the standard error. If the standard error is high in comparison to the coefficient, then

Table 5 Group centers from the self-organizing map. Group

Na2O

MgO

Al2O3

SiO2

P2O5

SO3

K2O

CaO

TiO2

Fe2O3

SrO

ZrO2

1 2 3 4 5 6 7 8 9

0.38 0.61 0.47 14.69 1.94 0.38 2.21 6.50 2.10

1.49 7.62 10.60 3.59 6.91 8.55 1.08 2.74 0.36

5.06 33.58 16.98 31.32 27.00 22.39 34.99 14.87 5.51

8.62 9.24 10.27 37.96 39.30 26.45 50.15 62.23 86.86

0.42 6.45 6.44 0.07 0.23 2.78 0.05 0.01 0.00

0.45 2.03 5.35 0.51 0.58 1.49 0.33 0.19 0.02

0.17 0.01 0.03 1.60 0.17 0.01 2.87 2.61 1.79

2.57 32.15 37.69 6.23 17.84 31.58 2.50 5.90 1.49

0.79 0.59 3.24 0.15 1.12 1.07 0.33 0.28 0.05

79.97 6.69 8.39 3.55 4.55 4.87 5.21 4.36 1.55

0.03 0.94 0.37 0.33 0.34 0.40 0.26 0.31 0.26

0.05 0.09 0.17 0.00 0.01 0.04 0.00 0.00 0.00

Table 6 In-class proportions for the measured fly ashes. Name

Group 1

Group 2

Group 3

Group 4

Group 5

Group 6

Group 7

Group 8

Group 9

C1 C2 C3 C4 C5 C6 C7 F1 F2 F3 F4 F5

0.10 0.10 0.05 0.20 0.30 0.00 0.45 1.10 0.15 1.00 0.15 1.15

3.50 3.55 6.10 6.75 4.10 2.85 2.55 0.25 0.65 0.25 3.20 0.20

2.90 5.65 3.15 1.75 5.60 0.90 8.70 0.40 0.25 0.30 2.25 0.50

15.55 18.95 13.00 10.50 18.15 12.30 9.60 0.00 0.65 0.60 4.90 0.40

15.30 7.20 9.50 18.25 7.85 0.35 9.60 19.90 22.10 8.35 21.70 0.50

13.30 8.30 12.65 19.45 8.45 1.55 11.70 6.50 8.90 2.45 16.20 0.45

3.30 0.60 1.75 1.50 1.00 0.05 5.00 41.95 28.20 57.40 9.45 71.70

2.90 4.45 3.65 3.20 1.95 0.05 4.80 7.25 9.80 8.65 3.35 3.95

2.80 5.75 6.20 3.85 4.00 0.45 4.50 4.65 6.80 8.55 4.95 6.55

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Table 7 Linear model parameters and statistical results from the nine compositional groups.

(Intercept) ln(Days) Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 Group 9

Coefficient

Std. Error

t value

Pr(>|t|)

2.6081 7.9467 14.6836 4.0304 3.0448 0.3159 1.2505 1.6672 0.5796 0.2789 1.8933

1.5799 0.0979 2.1430 0.5789 0.3537 0.0542 0.1554 0.2265 0.0754 0.1524 0.3013

1.65 81.16 6.85 6.96 8.61 5.83 8.05 7.36 7.68 1.83 6.28

0.1002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0686 0.0000

Table 8 Linear model results and statistical results after the ANOVA simplification with seven compositional groups.

ln(Days) Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 9

Coefficient

Std. Error

t value

Pr(>|t|)

9.9819 16.781 4.6736 3.3639 0.3495 1.3349 1.8008 0.6740 2.3946

0.09687 1.393 0.3321 0.2030 0.0525 0.0722 0.1332 0.0390 0.1985

82.40 12.04 14.07 16.57 6.66 18.49 13.52 17.26 12.06

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

the variance of that model parameter is likely very high. Nonsignificant model variables can be eliminated and the model is simplified while improving R-squared value. Of the identified coefficients, only Group 8 and the y-intercept have probability values greater than 0 (0.0686 and 0.1002, respectively). This suggests that the compressive strength at mixing is zero and that Group 8 is not a statistically significant variable. Then, the model was recalculated without Group 8 as shown in Table 8. With these changes, the model has an R-squared value of 0.9981.

Fig. 5. A plot showing the predicted performance for four concretes with the named fly ashes based on the Particle Model. The colored points on the graph represent the original data from each of the concretes.

benefits of the Particle Model, compressive strength development curves for concrete containing fly ash C2, C5, and C6 are shown in Fig. 6. As shown in Table 1, the bulk compositions from XRF for C2 and C5 are practically identical. C6 has slightly lower Ca content and higher alkali content than C2 and C5 but otherwise has a similar bulk chemical composition to the other two fly ashes. Because of the small differences in the bulk chemistry the users of the fly ash would expect to have similar strength performance in concrete. However, concrete with C6 fly ash had the lowest compressive strength among total 13 concrete mixtures after 56 d. The Particle Model shows fly ash C6 has a lower amount of Group 3 than those amounts in C2 and C5 and so this is why the strengths are lower. In comparing C2 and C5, the standard deviations at 90 days are 1.48 MPa for C2 and 1.06 MPa for C5 (see the Table A3). Consider-

3.4. Application of the particle method To demonstrate the quantitative aspect of the Particle Method, Eq. (1) is used to compare the predicted compressive strength to the measured values for four ashes.

Compressive stregnth ¼ 9:9819 lnðDays of hydrationÞ  16:781ð%Group 1Þ þ 4:6736ð%Group 2Þ þ 3:3639ð%Group 3Þ þ 0:3495ð%Group 4Þ  1:3349ð%Group 5Þ  1:8008ð%Group 6Þ þ 0:6740ð%Group 7Þ  2:3946ð%Group 9Þ

ð2Þ

Fig. 5 shows the predicted model and the measured data for several fly ashes. Many of the ashes used in this study had quite similar bulk compositions, but their compressive strength varies widely and the predicted results from the Particle Model were in good agreement with the experimental results. To highlight the

Fig. 6. Predicted performance with the Particle Model for concretes made with ash C2, C5 and C6. A plot showing the model can predict differences in compressive strength despite having similar bulk composition.

T. Kim et al. / Construction and Building Materials 165 (2018) 560–571 Table 9 Results of T-tests on bootstrapped models.

Ash Type Model Initial Model Final Model

R-squared

95% CI (Lower)

Measured Difference

0.9381 0.9688 0.9981

0.0328 0.0264 0.0264

0.0341 0.0307 0.0293

ing these small standard deviations and the 3.31 MPa difference in strengths, the ANOVA F-test with multiple t-tests using three samples with an equal variance shows that the differences of these strengths are statistically significant between C2 and C5. This was also done for C6 and again the differences were shown to be statistically different. More details of the statistical comparison are provided in the Appendix D. This indicates that the concrete with C5 gained strength more than the concrete containing C2 fly ash. This difference cannot be revealed by their bulk chemistries as both of them have identical bulk elemental compositions. Based on the above evidence, the Particle Model is a promising tool to predict the compressive strength of concrete and provides more insights than the bulk chemical composition of the fly ash. 3.5. Bootstrapping To determine if the calculated R-squared values for the various models are statistically significant, the difference of means is calculated by using a Students T Test [44]. However, each derived model has only one R-squared value. An ideal solution would be to run this experiment 30 or more times to determine the distribution of R-squared values. However, this is impractical, considering that it would require the creation, curing and testing of 12 600 cylinders. Instead, the data are sampled with replacement (this means it is possible that some observations occur multiple times in the data set), and the model is created using the sampled dataset. This process is repeated 30 or more times to generate a range of R-squared values. These results can then be subjected to the ordinary T test to determine whether the values are statistically significant. This is known as bootstrapping [41]. Table 9 summarizes the results of bootstrapping each of the three models. The R-squared values listed in the first column are the calculated Rsquared values for each model. In the second column, the lower value of the 95% confidence interval is listed, representing the smallest statistically significant difference between the means. The measured difference of the means is then shown in the third column. Table 9 shows the differences in the R-squared values between the Class C and F and the Particle Model are statistically significant.

4. Discussion The primary finding of this paper is that the Particle Model shows a promising method to classify fly ash and this classification can be correlated to the compressive strength performance of concrete that the Class C or F classification cannot do and is not intended to do. This improvement is because the Particle Model takes the particle chemical composition into account. It should be noted that the particle model accounts for the elemental composition of fly ash particle but does not distinguish between whether these compositions are glassy or crystalline. However, this does not hinder the model as it gives the reader a specific indication of how individual particles impact the resulting compressive strength of the concrete. This means that the Particle Model gives insight into the practical significance with respect to the contribution to the concrete strength. These findings can pro-

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vide further insights into the reactivity and chemical composition of the particle groups. For example, particles in Group 9 contain a significant amount of SiO2 of approximately 87% in Table 5 and Group 9 has a negative coefficient in Table 8. This means that increased percentages of this group will have a lower compressive strength gain over the first 180 d of hydration. It implies that particles in Group 9 are not very reactive in concrete. Previous researches [8,19] found that siliconrich phase containing almost no impurities was mainly observed as crystalline quartz and this quartz minerals are often observed in SEM investigation of fly ash. It is also possible that these particles might be a silica-rich glassy phase. It should be noted that the reactivity of both phases are very low [15,22]. This is being investigated in further testing. Table 8 shows that Group 1 has the largest negative coefficient, which means that the particles in this group do not improve the strength gaining. These particles seem to be non-reactive Fe rich particles. This is not unexpected because a fly ash particle made up of significant amounts of non-reactive Fe rich particles would not contribute to the strength gain of hardened concrete. This highlight of the role of Fe is also a source of criticism for the ASTM C618 method, which uses Fe content (i.e., the sum of Si, Al and Fe oxides) without considering the form of the oxides. Minor inclusion of iron in the glass phases (such as Groups 3 and 5) does not influence of the reactivity of that glass phase but the contents of iron richparticles in Group 1 seems to result in the slow strength gaining as these particles in Group 1 are not reactive. The model ANOVA also shows that the inclusion of the group into the model does not change the statistical performance of the overall model, further supporting the inference that the Group 1 particles are not reactive. Again, this is the strength of making individual particle observations. Groups 2 and 3 are correlated with the highest compressive strength values, and their composition indicates that they are Ca rich and are likely self-cementitious particles. It has been reported that Ca rich fly ash generally reacts faster than low Ca fly ash [41,45]. This has been attributed to the greater reactivity of calcium rich aluminosilicate glasses in fly ash [15,46,47]. According to Zachariasen’s glass model [48], Ca is a structural modifier that creates two non-bridging oxygens. Therefore, more Ca content in glass generally increases the degree of depolymerization in glass structures. The higher amounts of Ca and Al for Groups 2 and 3 may explain the improvement in compressive strength from these two particles. While the group compositions and model performance are in general agreement with an accepted theory about the reactivity of fly ash, it is important to note that this study is correlative in nature and it does not prove that the particles identified modify strength gain. Instead, this work shows that these particles are correlated or observed simultaneously with increasing or decreasing rates of strength gain. There are some similarities between these findings and previous publications by Durdzin´ski et al. [15,22]. They suggested that fly ashes can be grouped as four major chemical glasses: a) silicate, b) calcium silicate, c) alumino-silicate with low to moderate calcium, and d) calcium-rich alumino-silicate. Both studies [15,22] revealed that there are two reactive glasses (calcium-rich alumino-silicate and aluminum silicate. Calcium-rich aluminosilcate has the similar elemental composition of Groups 2 and 3. In addition, Groups 5 and 7 has the similar elemental composition to the aluminum silicate [15,22]. These four groups positively contribute to the strength development as shown in Eq. (2). 4.1. Origin of compositional groups and degree of crystallinity While not covered directly by this work, some comments can be made about the origins of the compositional groups and their

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degree of crystallinity. Since consistent compositional chemistries are found in each fly ash, regardless of the coal source or burner design, this means the coal and other fuel is likely vaporized during the combustion process. The particles then form by condensation at different temperatures and rates during the cooling process. The cooling rate and composition of the condensation will have an impact on the ultimate reactivity of the particle. Because the method relates the chemical composition to the resulting compressive strength than reactive particles would be assumed to be more amorphous than the non-reactive particles but this has not been verified in this work. This may provide more insights for modeling work and more detailed investigations that will be discussed in future publications. 4.2. Effect of particle size distribution If particles react on their surface, then the size of a particle will influence the reactivity. Fig. 4 show that the compositional groups did not have a unique size distribution and matched the overall particle distribution for the fly ashes investigated. This indicates that the different contribution of each group to the strength development is not due to the particle size distribution but mainly due to the chemical composition of each group. Because the particle size distribution is largely constant, this means that it does not need to be included in the linear model for the compressive strength. Despite the lack of the comprehensive understanding of each group, the Particle Model provides a promising way to improve the current classification method.

of variance (ANOVA) reduced the number of statistically significant compositionally distinct particle groups to seven. The prediction of the compressive strength change over time for the Class C or F classification has an R-squared value of 0.938. For the Particle Model, the R-squared improved to 0.998. Based on a Ttest from the bootstrapped data, the Particle Model showed a statistically significant improvement in the R-squared value over the Class C or F model. The size distribution of the seven compositional groups was found to be similar and so particle size is not included in this predictive model. This study shows that individual fly ash particle composition is useful to quantitatively predict the performance of concrete. Further studies can investigate other properties of concrete. On completing these studies, the Particle Model could be used to create ”designer concrete”, where certain particles are isolated and added to concrete to optimize a specific performance. Additionally, the Particle Model could be applied to any number of supplementary cementitious materials (SCM), such as silica fume, ground granulated blast furnace slag or rice husk ash. This could drastically change the usage of fly ash or other SCMs in concrete and create critical improvements in the economy, durability, sustainability, and life for the built concrete environment. Acknowledgments This work was sponsored by funding from the United States National Science Foundation CMMI 1150404 CAREER Award and by Oklahoma Transportation Center project 10.1.24.

4.3. Practical significance

Appendix A: ASEM method

Practitioners need a method of fly ash classification that better describes performance in concrete. This highlights the shortcomings of using bulk composition to classify fly ash as outlined in ASTM C618 and EN 450. This paper presents the first step to developing a classification protocol based on individual particle investigation named the Particle Model. While this paper used the Particle Model to predict the compressive strength of concrete, the method can be used to investigate a number of physical properties of concrete. Work is underway to correlate other properties such as the mass transport, resistivity, resistance to sulfate attack, and suppression of alkalisilica reaction. This creates a new tool to screen fly ash and predict the properties of concrete with changes in combustion conditions, coal source, collection system, or guide the reclamation of fly ash from landfills. These new tools can supplement or possibly replace existing methods used for classification. The benefit of the Particle Model is the ability to predict concrete performance with associated error bars and confidence intervals. This would increase the usage of fly ash and the ultimate quality of concrete. The authors emphasize that the Particle Method is not immediately ready for implementation. However, this paper shows a clear path forward for future research efforts that could ultimately make significant changes to the performance of concrete.

ASEM sample preparation

5. Conclusion Two thousand particles were measured from 20 different fly ashes using automated scanning electron microscopy based X-ray microanalysis (ASEM-EDS). The Self Organizing Maps (SOM) method found nine compositionally distinct particle groups from this data. This classification procedure is named the Particle Model. These particle groups were used in a linear model as predictive variables for the compressive strength of concrete with a 20% fly ash replacement by mass. Model simplification with an analysis

All detailed processes have been published [23]. This section briefly explains the sample preparation for ASEM. To use the ASEM technique, a small volume of each type of fly ash was dispersed on the aluminum sample stub. Between 0.015 g and 0.018 g of the material was then replaced in a 50 ml polypropylene conical vial with 25 ml of ethyl alcohol and 25 ml of isopropyl alcohol. The vial was capped, sealed and, then sonicated for 30 min to disperse the particle and hold them in suspension. After sonicating the sample, a few droplets (two to three drops using pipette) were placed on the double-faced adhesive carbon tape. These samples were then stored in vacuum desiccator until testing. The ASEM tests were performed under the high vacuum condition without coating the surface with the conductive materials. A.2 ASEM details The ASEM settings used are given in Table A1. The probe current was measured using a Faraday cup on the stage and represents the

Table A1 Summary of instrument setting, scanning setting, and EDS setting used for ASEM technique. Instrument Setting

Value

Accelerating Voltage Probe Current Magnification Working Distance Aspect Ratio Search dwell time Measure dwell time Minimum Count Rate Acquisition time

20 keV 1.20nA 2500x 17–18 mm 1.3 16 ms 32 ms 3500 counts/s 5s

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T. Kim et al. / Construction and Building Materials 165 (2018) 560–571 Table A2 Average values of standard deviation for three independent measurements of 50 fly ash particles. Element

Standard Deviation

Si Al Fe Ca Mg K Na Si P

0.30 0.40 0.70 0.80 0.30 0.60 0.60 0.20 1.60

Appendix C: Spectral angle analysis To generalize the results from the SOM analysis, a method was developed that allows other researchers to classify and sort fly ash particle data from ASEM using an ordinary spreadsheet program. This method requires the calculation of a value known as the spectral angle, which is calculated using an application of the dot product shown in Eq. (A1).

h ¼ arccos

approximate current that is being addressed to the sample. The aspect ratio is a measure of how circular the particles are. Particles with higher aspect ratios are likely clumps of particles rather than isolated particles. The minimum detected level is a grayscale value used to separate fly ash particles from ordinary dust particles that likely come from laboratory contamination. Table A2 shows the average standard deviation for three repeat measurements of 50 fly ash (Class C) particles. A constant beam performance was achieved by keeping the probe current constant. Standard deviations from three replicate measurements of 50 particle compositions are relatively small, meaning that the quantitative analysis is consistent. Appendix B: Compressive strength of concrete Table A3

~ a ~ b j~ ajj~ bj

ðA1Þ

In this application, the vector denoted as ~ a is simply the compositional vector of one of the groups, as listed in Table 5, and the vector ~ b is the compositional vector of any other fly ash particle. When Eq. (A1) is applied to a particle with a composition very similar to a given group center, then the value of theta is very small. When they are dissimilar, then the value is large. What is left is to derive a single value for theta, such that when the spectral angle is above a certain threshold, then the particle is not considered to be part of the group. To do this, the entire fly ash database is grouped according to the spectral angle method and then modeled as above. The process is repeated as the value of the threshold (h, in radians) is increased incrementally. The results are shown in Fig. 7. A value of 0.20 rad in Fig. 7 was selected as the maximum spectral angle. The danger of choosing a value for h that is too small is that particles may be falsely excluded from their class, as is shown by the lower R-squared value for low values of the maximum spectral angle. In the event that two groups match, the particle is

Table A3 Compressive strength and standard deviation from 13 concrete mixtures. Curing time (days)

Ctrl

C1

C2

C3

C4

C5

C6

C7

F1

F2

F3

F4

F5

3

#1 #2 #3 Ave. STD

28.02 28.19 25.65 27.29 1.42

28.43 31.10 29.03 29.52 1.40

28.46 30.39 30.66 29.84 1.20

30.12 29.55 29.46 29.71 0.36

23.89 25.17 26.02 25.03 1.07

35.13 35.23 35.26 35.21 0.07

28.57 28.97 29.09 28.88 0.28

29.26 29.72 28.68 29.22 0.52

24.89 23.73 24.41 24.34 0.59

26.68 25.98 25.72 26.13 0.50

24.97 23.88 25.39 24.75 0.78

25.41 24.70 24.28 24.80 0.57

25.60 23.51 25.29 24.80 1.13

7

#1 #2 #3 Ave. STD

34.51 35.37 34.45 34.78 0.52

35.54 35.64 38.47 36.55 1.66

37.84 37.21 37.51 37.52 0.32

36.58 35.47 37.33 36.46 0.93

33.31 33.66 33.40 33.46 0.18

41.00 42.81 42.86 42.22 1.06

35.41 36.70 36.38 36.16 0.67

36.78 36.33 37.16 36.76 0.42

30.01 31.58 28.59 30.06 1.50

31.81 31.61 31.61 31.68 0.11

32.21 32.37 31.32 31.97 0.57

30.92 30.05 31.32 30.76 0.65

30.23 31.88 31.10 31.07 0.83

14

#1 #2 #3 Ave. STD

39.07 40.09 40.12 39.76 0.60

43.02 43.87 42.60 43.16 0.65

40.84 43.04 41.31 41.73 1.16

42.24 43.28 41.91 42.48 0.72

41.27 40.27 39.16 40.23 1.06

50.96 49.93 51.40 50.76 0.76

39.18 42.02 39.99 40.40 1.46

42.18 41.73 42.28 42.06 0.29

36.51 34.85 35.82 35.73 0.83

35.89 37.41 36.66 36.65 0.76

36.63 37.98 36.01 36.87 1.01

37.72 36.84 36.81 37.12 0.52

34.78 35.30 34.54 34.87 0.39

28

#1 #2 #3 Ave. STD

44.71 43.98 42.02 43.57 1.39

50.09 50.23 50.29 50.20 0.10

47.33 49.02 47.87 48.07 0.87

45.33 47.81 46.34 46.49 1.25

44.98 45.14 44.64 44.92 0.26

54.19 52.73 50.58 52.50 1.81

44.86 44.76 44.82 44.81 0.05

49.05 49.75 48.73 49.18 0.53

42.32 40.27 39.76 40.78 1.36

43.29 44.45 42.77 43.50 0.86

43.21 43.14 42.65 43.00 0.30

42.25 43.71 41.88 42.61 0.97

38.96 40.34 40.83 40.04 0.97

56

#1 #2 #3 Ave. STD

46.80 44.65 44.32 45.26 1.35

54.43 59.29 56.86 56.86 2.43

56.95 56.28 52.16 55.13 2.59

49.70 50.62 49.38 49.90 0.64

50.22 50.12 51.76 50.70 0.92

55.97 56.63 53.46 55.35 1.67

47.18 48.68 48.09 47.98 0.76

53.43 55.37 56.10 54.97 1.38

49.44 48.44 48.85 48.91 0.50

49.85 48.62 51.42 49.97 1.40

54.27 52.64 50.42 52.44 1.93

50.40 49.49 49.19 49.69 0.63

51.51 49.66 49.71 50.29 1.05

90

#1 #2 #3 Ave. STD

49.88 49.72 50.13 49.91 0.21

57.39 55.48 54.02 55.63 1.69

57.81 59.57 56.64 58.01 1.48

52.73 53.94 54.53 53.73 0.92

57.80 56.98 52.77 55.85 2.70

62.50 60.45 61.01 61.32 1.06

47.19 50.48 51.70 49.79 2.33

56.86 56.64 59.66 57.72 1.68

54.87 57.02 54.03 55.31 1.54

53.64 54.73 57.39 55.25 1.93

54.90 58.78 54.59 56.09 2.33

54.61 53.82 55.49 54.64 0.84

54.84 53.03 52.78 53.55 1.12

180

#1 #2 #3 Ave. STD

54.19 54.46 53.25 53.97 0.64

62.56 65.41 62.42 63.46 1.69

62.70 61.92 62.54 62.39 0.41

60.12 58.28 60.06 59.49 1.04

58.96 55.75 60.15 58.29 2.27

60.03 66.96 60.74 62.58 3.81

56.45 57.10 55.79 56.45 0.66

60.29 59.84 61.61 60.58 0.92

58.36 60.54 60.28 59.73 1.19

57.41 60.74 60.90 59.69 1.97

57.35 61.23 59.55 59.38 1.95

57.99 59.47 61.02 59.49 1.51

58.43 59.61 57.44 58.49 1.09

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Fig. 7. Variation of the R-squared Value with Maximum Spectral Angle. A plot showing how the quality of the model changes with changes in the threshold value for theta. The plot reaches an optimum between 0.175 and 0.20 rad.

Table A4 Summary of F test analysis with t-test (samples assuming equal variance) for compressive strength for C2, C5 and C6 at 90 days. Summary of F test (ANOVA)

F(2, 6) = 50.072, p = .000

Summary of t-test (Posthoc analysis using Tukey’s HSD) Multiple Comparisons

C2 and C5

C2 and C6

C5 and C6

p value

.026

.002

.000

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