Guidelines for Concrete Mixtures Containing Supplementary Cementitious Materials to Enhance Durability of Bridge Decks (2007)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

97 Introduction After all the data from the individual tests conducted as part of Step 4 have been collected, the tested mixtures are compared in this step using the framework of desirability functions developed in Step 1. In addition, for each individ- ual test method, the response versus the factors tested is mod- eled. These models are used to predict the performance of potential concrete mixtures that were not tested but are within the range of the levels analyzed. The goal of the modeling is to use the trends in the data to identify mixtures that have not yet been tested but may give improved performance. When a limited amount of data is available for each factor level, as is the case in the type of experiments outlined in this methodology, using a compli- cated model is not warranted. A simple model that com- pares the average performance of each response at each factor level would be adequate for predicting a set of “best” factor levels. A model that matches the characteristics of the data should be chosen. For example, a model for predicting the strength of the concrete should never predict negative values. In addi- tion, the data collected should be chosen carefully to meet the model requirements. For example, because the models use the average response at each factor level, the same amount of comparable data should be collected for each of the levels of a factor. This parity is needed because the orthogonal exper- imental designs require that each level of each factor is used the same number of times in combination with each level of the other factors. Finally, before the model is used to predict the response of mixtures that have not been tested, the accuracy of its pre- dictions should be evaluated for the mixtures for which results are available. The coefficient of determination (R2) in standard regression analysis is a measure of how well the model fits the collected data; a similar concept will be used to assess the fit of our models. The objective of this step is to analyze the test results to find the Best Tested Concrete (BTC) and the Best Predicted Con- crete (BPC). The BTC is the concrete mixture that best meets the performance criteria as described by the desirability func- tions. The BPC is a concrete mixture that may not be in the design matrix (and thus has not been tested) but is likely to perform better than the BTC according to the statistical model. The Best Concrete (BC)—the concrete mixture that is recommended for the application—will be either the BTC or the BPC; it will be selected after the confirmation testing that is done in Step 6. Analysis Process The analysis depends heavily on the desirability functions that were introduced earlier. For each test performed on the concrete, there must be a desirability function that rates any feasible test result from that test on a scale from 0 to 1, where 0 means that the test result is unacceptable, and 1 means that there is no room for improvement. The analysis process is summarized as follows: 1. Review data to check for errors and to check for expected trends. 2. Review or create a desirability function for each test per- formed. These desirability functions must match the needs of the application for which this mixture is being de- veloped. 3. Convert each test result from each concrete into an indi- vidual desirability using the desirability function for that test. 4. Calculate the overall desirability for each concrete mixture in the design matrix. The overall desirability is the geo- metric mean of the individual desirabilities for that con- crete mixture. (This is discussed in the next section.) 5. Select the BTC as the concrete in the test matrix that has the highest overall desirability. S T E P 5 Analyze Test Results and Predict the Optimum Mixture Proportions

6. Create a regression model for each test response so that results can be predicted for concrete mixtures with factor settings that do not appear in the matrix. 7. Select the BPC as the mixture that has the highest pre- dicted overall desirability from all the potential concrete mixtures in the test space. A proposed optimization process is given below: a. Select a factor setting for each factor to produce a combination of factor levels that does not necessarily appear in the design matrix. (The settings should prob- ably be within the range tested during Step 4 of the methodology. Using the models to extrapolate beyond the tested range is computationally possible but should only be used if supported by additional testing.) b. Use the regression model for each response to predict the test results for that mixture. c. Convert each of these predicted test results into pre- dicted individual desirabilities using the desirability functions. d. Calculate the predicted overall desirability for this hypothetical mixture as the geometric mean of the predicted individual desirabilities. e. Repeat Steps 7a through 7d on a large grid of potential concrete mixtures, and choose the one that has the highest overall desirability. 8. Perform the confirmation testing and final selection in Step 6. The implementation of the design matrix and the analysis of the resulting data can be done in commercial statistical packages such as Minitab® or Design Expert®. However, a substantial amount of data manipulation and modeling will be required to use these packages. Otherwise, users may use SEDOC—the customized Microsoft® Excel–based tool and the user’s guide available on the TRB website (http://www. trb.org/news/blurb_detail.asp?id=7714). Data Plots and Verification An important part of any data analysis is to plot the data to verify their reasonableness and that they are correctly entered into the software that will be used for the analysis. Before making any calculations, the user should at least observe simple scatter or trend plots of each response versus each factor. This check will likely uncover any gross typographical errors (like typing in 1000 instead of 100) and will also allow the knowledgeable practitioner to see if data show expected trends. For example, increasing the w/cm is well known to decrease the strength of the concrete mixture. If a plot does not indicate that the data follow this trend, then an investigation should be done to determine if errors occurred. An example of a scatter plot that follows an expected trend is given in Figure S5.1. The trend simply connects the average strength of the mixtures with a w/cm of 0.37 with the average strength of the mixtures with a w/cm of 0.45. This plot shows that Mixture #6 has a fairly low strength despite having a low w/cm. Some quick checks would be appropriate to make sure that the data for Mixture #6 were correctly entered. Once the user is satisfied that the data are correctly observed and entered into the analysis tool, computational and statistical analysis can begin. Desirability Functions and Individual Desirabilities The desirability function for a particular performance test rates any feasible test result on a scale from 0 to 1. Step 1 pro- vides example desirability functions for most common concrete performance tests that can be used to calculate an individual de- sirability for any concrete mixture. The example desirability function for 56-day strength, Figure S5.2, shows that the indi- vidual desirability for Mixture #6 in the hypothetical case study that has a 56-day strength of about 4500 psi (31.0 MPa) is 0.87. The desirability function shown in Figure S5.2 indicates that a 56-day strength between 3500 and 4000 psi (24.1 and 27.6 MPa) is marginal, a 56-day strength between 4000 and 5500 psi (27.6 and 37.9 MPa) is generally acceptable, and a 56-day strength between 5500 and 8500 psi (37.9 and 58.6 MPa) is considered to be perfect (with no room for improve- ment and no preference for a strength greater than 8500 psi [58.6 MPa]). This function has been designed to give a lower desirability to concrete that is too strong because of its potential for early-age cracking. A desirability function has to be created for every property that is to be evaluated in the design matrix. The suggested de- fault desirability functions are piecewise linear functions, i.e., the function consists of line segments connecting various ver- tices (corner points). However, users can define the functions in different forms. The SEDOC tool has a separate worksheet for each performance test and contains the corner points for the sample desirability functions. The location of the corner points is easily changed by typing over the old corner points or elimi- nating unwanted corner points. For example, if there was an ad- vantage in being as close to 8500 psi (58.6 MPa) as possible, the fourth corner point might be changed to 5500 psi (37.9 MPa) and 0.8 desirability (from 5500 psi [37.9 MPa] and 1.0 desir- ability), yielding the desirability function shown in Figure S5.3 that gives a desirability equal to 1 only at 8500 psi (58.6 MPa). After the appropriateness of all the desirability functions for each of the performance tests is determined (based on an eval- uation of the test and performance requirements), every test response from each mixture is converted into an individual desirability. Each concrete mixture in the test matrix will have 98

a calculated individual desirability for each performance test. Once again, it would be desirable to examine the individual desirabilities to make sure that they appear to be reasonable. Comparing the range of calculated individual desirability val- ues and the range of measured test responses can help in eval- uating the appropriateness of the desirability function and in making adjustments to the desirability function to better fit the data response range or importance. Overall Desirability The overall desirability for each mixture is the geometric mean of the individual desirabilities for that mixture for each of the tests. For example, if only three performance tests were run on each mixture and the individual desirability values for the three different tests on Mixture #1 are represented by d1, d2, and d3, the overall desirability, D, for Mixture #1 is given by . In general for n desirabilities, the overall desirability is the nth root of the product of the individual desirabilities. Because the desirabilities range between 0 and 1, the overall desirability also ranges between 0 and 1, where 0 is unacceptable, and 1 is desirable. Therefore, if a single response results in a desirability of 0, the overall desirability will also be 0. If this situation occurs and it does not seem appropriate, the individual desirability function must be adjusted. In addition, for a fair comparison of overall desirability for each mixture, all mixtures must have an individual desirability calculated for each response included. Best Tested Concrete The first part of the analysis is to compare the concrete mixtures in the design matrix to identify the mixture provid- ing the best performance characteristics, the BTC. Selection of the BTC will be guided by comparison of overall desirabil- ities but ultimately should be confirmed by review of the ac- tual test results and verification that this mixture is best suited to the application. The SEDOC tool automatically calculates the individual desirabilities from the raw test data and then combines them into an overall desirability for each mixture. The following cases explain how the BTC is selected: • If there is one mixture that clearly stands out as having the best overall desirability with a relatively high overall desir- ability value (close to 1), this mixture will probably be con- sidered the BTC. Nevertheless, the user should review the individual desirabilities and test results for each of the tests to confirm that the performance of this mixture is good in all tests. If it is confirmed, then this mixture should be called the BTC. • If there are several mixtures with high overall desirabilities, the user should investigate the individual desirabilities and D d d d= × ×1 2 33 test results for each of these mixtures. The user may also reevaluate the desirability functions based on more infor- mation or consideration of the importance of the various test results. The mixture that is considered to best match the performance characteristics at minimum cost should be selected as the BTC. • If none of the mixtures has a high overall desirability, the desirability functions must be reevaluated. The user should investigate the individual test results of the mixtures with the highest desirability and reassess the weaknesses of the mixture and whether these weaknesses make the mixture unsuited for the application. Also, the desirability func- tions may be modified, and the BTC should be chosen based on the judgment of the user with consideration to the test results. • For all mixtures that have an overall desirability of 0, the user should investigate the individual desirabilities and determine which of the test results has failed. Before declaring the BTC, the user should reevaluate the desir- ability functions that produced the zero desirability value and confirm that the zero-desirability mixtures are unacceptable. Best Predicted Concrete Modeling The next part of the analysis involves a statistical modeling to help predict a combination of the levels of the factors and materials that will produce an untested mixture that will per- form better than the BTC, to be designated the BPC. The BPC will be determined through statistical prediction using the de- sirability functions (including any modifications that were made during the determination of the BTC). The purpose of the BPC analysis is to use trends in the data to predict better concrete mixtures than any of the concretes that were tested in the design matrix. For example, suppose that the four factors given in Table S5.1 are being tested; the relationships observed between the four factors and the response, 56-day strength, are those shown in Figure S5.4; and the objective is to maximize strength. Figure S5.4(a) shows that slag (GGBFS) produces higher strength than the other two supplementary materials that could be used as SCM1; the next plot suggests that the low level of slag is best; Figure S5.4(c) does not show a preferred level of silica fume but it in- dicates that 5% is slightly better than 8%; and Figure S5.4(d) shows that decreasing the w/cm is best. However, because all combinations of the factors were not tested, none of the con- cretes that were actually tested in the experimental design ma- trix have a low level of slag, a w/cm of 0.37, and 5% silica fume; the goal of the BPC analysis is to consider such situations and suggest a different, potentially better, concrete mixture. 99

To capture the trend and curvature in Figure S5.4(a), a simple quadratic equation of the form , where y represents the response (e.g., 56-day strength) and x1 represents the setting of the Factor 1, could be used. Because this is a type factor to be used in the equation, the levels for type of SCM1 are coded into the numerical levels: –1 for Class C fly ash, 0 for Class F fly ash, and 1 for slag. The parameters b0, b1, and b11 are determined by standard linear regression analysis to obtain the function that best fits the data. By including the other factors in a similar form, the following becomes the response equation: (1) where x2 represents the setting of the Factor 2 and so forth. Because there are only two levels for Factor 4, the squared term for x4 cannot be used. Most responses in concrete testing (e.g., strength, scaling mass loss, chloride diffusion coefficient, and modulus of elas- ticity) can take on only positive values. However, the model in Equation 1 can predict negative values for y, indicating inappropriateness for most of the responses. To correct this deficiency, the following model is employed: (2) where e is the natural constant such that ln(e) = 1. Because e is a positive constant, this model will yield only positive val- ues for y. A simple way to fit the model in Equation 2 is to take the natural log of the observed responses and fit the simple quadratic model to that transformed data using standard regression analysis: (3) Once the values for the parameters b0, b1, b11, b2, …, b4 are determined to make the function fit the natural log of the data, the response for any factor settings x1, x2, x3, x4 can be predicted using Equation 2. For ordinary amount factors, the levels can simply be input into Equation 2. For type factors and the amount fac- tor component of compound factors, the levels must be coded to allow numerical evaluation of the model coeffi- cients. For type factors, levels are coded as –1, 0, and 1 for three-level type factors and as 0 and 1 for two-level type fac- tors. When modeling is performed, these factors are only evaluated at the whole number points: –1, 0, and 1 (or 0 and 1). A similar coding approach can be applied for the generi- cally defined amounts in compound factors. However, un- like the procedure used for type factors, the amount factor component of the compound factor can be varied continu- ously over the range –1 to 1 (or 0 to 1). The coded value is then converted back to a specific amount of the associated ln( )y b b x b x b x b x b x b x= + + + + + +0 1 1 11 12 2 2 22 22 3 3 33 32 4 4+ b x y eb b x b x b x b x b x b x b= + + + + + + +0 1 1 11 1 2 2 2 22 2 2 3 3 33 3 2 4 4x y b b x b x b x b x b x b x b= + + + + + + +0 1 1 11 1 2 2 2 22 2 2 3 3 33 3 2 4 x4 y b b x b x= + +0 1 1 11 1 2 type factor based on how the generic ranges for that type were defined. To maximize overall performance, many responses need to be optimized with the understanding that the best settings to optimize one response will not be the best for other re- sponses. This case can be illustrated by the plots in Figure S5.5 representing the relationships between the same factors used in the previous example and the response, specific surface area (which is also to be maximized). Based on the data for this response, better performance is obtained with high amounts of Class C fly ash, no silica fume, and w/cm of 0.45—different levels from those required for optimizing strength. The desirability calculations will help to trade off between maximizing strength and maximizing specific sur- face area, but first the trends for specific surface area must be fitted (in the same way as was done for 56-day strength) to obtain a set of parameter values b0, b1, b11, b2, …, b4 for pre- dicting the effect of the mixture on specific surface area. If many responses are to be considered, this fitting process must be repeated for all the responses; then, for any settings of the factors x1, x2, x3, x4, each response can be predicted using Equation 2 and the respective values of b0, b1, b11, b2, …, b4 for each response. For any predicted value of the response, the desirability of that response can be determined based on the respective desirability function (desirability functions for 56-day strength and for specific surface area are shown in Fig- ure S5.2 and S5.6, respectively). To generate the BPC, the factor settings x1, x2, x3, x4 that maximize the overall desirability (defined as the geometric mean or the nth root of the product of n values) of the indi- vidual response desirabilities must be identified. Table S5.2 shows the calculations for the simple example of two responses (strength and specific surface area) for all possible combinations of the levels shown in Table S5.1. For these two responses, the factor settings that predict the highest overall desirability are fly ash (Class C) at the high level with 5% sil- ica fume and a w/cm of 0.45. The predicted value of 56-day strength for this mixture is 5515 psi, which gives an individ- ual desirability of 1.000. The predicted value of specific sur- face area is 757 in.2/in.3, which has an individual desirability of 0.989. The overall desirability is calculated as the square root of the product of 1.000 and 0.989, which is 0.995. When there are more than two responses, the process is simply expanded to include a prediction and desirability for each response. For factors such as the amount of SCM1, the amount of silica fume, and the w/cm, a finer grid that inter- polates between the specified levels of the factors can also be used to find a BPC; such a process involves more calculations and effort to do the optimization. Once a combination of factor settings that produces the highest predicted overall desirability has been identified, the user should review the predicted individual desirabilities and 100

the predicted test results for the new mixture to verify that it will in fact improve the performance. In this process, the observed data, the desirability func- tions, and modeling are used together to predict a BPC that may perform better than the BTC. However, because of the many approximations and assumptions in the modeling and prediction, confirmation testing (Step 6) must be conducted to compare the BTC and the BPC and confirm their per- formance before the BC is selected. Note on Extrapolation It is mathematically possible to choose factor levels that are outside of the range used in the experiment and predict the test result, the individual desirability, and the overall de- sirability. However, such predictions should be viewed with extreme caution. It is very likely that the regression model will not define the true performance of mixtures that are substantially different from the ones that were used in the design matrix because the regression model is based only on data from the mixtures in the design matrix. Thus, per- formance predictions will likely be more accurate when the factor levels selected for extrapolation are close to the tested range. Predicting new, high-performing concrete mixtures outside the experimental range would require substantial confirmation testing. If extrapolation is performed and a promising mixture is identified, the extrapolated mixture may be produced and tested in addition to the BTC and BPC during the confirmation testing conducted in Step 6 but should not be considered as replacement for either of these mixtures. Repeatability and Scaled Factor Effects A question that is intrinsic to any statistical model is whether the effects of the factors that are used in the model are due to random variability or are due to actual trends in the data. Statistically significant coefficients in the model can be identified by specific statistical tests, which require some estimate of the variability of the random error of the experiment (the repeatability). Multiple batches of some concrete mixtures must be tested to get an estimate of repeatability. A formal test of statistical significance is impractical because of the very limited amount of data in the experiments. However, three methods may be used to estimate repeatability for each performance test and to esti- mate the effect of each factor. • Use the standard deviation or coefficient of variation that is published by ASTM and obtained from repeated meas- urements of the same concrete mixture by various labora- tories that have followed the ASTM standard being used. This standard deviation/coefficient of variation is usually based on repeated testing of a single batch. • Use the standard deviation of repeated measurements on the same concrete from the testing laboratory’s own records for the test procedure being used. • Make and test multiple batches of the control or other mix- ture concrete and use the standard deviation of the test re- sults from these replicates to estimate repeatability. This estimate also includes any variation resulting in the batch- ing process. Published ASTM data account for multiple laboratories and often have a large number of replicates; however, these data are sometimes not available or may not be a good repre- sentation of the repeatability in the laboratory where testing is being conducted because of the batch-to-batch variations. The testing laboratory’s historical data are probably best if good records of the same test being run on multiple batches of the same concrete are available. However, these data often do not exist. Making and testing multiple batches as part of this test has the advantage that the same procedures can be used for both the controls and the mixtures in the design ma- trix and thus the repeatability measured will be similar to the repeatability for the rest of the experiment. However, making and testing a large number of control batches is expensive, and using a small number of control batches will yield a poor estimate of repeatability. In some cases, the best choice may be to defer to the ASTM-published data. A very simple test is used for assessing the factor effects with respect to variability and with respect to each other. The re- gression analysis is used to estimate the amount of variability that is explained by each factor and then the ratio of the vari- ability estimate to the variance (the square of the standard deviation) of repeatability. This ratio is the standard “partial F-ratio” for each factor in a standard regression analysis or ANOVA (analysis of variance), where the mean square error is the square of the standard deviation selected to represent re- peatability (61), and is referred to as the “scaled factor effect.” Because the accuracy of the repeatability estimate is unknown, no attempt will be made to perform a precise statistical test of significance on this ratio as is done in most regression analy- ses. However, the user may observe the scale of the factor effects: first, checking to see if the scaled factor effects are less than or much greater than 1 and then comparing the scaled factor effects of the different factors to see the relative size of the factor effects with respect to each other. If this ratio is less than one, then the factor effect is smaller than the repeatabil- ity; and it should not be considered to be an actual trend in the data. If the ratio is much larger than one, for example, greater than 10, then the factor probably is statistically significant. For example, the factor effects chart for the scaled factor effect on electrical conductivity (Figure S5.7) shows that the 101

amount of silica fume and the w/cm probably have a real effect on the conductivity and that the type and amount of SCM1 may have an effect, but there is no clear trend. Because none of the ratios are below 1, all of these factor effects could be real trends in the data. Because of the uncertainty of this test, no attempt is made to reduce the regression models by removing terms. Statistical Experimental Design for Optimizing Concrete Computational Tool To help the user implement the analysis process, SEDOC, a Microsoft® Excel–based computational tool, is provided with these Guidelines. While the tool supports all the steps in the methodology except for the actual mixture proportioning and batching, it is most useful during Steps 5 and 6. It is designed to perform conversions to individual desirabilities based on data generated by the experimental testing program, as well as the calculation of the overall desirability, the selection of the BTC, and the modeling and prediction of the BPC. The tool includes many pre-formatted plots and tables designed to help the user analyze and discover trends within the data. SEDOC and the user’s guide are available on the TRB website (http://www.trb.org/news/blurb_detail.asp?id=7714). Example from Hypothetical Case Study The following discussion is based on the test results col- lected as part of the hypothetical case study presented in Appendix A of NCHRP Web-Only Document 110 (http:// www.trb.org/news/blurb_detail.asp?id=7715). While every experiment will have different considerations depending on the performance objectives and the results obtained, this ex- ample will show how a given set of results can be interpreted relative to the hypothetical objective of a durable bridge deck in a northern climate. After the tests were conducted in Step 4, the responses were tabulated and converted into individual desirability values based on the initially assumed desirability functions. The results of this analysis were reviewed and the responses to be included in the overall desirability calculations were reevalu- ated. The initial assumptions for the desirability functions were also reevaluated to ensure that they accurately inter- preted the performance of the mixtures (i.e., properly reflected differences or similarities in performance). Table S5.3 lists the individual responses that were initially planned in Step 1 and tested in Step 4 and those that were ac- tually used to calculate the overall desirability for the mix- tures in Step 5. One of the primary changes made was the elimination of fresh properties (i.e., slump, slump loss, plas- tic air content, and air content of hardened concrete) because these properties can be adjusted by the concrete producer based on admixture dosage and were not uniquely deter- mined by the factors investigated in this experiment. Also, no measure of the hardened air parameters was included since cyclic freezing resistance was tested directly. Another change that was made was the inclusion of 56- day strength in place of 28-day strength. This change was necessary because the mixture containing a high content of Class F fly ash had a 28-day strength of 3620 psi (25.0 MPa), which was well below the minimum of 5000 psi (34.5 MPa) used to develop the desirability function. This change pe- nalizes all mixtures containing Class F fly ash because the in- fluence of a type factor is based on the average response for all mixtures containing that type. While the desirability function for 28-day strength was reasonable, a designer may be willing to wait for the concrete to reach design strength at 56 days, if that means that a more durable concrete with a lower diffusion coefficient and other more desirable responses may be achieved. Using the 56-day strength, which was 4490 psi (31.0 MPa) for the high-content Class F fly ash mixture, gave a much more acceptable overall desir- ability for that mixture. Finally, scaling resistance was evaluated visually and by mass loss. To limit the weight applied to scaling relative to the other performance measures, mass loss (the most definitive measure) was included, and the visual rating was not. Modifications to the desirability functions were made in some cases after the data were examined. For example, the desirability function for temperature rise due to heat of hydration was adjusted based on the test results. It was ini- tially assumed, based on the insulation vessels, that the tem- perature rise would not be much above 30°F (17°C), and the desirability function was designed accordingly. However, the test results ranged from 30°F to 50°F (17°C to 29°C). There- fore, the desirability function was adjusted to give some credit to those mixtures that produced a lower temperature rise without overly punishing the mixtures at the higher end of the scale; Figure S5.8 shows the original and adjusted desir- ability functions. To generate the BPC, the factors that maximize the overall desirability must be identified by evaluating the overall desir- ability for many possible combinations of factor levels and finding the combination that produced the highest overall desirability. For amount factors such as the amount of SCM1, the amount of silica fume, and the w/cm, the responses were evaluated at several, evenly spaced sets of levels between the level ranges specified in the test experimental matrix to find the BPC. For the type factor type of SCM1, the responses were evaluated for each discrete type. In this way, the observed data, the desirability function, and the response models were used together to predict a BPC that would perform better than the BTC. The BTC and BPC that were selected based on 102

the test program results are given in Table S5.4. The predicted overall desirability and the mixture number from the Step 4 test program are also shown. The models predict that for the materials tested, using the same amount of slag tested as the medium level in the previous matrix is, in fact, optimum but that the amount of silica fume should be increased to 8% and that the w/cm should be increased by 0.02, from 0.37 to 0.39. The predictions of the performance of the BTC and BPC are given in Table S5.5. These predictions were taken from SEDOC output used to perform this analysis. Predicted responses are given for all properties tested and predicted desirabilities are given for those responses used to determine the overall desirabilities. A review of this table, specifically where the individual desirabilities of the BPC are greater than those of the BTC, identifies the responses that were most sig- nificant in the selection of the BPC. Despite a slightly lower individual desirability for finishability and mass loss, the pre- dicted individual desirabilities for the BPC for the chloride diffusion, electrical conductivity, and cracking tendency were all higher; these individual desirabilities contributed to the greater overall desirability and the selection of this mixture as the BPC. 103

104 Mixture #2 Mixture #1 Mixture #3 Mixture #5 Mixture #4 Mixture #9 Mixture #6 Mixture #7 Mixture #8 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 54.073.0 w/cm ps i 0 0.2 0.4 0.6 0.8 1 0 2000 4000 6000 8000 10000 12000 56-day strength (psi) D es ira bi lit y 0 0.2 0.4 0.6 0.8 1 0 2000 4000 6000 8000 10000 12000 56-day strength (psi) D es ira bi lit y Figures for Step 5 Figure S5.1. Scatter plot of 56-day strength vs. w/cm with trend line. Figure S5.3. Modified desirability function for 56-day strength. Figure S5.2. Desirability function for 56-day strength.

105 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Fly Ash (Class C) Fly Ash (Class F) GGBFS SCM1 Type St re n gt h (p s i) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Low Med High Amount of SCM1 St re n gt h (p s i) (b)(a) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0.00 0.02 0.04 0.06 0.08 0.10 Amount of Silica Fume St re n gt h (ps i) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 54.073.0 w/cm St re n gt h (p s i) (d)(c) Figure S5.4. Relationships between 56-day strength and factors.

106 0 100 200 300 400 500 600 700 Fly Ash (Class C) Fly Ash (Class F) GGBFS SCM1 Type Sp e c ifi c Su rfa c e (in 2/i n3 ) 0 100 200 300 400 500 600 700 Low Med High Amount of SCM1 Sp e c ifi c Su rfa c e (in 2/i n3 ) (b)(a) 0 100 200 300 400 500 600 700 0.00 0.02 0.04 0.06 0.08 0.10 Amount of Silica Fume Sp e c ifi c S u rfa c e (in 2/ in 3) 0 100 200 300 400 500 600 700 54.073.0 w/c Sp e c ifi c S u rfa c e (in 2/ in 3) (d)(c) Figure S5.5. Relationships between specific surface area and factors.

107 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 Specific Surface Area (in2/in3) D es ira bi lit y Ratio of Factor Effects to Repeatability (Repeatability Level =1) Note: Factor Effects that are less than 1 are negligible. 0 5 10 15 20 25 30 Type of SCM1Amount of SCM1Amount of silica fumew/cm Ef fe ct Si ze C o m pa re d to R e pe at ab ilit y 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 Temperature Rise (°F) De s ira bi lit y Original Desirability Function Revised Desirability Function Actual Data Controls Figure S5.6. Desirability function for specific surface area. Figure S5.7. Ratio of factor effects to repeatability for electrical conductivity test. Figure S5.8. Example of modification to temperature rise desirability function.

108 Tables for Step 5 Factor No. Factor Name Level 1 Level 2 Level 3 Factor 1 (3 levels) Type of SCM1 Fly ash (Class C) Fly ash (Class F) GGBFS Factor 2 (3 levels) Amount of SCM1 Low Medium High Factor 3 (3 levels) Amount of silica fume (%) 0 5 8 Factor 4 (2 levels) 54.0 73.0 mc/w Factor 1 Factor 2 Factor 3 Factor 4 Predicted 56-Day Strength Predicted Specific Surface Area 56-Day Strength Desirability Specific Surface Area Desirability Overall Desirability Fly ash (Class C) Low 0% 0.37 5843 504 1.000 0.878 0.937 Fly ash (Class C) Low 0% 0.45 4703 657 0.971 0.964 0.968 Fly ash (Class C) Low 5% 0.37 7239 467 1.000 0.850 0.922 Fly ash (Class C) Low 5% 0.45 5827 609 1.000 0.952 0.976 Fly ash (Class C) Low 8% 0.37 6630 479 1.000 0.859 0.927 Fly ash (Class C) Low 8% 0.45 5336 625 1.000 0.956 0.978 Fly ash (Class C) Med 0% 0.37 5574 489 1.000 0.867 0.931 Fly ash (Class C) Med 0% 0.45 4486 637 0.925 0.959 0.942 Fly ash (Class C) High 5% 0.45 5515 757 1.000 0.989 0.995 GGBFS High 5% 0.37 8701 495 0.973 0.871 0.848 GGBFS High 5% 0.45 7000 646 1.000 0.962 0.962 GGBFS High 8% 0.37 8277 508 1.000 0.881 0.881 GGBFS High 8% 0.45 6659 663 1.000 0.966 0.966 Table S5.1. Factors and levels for 9-mixture design. Table S5.2. Predicted responses and associated individual and overall desirabilities at each level combination (examples).

109 Table S5.4. Overall desirabilities of Best Tested and Best Predicted Concretes. Proposed Responses from Step 1 Selected Responses for Step 5 Design Matrix Analysis Selected Responses for Step 6 Confirmation Analysis pmulS .1 2. Slump Loss 3. Plastic Air Content 4. Air Content of Hardened Concrete tes laitinI .1 tes laitinI .1 teS laitinI .5 6. Finishability 2. Finishability 7. Cracking Tendency 3. Cracking Tendency 8. Heat of Hydration - Temperature Rise 4. Heat of Hydration - Temperature Rise 2. Heat of Hydration - Temperature Rise egaknirhS .3 egaknirhS .5 egaknirhS .9 aerA ecafruS cificepS .01 11. Compressive Strength, 7-Day 6. Compressive Strength, 7-day 4. Compressive Strength, 7-day yaD-82 ,htgnertS evisserpmoC .21 13. Compressive Strength, 56-Day 7. Compressive Strength, 56-day 5. Compressive Strength, 56-day 14. Modulus of Elasticity 8. Modulus of Elasticity, 28-day 15. Electrical Conductivity 9. Electrical Conductivity 6. Electrical Conductivity )gnitar lausiv( gnilacS .61 17. Scaling (mass loss) 10. Scaling (mass loss) 7. Scaling (mass loss) 18. Freezing and Thawing Resistance (durability factor) 11. Freezing and Thawing Resistance (durability factor) 19. Chloride Penetration Resistance (diffusion coefficient) 12. Chloride Penetration Resistance (diffusion coefficient) 8. Chloride Penetration Resistance (diffusion coefficient) Mixture Type of SCM1 Amount of SCM1 (%) Amount of silica fume (%) w/cm Actual Overall Desirability Predicted Overall Desirability Mixture No. BTC GGBFS 35 0 0.37 0.9648 0.9653 8 BPC GGBFS 35 8 0.39 – 0.9744 – Table S5.3. Responses for overall desirability calculation.

110 Predicted Response Predicted Desirability Property BTC BPC BTC BPC – – 01.7 50.8 ).ni( pmulS Slump Loss (in.) 1.89 2.49 – – Plastic Air (%) 6.34 6.44 – – Hardened Air (%) 6.09 6.70 – – Initial Set (h) 5.33 5.66 1.00 1.00 Finishability 11.83 11.41 0.95 0.94 Cracking Tendency (wks) 7.43 15.67 0.96 1.00 Heat of Hydration (°F) 44.63 43.83 0.96 0.96 Shrinkage (%) -0.0445 -0.0434 0.98 0.98 Specific Surface Area (in.-1) 417 424 – – Compressive Strength at 7 Days (psi) 5366 5503 1.00 1.00 Compressive Strength at 28 Days (psi) 7193 7730 Compressive Strength at 56 Days (psi) 7792 8383 1.00 1.00 Modulus of Elasticity (x 106 psi) 4.25 4.24 1.00 1.00 Electrical Conductivity (Coulombs) 1144 397 0.93 0.98 Scaling: Visual 0.00 0.01 – – Scaling: Mass Loss (g/m2) 93.4 183.0 0.97 0.95 Freeze-Thaw Durability Factor (%) 103.7 104.0 1.00 1.00 Chloride Diffusion Coefficient (x 10-12 m2/s) 1.95 1.38 0.85 0.90 Table S5.5. Predicted responses of Best Tested and Best Predicted Concretes.