Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks (2007)

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NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks FINDINGS Statistical Design of Experiments An experiment that is “designed” is one that is conducted based on a test program laid out to produce results that answer a question or verify a hypothesis. Statistical design of experiments involves selecting the experimental parameters so that the experiment will produce data that supports analysis and modeling with statistical tools. The great advantage of statistical experimental design is that experiments conducted in this way are more efficient, i.e., they allow predictions regarding large numbers of possible variations based on a limited number of tests. Terminology Before discussing the details of how statistical experimental design can be applied to the design of concrete mixtures, a review of the relevant terminology is needed. Table 1 summarizes the terminology. The three most common terms are “factor,” “level” and “response”. The term “factor” refers to the independent variable, or “x”-variable, to be examined in the experiment. There are multiple kinds of factors. “Type factors” and “Source factors” are factors that describe the type or source of material that is used and are defined discreetly to be either one type of material or another or a material from one source (or supplier) or another, respectively. “Amount factors” vary the amount of a raw material in the mixture and can be defined continuously over the range to be tested. It is also possible to combine two factors in a “Compound factor,” to be discussed later. The term “level” refers to the chosen value of the factor in a particular mixture. For example, if an Amount factor for a given experiment was selected to be w/cm, three levels to test could be chosen as 0.38, 0.40, and 0.44. For a Source factor, the levels are the actual sources used such as Plant A and Plant B. A Type factor is used when it is desired to change the type of cement, SCM, or other raw material. For example, a Type factor might be Type of Fly Ash, and the levels of the Type factor could be Class F and Class C. One could then also have an Amount factor for fly ash (at levels of perhaps 15% and 30%) that would then apply to whichever type of fly ash was used in the mixture. Another term used is “response.” This is the y-variable, or test result, when a mixture is tested for a certain property using a specific test method, such as strength or apparent diffusion coefficient. “Response” means test result. The “experimental matrix” is the matrix of combinations of factors and levels that is generated by the user with the aid of tables or computational tool. It includes the number of “mixtures” to be evaluated and details how the levels of each of the factors should be set for each mixture. One of the most important concepts for the analysis process in the Methodology is the “desirability function”. The desirability function refers to a plot or equation that rates a given response (test result) on a scale from 0 to 1, where 0 is an unacceptable result, and 1 is a result that cannot or does not need to be improved. The desirability function for a response maps every possible outcome of the test to a desirability value. Through the desirability function, which can vary depending on the application, the relative importance (rating) of each test result (response) is defined. 8

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 1. Terminology related to statistical design of experiments Term Definition Example Factor X-variable or independent variable (see below) Type factor A factor that varies the type of material used in a mixture “Type of fly ash” Source factor A factor that varies the source or supplier of raw material “Cement producer” Amount factor A factor that varies the amount of a material “Amount of GGBFS” Compound factor Multiple factors where the levels of one factor depend on the level of another factor. (The two factors work together to define the type and amounts of material used in a mixture.) Factor 1 is a type factor for defining the type of SCM, and its levels are fly ash or slag. Factor 2 is an amount factor whose levels are low and high. The amounts specified for low and high for each type of SCM are different. For example, low and high for fly ash might be 15 % and 40%, but low and high for slag might be 25% and 50%. Thus the levels of the second factor change (from 15% and 40% to 25% and 50%) depending on the level of the first factor (either fly ash or slag). Factor level A level associated with a specific factor. Silica fume content = 5% Levels The values of the factor to be tested Class C or Class F for type of fly ash; Plant A or Plant B for source of cement; 15% or 25% for amount of GGBFS Response A measured test result Strength at 7 days = 5000 psi Experimental matrix A list of mixtures to be tested linking specific factors and levels that have been chosen to facilitate the statistical analysis. See tables in “Selected Orthogonal Designs” at end of Step 3 in NCHRP Report 566. Desirability function A function that rates the test result from very good, i.e. non-improvable (desirability=1) to unacceptable (desirability=0) See Figures S1.2 to S1.23 in NCHRP Report 566. Overall desirability Combined desirability for a single mixture based on all the individual desirabilities. This is calculated as the geometric mean of the individual desirability functions for each response Overall desirability = 0.984 for Mixture #1 The overall performance or “overall desirability” of a mixture is the combined desirability of each test response and allows a direct comparison of the overall properties of one mixture with another. This comparison is used to decide which mixture is best overall. This is possible because the overall desirability is derived from the individual desirabilities for each response and so reflects the individual properties of the mixture and importance of each of these properties to the overall concrete performance. The concepts of desirability and overall desirability are discussed further in the section titled “Combining Test Results” below. 9

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Methods of Designing Experiments Through the use of statistical design of experiments, it is possible to obtain useful information without testing every combination of variables at every level. There are several types of designed experiments, including one-factor-at-a-time, orthogonal main-effects designs, mixture approaches, and central composite designs. Each has its advantages and disadvantages. In this Methodology, a straightforward design method called fractional orthogonal design is used. The biggest advantage of this approach is that it requires a relatively small number of mixtures be tested to cover a large test space. For example, for an experiment of four three-level factors (four materials at three dosages each), careful selection of the combinations of factor levels to be tested would permit conclusions to be made regarding the full test space (all possible combinations within the factor ranges) from tests of only 9 mixtures instead of all 81 (=34) possible discrete combinations of the factor-levels. This method also permits modeling with non- quantitative factors (such as source of material), which are often important variables to consider in concrete mixture proportioning. Also, there are no limitations on the number of responses or on the form of the desirability functions. Using the results from only the selected combinations tested, the fractional orthogonal design method is able to provide a prediction of the best level for each of the factors in the experiment. However, the fractional orthogonal approach is a main-effects method. This means that interactions between factors are not modeled as well as by other experiment designs that require a larger number of mixtures. In other words, if the optimum level for any factor substantially changes for different levels of other factors, the optimum level of that factor may be poorly predicted. However, this will not affect the evaluation of the concretes that are actually batched and tested. Since the mixtures in a fractional orthogonal design are quite different from each other, there is an increased chance of finding a good mixture even in the cases where the optimum level for some factors is difficult to predict. A confirmation testing strategy, where the model predictions are tested directly, addresses this issue. The alternative is to test substantially more concrete as in the mixture or central composite design approaches (at least 24 of the 81 possible combinations discussed in the example above would need to be tested for these methods). Combining Test Results If only one test were to be performed, the concrete performance can be easily compared based only on the measured value of that test for each mixture. However, since many different tests will be performed, and the selected mixture must perform well in all of these tests, a method of combining the responses (test results) from the different tests is needed. This is done by defining a desirability function for each response (1). As previously stated, this function is a rating for all potential values of the test response on a scale from 0 to 1, where 0 means an unacceptable response, and 1 means no more improvement is needed. Each test response has its own desirability function. The advantage of the desirability function is that all test responses are considered using an equivalent scale and can be combined to produce one score or measure of the quality of a given mixture called the “overall desirability function.” When maximized, the overall desirability identifies the best possible combination of performance in all the tests. To build the desirability function for a specific test result, an optimum target for the measured response of each test is specified. At the target, the individual desirability for that test is 1. Then an allowable range for the measured response is specified. Outside of this range, the 10

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks individual desirability is 0 or totally unacceptable. The shape of the desirability function between the target and the range is also specified to reflect the importance of being near the target. If the measured response of a particular test is to be maximized (or minimized), then the upper (lower) range of the desirability is considered to be perfect and thus any measured value above (below) this level has a desirability of 1. Figure I.1 demonstrates the shape of three possible desirability functions. Mathematically, the overall desirability is defined for this Methodology to be the geometric mean of the desirability functions for each of the tests. For example, suppose that the desirability functions for three different tests are represented by d1, d2, and d3. The overall desirability, D, is 3 321 dddD ××= . In general for n desirabilities, the overall desirability is the nth root of the product of the desirability functions. Since the desirabilities range between 0 and 1, the overall desirability function also ranges between 0 and 1, where 0 is unacceptable and 1 is desirable. Another method of calculating the overall desirability is to use an arithmetic mean of the individual desirabilities. When using the geometric mean to calculate overall desirability, the effect of low individual desirabilities is accentuated compared with arithmetic mean-based approaches. However, the big advantage of the geometric mean is that if a single individual desirability is 0, then the overall desirability is 0. As a result, the individual desirability functions can be defined so that a desirability of 0 is assigned to those test outcomes that make the mixture unacceptable regardless of how it performs in other tests. It should be noted that since the desirability function provides the link between the test, which may be influenced by the method and testing conditions, and the predicted actual behavior, the desirability function requires subjective interpretation by the engineer or scientist conducting the study. However, it is through the desirability function that the interpretation of the experimental program is customized to the local performance requirements. Overview of Methodology The Methodology for designing concrete mixtures containing supplementary cementitious materials (SCMs), presented in NCHRP Report 566, is aimed at aiding the user select the optimum combination of locally available materials for maximum durability. This Methodology relies on established practices of statistical design and analysis of experiments. It is targeted for use in the development phase of concrete construction projects. This Methodology will help highway agency personnel and other engineers optimize and specify the material proportions and performance criteria for a specific project or set of conditions. The Methodology that was developed primarily considers the use of fly ash, silica fume, slag, and natural pozzolans both singularly and in combination. However, any combination of materials and performance criteria can be analyzed. A basic understanding of concrete mixture proportioning and concrete technology is assumed of the user; however, background specifically related to durability issues and guidance for avoiding harmful material interactions is provided that may be referred to as needed. It is expected that all users, even experienced concrete practitioners, will find the Methodology valuable since the defined procedure provides an efficient method for optimizing concrete mixtures relative to locally applicable performance criteria with locally available materials. This is an objective that cannot be achieved through any means other than a large experimental investigation. The Methodology consists of the following steps: 11

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks • Step 1: Define Concrete Performance Requirements - The service environment of the concrete is evaluated, and likely deterioration mechanisms are identified. The concrete properties required to resist deterioration are determined, and test methods to evaluate these properties are selected for inclusion in the testing program. A desirability function is defined for each response (measured property). Finally, SCM types and content ranges likely to produce desirable concrete performance for each property to be tested are identified. • Step 2: Select Durable Raw Materials - The locally available raw materials under consideration for the project are evaluated. The various potential sources of each type of material are compared based on the information available in mill reports and elsewhere, and the specific materials types and sources most likely to produce durable concrete are selected as candidates for making the concrete mixtures. The potential for aggregate sources to participate in deleterious alkali-silica reactions is considered. A testing process, to be used where insufficient information is available, and mitigation strategies for ASR are recommended. • Step 3: Generate the Experimental Design Matrix - Based on the scope of the testing program and the available resources, an orthogonal experimental design is selected. The size and shape of the design, i.e., the number and levels of factors to be tested, are controlled by the number of mixtures that can be tested within the allowable time and budget. The specific factors (such as material type, source, or content) and the corresponding levels (the specific types, sources or dosages) for testing are chosen from the candidate materials to fit within a predefined design matrix. • Step 4: Perform Testing - The concrete mixtures listed in the experimental design matrix are produced and tested according to the program defined in Step 1. • Step 5: Analyze Test Results and Predict the Optimum Mixture Proportions - The individual responses are converted to desirabilities for each mixture, and the Best Tested Concrete (BTC) is chosen as the mixture produced in the test program with the highest overall desirability. Empirical models relating response to factor levels are developed for each response, and an optimization routine is used to determine the combination of factors and levels that produce the highest predicted overall desirability. This combination is called the Best Predicted Concrete (BPC). • Step 6: Perform Confirmation Testing and Select the Best Concrete - The BPC and BTC are batched and tested to confirm their performance. The test results are evaluated in terms of desirabilities, and the repeatability of the testing and accuracy of the modeling is assessed. Finally, the optimum performer, or Best Concrete (BC), is selected from these two candidates. Implementation of Methodology NCHRP Report 566 provides tools to aid in the application of each of the steps of the Methodology. These include flowcharts, worksheets for summarizing information, background discussions of the issues relevant to decisions that need to be made, tables of experimental matrices, and an explanation of the statistical analyses. The decisions to be made in Step 1 and 2 have been laid out in two flowcharts. The product of the first flowchart (Figure S1.1: Selecting concrete service environment and properties) is a list of laboratory tests to be conducted (the responses) and the associated performance 12

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks requirements for the concrete. These requirements are quantified in the form of desirability functions, and a discussion of how these functions work and how they are defined is provided. Guidance is given to support the flowchart regarding suitable ranges of various SCMs that have been shown in the literature to improve the responses. The information gathered from Figure S1.1 is collected by the user on a worksheet. This worksheet and others given in NCHRP Report 566 are intended to provide a location for the user to record information relevant to the specific experiment being designed. The second flowchart (Figure S2.1: Selecting durable raw materials) outlines a process for evaluating the candidate raw materials and sources. Test data regarding these raw materials are collected, and combinations of materials that are likely to be durable are identified. The sources or types of raw materials will be the levels of “source or type factors” in the experimental design matrix. The quantities to which these raw materials will be varied are the levels of the “amount factors” in the experimental design matrix. The information gathered from Figure S2.1 is also collected in worksheets. These worksheets are combined into the set of factors and levels in Step 3, where the experimental design to be used is selected from a table (Table 2) of orthogonal experimental designs defined by the number of mixtures to be tested and the number of two- and three-level factors to be investigated. This table shows that only certain sizes of experiments, namely those that permit a symmetric distribution of the number of test mixtures containing each level for each factor, are eligible for use. Figure I.2 shows schematically the relationship between the flowcharts and how they support the experimental design. This figure is intended to illustrate that, during this selection process, there will likely be compromises between the materials selected based on the performance objectives, the cost and scope of testing program, the selection of the experimental design matrix, and the number of materials that can be tested. For each experiment, a numeric analysis (Step 5) will be performed. The analysis consists of two parts: • The first part of the analysis is to compare the concrete mixtures that were tested to determine which one best matched the performance requirements. This is called the "Best Tested Concrete" (BTC). The identification of the BTC will involve tradeoffs between the different performance measures and uses the overall desirability function as a basis for comparison. • The next part of the analysis is empirical modeling to determine the combination of the levels of the factors that will produce the "Best Predicted Concrete" (BPC), identified by the highest overall predicted desirability. This is estimated based on individual predictions for each of the responses (performance measures) for all possible combinations of the factors in the range tested. The empirical models can also be used to predict the response for any mixture (combination of factors) in each of the individual tests. 13

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 2. Table S3.1 Number of mixtures required for an orthogonal design for various combinations of two- and three-level factors. The 9-mixture design selected for hypothetical case study is highlighted. # of 3-level factors 0 1 2 3 4 5 6 7 # of 2-level factors 0 3 9 9 9 16 18 18 1 2 8 9 9 16 18 18 18 2 4 8 9 16 16 18 18 >18 3 4 8 16 16 16 18 >18 >18 4 8 8 16 16 18 >18 >18 >18 5 8 16 16 16 >18 >18 >18 >18 6 8 16 16 16 >18 >18 >18 >18 7 8 16 16 >18 >18 >18 >18 >18 8 12 16 16 >18 >18 >18 >18 >18 9 12 16 16 >18 >18 >18 >18 >18 10 12 16 >18 >18 >18 >18 >18 >18 11 12 16 >18 >18 >18 >18 >18 >18 12 16 16 >18 >18 >18 >18 >18 >18 13 16 >18 >18 >18 >18 >18 >18 >18 14 16 >18 >18 >18 >18 >18 >18 >18 15 16 >18 >18 >18 >18 >18 >18 >18 Since the amount of data available to support the empirical modeling is limited with this experimental design approach and interactions are not estimated, the results of the modeling need to be confirmed by a second round of testing (Step 6). The BPC is not expected to be among the mixtures that were actually tested in the original matrix and thus, if it is to be used in construction with confidence, a confirmation batch of the BPC must be mixed and tested. Realistically, the amount of testing of the BPC that is conducted will be based on the amount of time available for Confirmation Testing and the predicted performance difference between the BPC and the BTC. At the end of the Confirmation Testing, the Best Concrete (BC), the mixture recommended for implementation, is chosen. The BC is expected to be the BPC. However, the BPC should be chosen only if the overall desirability based on the Confirmation Testing for that mixture is indeed higher than that for the BTC. Additional considerations may come into this selection, such as the actual difference in overall desirabilities between the BTC and BPC relative to the repeatability of the test methods, performance in areas determined to be critical to 14

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks the application, and factors that may not have been included in the scope of the experiment, like cost or ease of production. Hypothetical Case Study To provide a basis for evaluating this Methodology, a case study, called the Hypothetical Case Study, was investigated. The service environment for this study was chosen as a bridge deck in a northern, Midwest environment subject to freezing and thawing and deicing salt exposure. Performance requirements were developed and locally available materials were obtained and used to perform an experimental study. This test program was conducted according to the process outlined in the Guidelines. The full, step-by-step details of this study are provided in Appendix A, but an overview of the process and the evaluation of accuracy of the analysis and modeling based on the actual results are presented here. Step 1: Service Conditions Based on a bridge deck application in a northern climate, the steps outlined by Figure S1.1 were used to characterize the universal design requirements and to evaluate issues relevant to a freezing climate subjected to chemical deicers, and where cracking was a concern. This environment was assumed to be neither coastal nor abrasive. The required testing based on the service environment of the Hypothetical Case Study was summarized using Worksheet S1.1, which lists the properties of interest, the test methods to measure each property, and optimum target values. These target values were then used to develop a desirability function for each property. After each property of the concrete was considered, the recommended ranges of SCM contents expected to produce desirable performance were collected and summarized to form the basis for selecting the ranges for testing. Step 2: Materials Selected In Step 2, suitable raw materials were selected. The worksheets in Step 2 of the Guidelines were used to organize the available information regarding the locally available materials and facilitate decisions about the materials. For the Hypothetical Case Study, materials local to the Chicago area were used. Multiple sources of cement, fine and coarse aggregate, Class C fly ash, slag and admixtures were evaluated using this process, and those materials deemed most likely to produce durable concrete were chosen. Step 3: Experimental Design Matrix The review of the Hypothetical Case Study environment conducted in Step 1 suggested that a large test program was necessary to characterize each mixture’s performance. As a result, it was determined that the experimental program was constrained by the available budget to a 9-mixture experiment. This number of experiments controlled the possible numbers of factors and levels as listed in Table S3.1 (Table 2). Given this constraint, the next step was to select which factors and levels to include. The main focus chosen for the hypothetical experiment was to evaluate as wide a range of SCMs as possible. Therefore, to maximize the number of SCMs while limiting the size of the experimental 15

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks design matrix to nine mixtures (based on three three-level factors and one two-level factor), the factors defined were: “First SCM Type,” “First SCM Amount,” “Amount of Silica Fume” and “w/cm.” The range of the investigation for each of the factors was chosen to span the region where the optimum level was expected. When the ranges recommended in Step 1 for silica fume were compiled for all the desired properties, one level resulted: 5%. The same was true for GGBFS (30%) and Class C Fly ash (25%). Since the objective of this research is to optimize SCMs, it was decided to center the test program on these recommended values, and levels for testing were chosen above and below these values. Ordinarily, an Amount Factor such as “First SCM Amount” would have simple numerical values given as levels. However, since the appropriate ranges for types of SCMs may be dependent on that specific type, a Compound Factor was used. This Compound Factor, which links the definition of the Amount Factor to a Type Factor, allowed additional freedom in the definition of SCM contents. The levels of the First SCM Type factor were defined as slag, Class C fly ash, and Class F fly ash. Then, the levels of the First SCM Amount factor were defined generically as Low, Medium, and High, with different specific values of the SCM content associated with the generic definitions for the slag and for the fly ashes. Despite the generic definition, the “Amount of SCM1” is an Amount Factor, and the performance modeling is still capable of interpolating between the levels tested. The factors and levels used for the Hypothetical Case Study are given in Table 3. The definitions of Low, Medium, and High are shown in Table 4. Type, Source, and Amount Constants are those characteristics of the mixture design that will be consistent throughout the experiment. These included single sources for each raw material type, and defining a constant cementitious material content (658 lb/yd3 [391 kg/m3]) and coarse aggregate content (1696 lb/yd3 [1007 kg/m3]). The coarse aggregate content was selected based on the fineness modulus of the fine aggregate as recommended by ACI 211.1 (2). All SCM amounts were calculated as percentages by mass replacement of portland cement. Accordingly, changes in cementitious materials volumes were compensated by changes in fine aggregate content. Two batches of a control mixture were also incorporated in this study. The control mixtures were made with no SCMs at a w/cm of 0.40. The mixture included 263 lb/yd3 [156 kg/m3] water, 658 lb/yd3 [391 kg/m3] cement, 1280 lb/yd3 [760 kg/m3] fine aggregate, and 1696 lb/yd3 Table 3. Factors and levels for 9-mixture design used in Hypothetical Case Study 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 Med High Factor 3 (3 levels) Amount of silica fume (%) 0 5 8 Factor 4 (2 levels) w/cm 0.45 0.37 - 16

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 4. Definition of compound factor for Hypothetical Case Study Factor 1, Factor 2 Combinations Type of SCM Amount of SCM Type 1, Low level Class C fly ash 15% Type 1, Medium Level Class C fly ash 25% Type 1, High Level Class C fly ash 40% Type 2, Low level Class F fly ash 15% Type 2, Medium Level Class F fly ash 25% Type 2, High Level Class F fly ash 40% Type 3, Low level slag 25% Type 3, Medium Level slag 35% Type 3, High Level slag 50% [1007 kg/m3] coarse aggregate. The intent of this mixture was to provide a comparison to assess relative performance of mixtures with SCMs. The replicate control mixture was added to provide an assessment of batch-to-batch variability for each test so that the significance of differences in test results could be evaluated. As mentioned, the orthogonal design selected required that nine mixtures be evaluated to provide sufficient information to optimize these factors and levels. These mixes must be chosen according to the applicable table from the collected orthogonal experimental design matrices at the end of Step 3 of the Guidelines. The generic design matrix that applies for the nine-mixture experiment, three three-level factors and one two-level factor design is given in Table 5. Table 6 lists the specific design matrix after the factor levels were substituted into this generic matrix. The actual mixtures and batch weights tested are listed in Table 7. The admixture dosage rates were determined based on trial batches. Table 5. The levels for the 9-mixture design matrix with 3 three-level and 1 two-level factors. (The numbers in the columns refer to the levels indicated in Table 3.) Mixture # Factor 1 (3-Level) Factor 2 (3-Level) Factor 3 (3-Level) Factor 4 (2-Level) 1 1 1 1 1 2 1 2 2 2 3 1 3 3 2 4 2 1 2 2 5 2 2 3 1 6 2 3 1 2 7 3 1 3 2 8 3 2 1 2 9 3 3 2 1 (If the font is underlined and bold, the level chosen for that Factor should be the one expected to produce the best result.) 17

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 6. Experimental design matrix for Hypothetical Case Study Mixture First SCM Type First SCM Amount Amount of Silica Fume w/cm 1 Fly Ash C Low (15%) 0 % 0.45 2 Fly Ash C Medium (25%) 5 % 0.37 3 Fly Ash C High (40%) 8 % 0.37 4 Fly Ash F Low (15%) 5 % 0.37 5 Fly Ash F Medium (25%) 8 % 0.45 6 Fly Ash F High (40%) 0 % 0.37 7 GGBFS Low (25%) 8 % 0.37 8 GGBFS Medium (35%) 0 % 0.37 9 GGBFS High (50%) 5 % 0.45 Step 4: Test Program The test program outlined in Step 1 (defined using Worksheet S1.1) was modified slightly in practice, and the actual program is summarized in Table 8. Appendix A gives the full details of the testing program. Step 5: Best Tested Concrete, Best Predicted Concrete Analysis After the tests were conducted, the responses were tabulated and converted into individual desirability values based on the desirability functions developed during the definition of the performance requirements. The results of this analysis were reviewed, and the responses to be included in the overall desirability calculations were re-evaluated. The initial assumptions for the desirability functions were also re-evaluated based on the test results. The purpose of the re- evaluation is to ensure that the combined desirability functions accurately interpret the performance of the mixtures and support model predictions that are realistic and practical. The results of the Hypothetical Case Study were interpreted relative to the objective of a durable bridge deck in a northern climate, and what follows is a description of how the particular test data were reconciled with this objective. Analysis of Results and the BTC Table 9 lists individual responses that were initially planned for use in Step 1 and tested in Step 4 as well as those that were actually used to calculate the overall desirability for the mixtures in Step 5. The following changes were made: The fresh concrete properties (slump, slump loss, plastic air content, and air content of hardened concrete) were eliminated from consideration in the calculation of the Overall Desirability. This was done since many of these properties can be adjusted by the concrete producer based on admixture dosage and were not uniquely determined by the factors defining the mixtures. No measure of the hardened air parameters was included since cyclic freezing resistance was tested directly. 18

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 7. Mixtures as batched Mixture ID C1 1 2 3 4 5 6 7 8 9 C2 BTC (8) BPC w/cm 0.4 0.45 0.37 0.37 0.37 0.45 0.37 0.37 0.37 0.45 0.4 0.37 0.39 Percent replacement of cement (by wt.) Fly Ash (Class C) 15 25 40 Fly Ash (Class F) 15 25 40 Slag 25 35 50 35 35 Silica Fume 0 5 8 5 8 0 8 0 5 0 8 Theoretical weight per unit volume (lbs./cu. yd.) Water content 263 296 243 243 243 296 243 243 243 296 263 243 257 Cement 658 559 461 342 526 441 395 441 428 296 658 428 375 Fly Ash (Class C) 0 99 165 263 0 0 0 0 0 0 0 0 0 Fly Ash (Class F) 0 0 0 0 99 165 263 0 0 0 0 0 0 Slag 0 0 0 0 0 0 0 165 230 329 0 230 230 Silica Fume 0 0 33 53 33 53 0 53 0 33 0 0 53 Fine Aggregate 1280 1180 1300 1280 1294 1128 1261 1302 1316 1156 1280 1316 1262 Coarse Aggregate 1696 1696 1696 1696 1696 1696 1696 1696 1696 1696 1696 1696 1696 Admixture dosage (fl. oz./cwt.) AEA 1.70 2.32 3.10 3.83 2.61 3.89 3.35 2.33 2.64 4.78 1.28 2.43 4.01 Superplasticizer 9.07 4.87 25.50 36.60 22.70 16.01 12.59 33.49 24.27 14.81 8.74 18.33 34.15 Actual weight per unit volume as batched (lbs./cu. yd.) Water content 258 295 235 243 239 291 238 242 241 301 263 234 250 Cement 645 558 445 341 517 433 386 438 423 301 658 411 365 Fly Ash (Class C) 0 98 159 262 0 0 0 0 0 0 0 0 0 Fly Ash (Class F) 0 0 0 0 97 162 257 0 0 0 0 0 0 Slag 0 0 0 0 0 0 0 163 228 335 0 221 224 Silica Fume 0 0 32 52 32 52 0 52 0 33 0 0 51 Fine Aggregate 1255 1177 1256 1276 1271 1109 1233 1292 1303 1177 1280 1264 1227 Coarse Aggregate 1662 1693 1638 1690 1665 1667 1658 1684 1679 1727 1696 1629 1650 19

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 8. Test methods used for the evaluation of mixture properties Property Test Methods Total air content, plastic concrete AASHTO T 152 Slump after High Range Water Reducer (HRWR) addition AASHTO T 119 Slump, after 45 minutes AASHTO T 119 Initial set time, minimum AASHTO T 197 Finishability Qualitative assessment Cracking tendency (restrained shrinkage) AASHTO PP 34-99 Thermal effects (heat of hydration) Temperature rise in cylinder Shrinkage (1, 3, 7, 14, 28, 56, 90 days after curing) AASHTO T 160 Compressive strength (at 3, 7, 28, 56 days) AASHTO T 22 Modulus of elasticity (at 7 and 28 days) AASHTO T 22 Hardened air analysis ASTM C 457 Freeze/thaw resistance AASHTO T 161A Electrical conductivity test AASHTO T 277 Chloride penetration resistance (one 3-in. core from each slab, evaluated at 6 mos.) Modified AASHTO T 259/T 260 Salt scaling resistance ASTM C 672 Table 9. Responses used for calculation of overall desirabilities Proposed Responses from Step 1 Selected Responses for Step 5 Design Matrix Analysis Selected Responses for Step 6 Confirmation Analysis 1. Slump 2. Slump Loss 3. Plastic Air Content 4. Air Content of Hardened Concrete 5. Initial Set 1. Initial set 1. Initial set 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 9. Shrinkage 5. Shrinkage 3. Shrinkage 10. Specific Surface Area 11. Compressive Strength, 7-Day 6. Compressive Strength, 7-day 4. Compressive Strength, 7-day 12. Compressive Strength, 28-Day 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 16. Scaling (visual rating) 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) 20

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Another change that was made was the inclusion of 56-day strength in place of 28-day strength, based on the effect that one mixture that was slow to develop strength had on the analysis. This was rationalized since the age at which compressive strength is specified for a given project usually can be delayed if the rest of the performance justified such a change. In the testing program, scaling resistance was evaluated in two ways: by visual rating and by mass loss. To limit the emphasis applied to scaling relative to the other performance measures, only the one measure deemed to be the best descriptor of scaling performance (mass loss) was included in the Overall Desirability Calculation. 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 initially assumed, based on the insulation vessels, that the temperature rise would not be above 30°F (17ºC), and the desirability function was designed accordingly. However, the actual test results ranged from 30 to 50°F (17 to 29ºC). Therefore, the desirability function was adjusted to give credit to those mixtures that produced a lower temperature rise but not to overly punish the mixtures at the higher end of the scale. The individual responses and overall desirabilities of all mixtures based on the test data are shown in Table 10. The Best Tested Concrete (BTC) is the mixture that had the highest overall desirability. Therefore, the BTC was Mixture #8. Response Modeling and the BPC By definition, the Best Predicted Concrete (BPC) is the mixture with the combination of factor levels that maximizes the overall desirability. This was identified based on empirical models for each of the responses. Linear models were fit to two-level factors while quadratic models were fit to three-level factors. The BPC was found by successively evaluating the calculated overall desirability based on the desirabilities for the individual responses predicted for many possible combinations of factor levels. The combinations of factor levels were produced by breaking the ranges for each factor specified in the experimental design matrix into small evenly spaced sets of levels. All combinations of these levels were evaluated. Of the more than 22,000 alternatives that were evaluated, the single combination that produced the highest overall desirability was selected as the BPC. In this way, the observed data, the desirability function, and the response models were used together to predict a BPC that is expected to perform better than the BTC. The predicted overall desirabilities based on the response models for the BTC and BPC from the Step 4 test program is given in Table 11. Note that the predicted overall desirability for the BTC is slightly different from the actual overall desirability because the predicted value is calculated based on the models and not the actual test data. While small differences between the actual and predicted desirability of the BTC (and of all the other design matrix mixtures) is expected, large differences indicate that the models may not be predicting actual performance well and the test variability and data should be reviewed further. In determining the BPC, the models predict that for the materials tested, using the medium level of slag in the experimental design 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 prediction of the performance of the BTC and BPC mixtures in each of the individual responses is given in Table 12. Predicted responses are given for all properties tested in the initial test program, and predicted desirabilities are given for those responses used to determine 21

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 10. Individual response desirabilities and overall desirabilities for design matrix testing Mixture C1 1 2 3 4 5 6 7 8 9 C2 Initial Set 1 1 1 0.8340 1 1 1 1 1 1 1 Finishability 0.9856 0.9725 0.8850 0.9425 0.9075 0.9688 0.9744 0.9500 0.9325 0.9600 0.9706 Cracking Tendency 0.9889 1 1 1 1 0.9833 0.9722 1 0.9556 1 0.9889 Heat of Hydration Temp. Rise 0.8917 0.9517 0.9550 0.9650 0.9617 0.9717 0.9800 0.9583 0.9567 0.9650 0.8800 Shrinkage 0.9105 0.7938 0.9585 0.9690 0.9650 0.9085 0.9580 0.9850 0.9795 0.9645 N/A Compressive Strength - 7 Day 1 1 1 1 1 0.8608 0.6304 0.9040 0.9795 1 N/A Compressive Strength - 56 Day 1 0.9711 1 1 1 0.9020 0.8655 0.9707 1 1 1 Modulus of Elasticity 1 1 1 1 1 1 1 1 1 1 N/A Electrical Conductivity 0.5366 0.3806 0.9594 0.9658 0.9583 0.9544 0.7784 0.9801 0.9296 0.9653 0.4079 Scaling - Mass Loss 0.9849 0.9874 0.9304 0.7491 0.9838 0.9365 0.8889 0.9820 0.9740 0.7082 N/A Freeze- Thaw Durability Factor 1 1 1 1 1 1 1 1 1 1 N/A Chloride Diffusion Coefficient 0.1030 0.1245 0.6682 0.7199 0.6723 0.5029 0.1216 0.8561 0.8787 0.7062 N/A Overall Desirability 0.7695 0.7532 0.9412 0.9231 0.9490 0.9029 0.7660 0.9645 0.9648 0.9323 0.8373 Desirability Rank 8 10 4 6 3 7 9 2 1 5 * * Mixture Missing Data, was not considered for BTC. 22

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 11. Selection of Best Tested (BTC) and Best Predicted Concrete (BPC) based on overall desirabilities Mix Type of SCM 1 Amount of SCM 1 (%) 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 12. Predicted responses of Best Tested (BTC) and Best Predicted Concrete (BPC) Predicted Response Predicted Desirability Property BTC BPC BTC BPC Slump (in) 8.05 7.10 Slump Loss (in) 1.89 2.49 Plastic Air (%) 6.34 6.44 Hardened Air (%) 6.09 6.70 Initial Set (hr) 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 - 7 Day (psi) 5366 5503 1.00 1.00 Compressive Strength - 28 Day (psi) 7193 7730 Compressive Strength - 56 Day (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 (x 10-12 m2/s) 1.95 1.38 0.85 0.90 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 significant in the selection of the BPC. Despite a slightly lower individual desirability for finishability and scaling-mass loss, the predicted individual desirabilities for the BPC for the chloride diffusion, cracking tendency, and electrical conductivity tests were higher. This led to the greater overall desirability and the selection of this mixture as the BPC. 23

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Step 6: Confirmation Testing and Final Selection of Best Concrete The BPC and BTC were tested according to a revised list of test methods outlined in Table 13. It is not essential that the confirmation testing be identical to the original test program. However, changes to the test program will affect the overall desirability. Changes limit direct comparison to the original test program and the assessment of repeatability. However, the primary goal is to compare the performance of the BTC and BPC, which can be done with a more limited test program. Table 9 lists the responses that were included in the calculation of the overall desirability for the Confirmation Testing. The test program varied from the program used in Step 5 in that it was limited only to those responses that showed significant performance differences and could be completed in the available timeframe. Therefore, the finishability, modulus of elasticity, and freezing and thawing tests were eliminated, since in these tests, the BTC and BPC mixtures were predicted to have a similar desirability value. The cracking tendency test was eliminated because that test could not be completed in the necessary time frame. One additional modification to the testing procedure was made because of time constraints; the method used to evaluate the chloride penetration resistance was changed to ASTM C 1556 with 56 days of exposure. However, since both of the chloride penetration test methods used measure similar performance and no other changes in the testing procedures were made, the initial and Confirmation test programs were considered essentially comparable. Therefore, the results from both rounds of testing could be fairly compared. The mixture proportions and batch weights of the Confirmation Testing program are given in Table 7. The overall desirabilities of these mixtures were determined using the same individual desirability functions used to evaluate the design matrix mixtures. The measured overall desirabilities are compared with the predicted overall desirabilities in Table 14, which also includes the overall desirability of the original BTC batch calculated using the subset of responses included in the Confirmation Testing program. Note that the overall desirabilities based on the Confirmation Testing are slightly different than those calculated in Step 5 since the responses included in this calculation have been modified. For the Hypothetical Case Study, the actual and predicted performances of the Confirmation BTC and BPC agreed very well, with less than 0.2% error in each of these predictions. In addition, the difference between the actual BPC and BTC performance was nearly nine times greater than the difference between the Original and Confirmation batch of the BTC. This provides confidence that the test program produced repeatable results and that the increase in desirability measured in the BPC is a significant and measurable improvement in the overall performance. Table 13. Set of Confirmation tests for BPC and BTC Property Test Method Compressive strength (at 3, 7, 28, 56 days) AASHTO T 22 Electrical conductivity test (56 days) AASHTO T 277 Shrinkage (1, 3, 7, 14, 28, 56, 90 days after curing) AASHTO T 160 Thermal effects (heat of hydration) Temperature Rise in Cylinder Chloride diffusion (to 56 days) ASTM C 1556 Scaling (mass loss) ASTM C 672 Hardened air analysis (at greater than 7 days) ASTM C 457 24

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 14. Comparison of actual and predicted overall desirabilities from Confirmation Testing Mixture Actual Overall Desirability Predicted Overall Desirability % Difference BTC Original Batch (Mixture #8) 0.9615 0.9601 0.1% BTC Confirmation Batch 0.9601 0.9601 0.0% BPC Confirmation Batch 0.9724 0.9700 0.2% Table 15 and Table 16 present the actual and predicted individual responses and corresponding desirabilities for the Confirmation Testing for the BTC and BPC. These tables provide an opportunity to evaluate the accuracy of the predictions of the test responses and the corresponding desirabilities. The mixture responses that were least well-predicted, i.e., that showed the greatest percent difference, in terms of the test results for the BTC and BPC were the electrical conductivity and scaling-mass loss tests. However, the corresponding desirability values varied only slightly because the desirability functions placed only limited significance on these performance differences. In fact, only one desirability prediction was different by more than 5% and that was the 7-day strength prediction for the BTC which was off by 5.2%. The Confirmation test results and the excellent agreement between the test responses and the model predictions used to select the BPC all contribute to the confidence in the accuracy of this statistical analysis. The result of this program justifies the selection of the BPC as the Best Concrete (BC), the mixture recommended for use. With this selection, the objective of this Methodology, which is the identification of an optimum mixture based on the available raw materials, was achieved. 25

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 15. Comparison of individual responses and desirabilities for BTC Individual Responses Individual Desirabilities Property Original BTC Batch (Mixture #8) BTC Confirmation Test BTC Prediction BTC % Difference Response BTC Confirmation Test BTC Prediction BTC % Difference Desirability Slump (in) 7.75 6.25 8.05 Slump Loss (in) 1.75 2.25 1.89 Plastic Air (%) 6.10 7.00 6.34 Hardened Air (%) 5.70 7.50 6.09 Initial Set (hr) 5.50 5.08 5.33 -4.8% 1.000 1.000 0.0% Finishability 11.3 No test 11.8 - Cracking Tendency (wks) 7.0 No test 7.4 - Heat of Hydration Temp. Rise (ºF) 46 46 45 3.1% 0.957 0.959 -0.2% Shrinkage (% ) (negative) -0.0441 -0.0452 -0.0445 1.7% 0.974 0.978 -0.4% Specific Surface Area (in-1) 408 No test 417 - Compressive Strength - 7 Day (psi) 5705 6020 5367 12.2% 0.948 1.000 -5.2% Compressive Strength - 28 Day (psi) 7888 7970 7194 10.8% Compressive Strength - 56 Day (psi) 8460 8520 7793 9.3% 0.997 1.000 -0.3% Modulus of Elasticity (x 106 psi) 4.26 No test 4.25 - Electrical Conductivity (Coulombs) 1136 778 1143 -31.9% 0.961 0.929 3.5% Scaling - Visual 0.0 0.0 0.1 - Scaling - Mass Loss (g/m2) 86.7 25.0 93.4 -73.3% 0.993 0.972 2.1% Freeze-Thaw Durability Factor (%) 103.8 No test 103.7 - Chloride Diffusion Coefficient (x 10-12 m2/s) 1.62 1.88 1.95 -3.8% 0.859 0.853 0.7% 26

NCHRP Web-Only Document 110: Supplementary Cementitious Materials to Enhance Durability of Concrete Bridge Decks Table 16. Comparison of individual responses and desirabilities for BPC Individual Responses Individual Desirabilities Property BPC Confirmation Test BPC Prediction BPC% Difference Response BPC Confirmation Test BPC Prediction BPC % Difference Desirability Slump (in) 7.25 7.10 Slump Loss (in) 3.00 2.49 Plastic Air (%) 6.7 6.4 Hardened Air (%) 6.3 6.7 Initial Set (hr) 6.42 5.66 13.5% 1.000 1.000 0.0% Finishability No test 11.4 - Cracking Tendency (wks) No test 15.7 - Heat of Hydration Temp. Rise (°F) 44 44 0.4% 0.960 0.960 0.0% Shrinkage (% ) -0.0476 -0.0434 9.6% 0.962 0.983 -2.1% Specific Surface Area (in-1) No test 424 - Compressive Strength - 7 Day (psi) 5570 5504 1.2% 0.993 1.000 -0.7% Compressive Strength - 28 Day (psi) 7710 7731 - Compressive Strength - 56 Day (psi) 8560 8383 2.1% 0.992 1.000 -0.8% Modulus of Elasticity (x 106 psi) No test 4.24 - Electrical Conductivity (Coulombs) 244 397 -38.5% 0.988 0.980 0.8% Scaling - Visual 0.0 0.3 Scaling - Mass Loss (g/m2) 52.8 183.0 -71.2% 0.984 0.945 4.1% Freeze-Thaw Durability Factor (%) No test 104.0 - Chloride Diffusion Coefficient (x 10-12 m2/s) 1.28 1.38 -6.8% 0.904 0.897 0.8% 27