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.

116 The following are definitions of the terms used in the statistical experi- mental design. Amount Constant: An unchanging amount of material to be used in all mixtures to be tested. Amount Factor: A variable (factor) that varies the amount of raw material for the mixture. ANOVA Analysis: Analysis of Variance, a statistical method used to compare relative statistical significance of the effects of a factor by com- paring the ratio of the variation explained by each factor to the variance of the random error. Bar Chart: A graph used to show relationships and trends by com- paring the height of two or more bars. (In this document, the charts are used to compare the relative scale of the factor effects.) Best Concrete (BC): The concrete mixture that is to be recom- mended for the application after collection and analysis of the data. The final decision is made by comparing the experiment’s Best Tested Concrete (BTC) with the Best Predicted Concrete (BPC) in the confir- mation testing step. Best Predicted Concrete (BPC): A concrete mixture that is predicted to have the best performance through statistical modeling of the data from the design matrix. Best Tested Concrete (BTC): The concrete mixture from the design matrix that has the best tested performance as determined by the over- all desirability. Compound Factor: A pair of variables (factors) that act together to define the type and amount of a certain material so that the amount of each material can be customized for each type. Confirmation Testing: A second round of testing to confirm the per- formance of the BTC and BPC. Constant: A single level that is necessary for defining the experiment but which is not varied. Corner Points: Vertices of a piecewise linear function. In this docu- ment, they are the points at which a desirability function changes slope. Design Matrix: The table (matrix) of combinations of factors and lev- els that defines which concrete mixtures to mix and test. Desirability Function: A function that converts any test result into a value between 0 and 1, where 0 means the result is unacceptable, and 1 means the result needs no improvement. Intermediate values show the level of acceptability (desirability) of the result. Expert Opinion Method: An experimental methodology that begins by using the experts’ prediction of best performance. Samples of these mixtures are cast and tested in various tests, and the concrete that performs the best is chosen for the application. This method is probably the most typical used for identifying a concrete mixture for an application. Extrapolate: Using test results to predict performance for mixtures that have factor levels that are outside the range of factor levels tested. This procedure is not recommended. Factor: The independent variables, or x-variables, that are intention- ally varied in an experiment. Factor level: A level associated with a specific factor. F-ratio: A ratio used in ANOVA analysis. The F-ratio for a certain factor is the amount of variation explained by that factor divided by the variance of random error. A large (substantially larger than 1) F-ratio indicates a large statistical significance of the effects of the factor. Geometric Mean: The nth root of the product of n values. For exam- ple, the geometric mean of the numbers 4, 5, 6, 7, and 8 is the fifth root of 4 × 5 × 6 × 7 × 8, which is . Individual Desirability: A mathematical value assigned to an indi- vidual test result to determine acceptability of that result. The scale ranges from 0 to 1, with 0 being unacceptable and 1 being a result that needs no improvement. Individual desirabilities for each test performed are used to calculate a geometric mean to determine an overall desir- ability for the concrete mixture. Interpolate: Using test results to predict performance for mixtures that have factor levels that are within the range of factor levels tested. Level: The setting of a factor. For example, if the factor is amount of silica fume, the level (or setting) might be 5%. Linear Function: A mathematical formula that represents the line that best fits data. Mean Square Error: The average variance due to random error. Mixture: A combination of factor levels that define the concrete to be tested. It is assumed that the mixture is batched according to the factor levels and cast into proper specimens for testing. One Factor-at-a-Time Method: An experimental methodology that begins by having experts select a single mixture, called the “control mix- ture,” that is considered to be most likely to perform well. Each factor that is chosen for the study is varied from its level in the control mix- ture, and a new mixture is cast and tested with only that factor changed. Orthogonal Design Method: An experimental methodology where an orthogonal design matrix is chosen that contains a list of mixtures to be tested. Orthogonal designs are created so that each factor level is balanced with every other factor level such that an independent estimate of each factor effect is possible. This is the method used in this report. Quadratic Model: A mathematical function that includes second order (squared) terms to model curvature. 6720 5 835 = . Glossary of Statistical Experimental Design–Related Terms

Random Error or Random Variability: Variability due to uncontrol- lable changes in materials, mixing and measurement procedures. (Also called random variability or repeatability.) Regression Analysis: A statistical method of fitting lines and curves to data to create a prediction model. Repeatability: Variation due to repeated mixing and testing of the same concrete mixture. Same as Random Error. Response Surface Approach: An experimental methodology that requires a large enough design matrix to estimate both curvature and two-factor interactions between factors. This approach is more thorough than the Orthogonal Design Approach but often requires more testing than is feasible (typically 17 to 32 mixtures for three to five factors). Response: The measured value from a performance test. This value is the dependent, or y-variable, used in an experiment. Same as “test result.” Scatter Plot: A graph of two columns of numbers used to show rela- tionships and trends by plotting the response as a function of the factor level. (See Trend.) Setting: The level of a factor. For example, if the factor is amount of silica fume, the level (or setting) might be 5%. Source Constant: An unchanging source of material used in all mix- tures to be tested. Source Factors: Variables (factors) that vary the source of raw mate- rial for the mixtures. Standard Deviation: A mathematical measure of variability of data. For example, the standard deviation of the numbers 3, 4, 5, 6, 7, and 8 is 1.87. Statistical Experimental Design for Optimization of Concrete (SEDOC): Microsoft Excel®–based tool developed with this method- ology to support this orthogonal design experiment. Functionality includes guidance in the design of the experiment, calculation of indi- vidual and overall desirabilities, modeling of individual responses, selection of BTC and BPC, and evaluation of prediction accuracy. Type Constant: An unchanging type of material used in all mixtures to be tested. Trend: The general pattern of the data. Trends on scatter plots are found by connecting the average of y-values at each level of the factor (x-values). Type Factors: Variables (factors) that change the type of material used to accomplish the particular function. Vertices: A point where a function abruptly changes slope. In this document, they are the points at which a desirability function changes slope. Same as corner points. 117