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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
This report is an archived publication and may contain dated technical, contact, and link information 

Publication Number: FHWARD03060 
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This report presents the results of a study conducted jointly by the Federal Highway Administration and the National Institute of Standards and Technology to assess the feasibility of using statistical experiment design and analysis methods to optimize concrete mixture proportions. The laboratory phase of the study indicated that both the classical mixture method and the factorial approach could be applied to the problem of optimizing concrete mixture proportions. The factorial approach was used as the basis for developing an Internetbased computer program, the Concrete Optimization Software Tool, in the second phase of this project. This tool, accessible on the Web, allows a potential user to learn about and try this statistical approach. This report will be of interest to materials engineers and others who are involved in concrete construction and concrete mixture design, materials selection, and proportioning.
Paul Teng, P.E.
Director, Office of Infrastructure Research and Development
Notice
This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document. This report does not constitute a standard, specification, or regulation.
The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the objective of the document.
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The Federal Highway Administration (FHWA) provides highquality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.
Technical Report Documentation Page
1. Report No. FHWARD03060 
2. Government Accession No. 
3. Recipient's Catalog No.  
4. Title and Subtitle 
5. Report Date  
6. Performing Organization Code 480017  
7. Author(s) M.J. Simon 
8. Performing Organization Report No.  
9. Performing Organization Name and Address FHWA Office of Infrastructure Research and Development, 6300 
10. Work Unit No. (TRAIS)  
11. Contract or Grant No. DTFH6197Y30033  
12. Sponsoring Agency Name and Address Office of Infrastructure Research and Development 
13. Type of Report and Period Covered Final Report  
14. Sponsoring Agency Code
 
15. Supplementary Notes This project was a cooperative effort between the FWHA Office of Infrastructure Research and Development, the NIST Building  
16. Abstract This report presents the results of a research project whose goals were to investigate the feasibility of using statistical experiment  
17. Key Words Building technology, pavements, structures, concrete, mixture proportioning, experiment design, optimization, response surface methods 
18. Distribution Statement No restrictions. This document is available to the public through  
19. Security Classif. (of this report) Unclassified 
20. Security Classif. (of this page) Unclassified 
21. No. of Pages 167 
22. Price 
Form DOT F 1700.7 (872)  Reproduction of completed pages authorized 
1.1 Statement of Problem and Project Goals
2.1 Response Surface Methodology
2.2.2 Factorial (MIV) Approach
2.3 Model Fitting and Validation
3.2 Selection of Materials, Proportions, and Constraints
3.4 Specimen Fabrication and Testing
3.5.2 Model Identification and Validation for 28Day Strength
3.5.3 Models for Other Responses
3.6.3 Accounting for Uncertainty
4.2 Selection of Materials, Proportions, and Constraints
4.4 Specimen Fabrication and Testing
4.5.2 Exploratory Data Analysis for 1Day Strength
4.5.3 Model Fitting and Validation for 1Day Strength
4.5.4 Models for Other Responses
4.6.3 Accounting for Uncertainty
5.3 Considerations in Development
5.4 Description of the Software and Web Site
5.4.2 Overview of COST SixStep Process
A.1 Experiment Design and Response Data
A.2 Data Analysis and Model Fitting
B.1 Experiment Design and Response Data
B.2 Data Analysis and Model Fitting
B.2.4 RCT Charge Passed (coulombs)
C1.5.1 COST Homepage and Main Menu
C2.1 Background and Preliminary Planning
C2.3.1 Instructions for Section 1: Number of Parameters (Factors) to Vary
C2.3.2 Instructions for Section 2: Select w/c or w/cm
C2.3.3 Instructions for Section 3: Select Other Mixture Components
C2.3.4 Specific Instructions for Mineral Admixtures
C2.3.5 Specific Instructions for Chemical Admixtures
C2.3.6 Specific Instructions for Aggregates
C2.3.7 Instructions for Section 4: Additional Information
C2.4.1 Guidelines for Running Trial Batches
C2.4.2 Nuisance Factors and Run Sequence Randomization
C2.5.1 Instructions for Changing Cost Information
C2.5.2 Instructions for Entering/Editing Data
C2.6.1 Instructions for Changing Response Information
C2.7 Step 6Summarize Analysis
1 Example of triangular simplex region from threecomponent mixture experiment
2 Simplexcentroid design for three variables
3 Example of subregion of full simplex containing range of feasible mixtures
4 Schematic of a central composite design for three factors
5 Examples of desirability functions
6 Response trace plot for 28day strength (mixture experiment)
7 Contour plot for 28day strength in water, cement, and HRWRA
8 Contour plot for 28day strength in water, cement, and silica fume
9 Contour plot for 28day strength in water, coarse aggregate, and fine aggregate
10 Contour plot for 28day strength in silica fume, coarse aggregate, and fine aggregate
11 Desirability functions for responses in mixture experiment
12 Raw data plot for 1day strength (factorial experiment)
13 Scatterplot showing effect of w/c on 1day strength (factorial experiment)
14 Means plot for 1day strength (factorial experiment)
15 Example of cube plot for factorial points
16 Example of a normal probability plot for model validation
17 Example of a residual plot (residuals vs. run) for model validation
18 28day strength in w/c and silica fume (HRWRA at middle setting)
19 28day strength in w/c and silica fume (HRWRA at high setting)
20 Overlay plot for RCT < 700 and slump = 50100 mm
21 Overlay plot for RCT < 700, slump 50100 mm, and 28day strength > 51 MPa
22 Desirability functions for factorial experiment
A1 Mixture experiment: normal probability plot for slump
A2 Mixture experiment: residuals vs. run for slump
A3 Mixture experiment: Cook's distance for slump
A4 Mixture experiment: trace plot for slump
A5 Mixture experiment: contour plot for slump in water, cement, and silica fume
A6 Mixture experiment: contour plot of slump in water, cement, and HRWRA
A7 Mixture experiment: normal probability plot for 1day strength
A8 Mixture experiment: residuals vs. run for 1day strength
A9 Mixture experiment: trace plot for 1day strength
A10 Mixture experiment: contour plot of 1day strength in water, cement, and silica fume
A11 Mixture experiment: contour plot of 1day strength in water, cement, and HRWRA
A12 Mixture experiment: contour plot of 1day strength in water, cement, and fine aggregate
A13 Mixture experiment: contour plot of 1day strength in silica fume, HRWRA, and fine aggregate
A15 Mixture experiment: normal probability plot for 28day strength
A16 Mixture experiment: residuals vs. run for 28day strength
A17 Mixture experiment: Cook's distance vs. run for 28day strength
A18 Mixture experiment: trace plot for 28day strength
A19 Mixture experiment: contour plot of 28day strength in water, silica fume, and HRWRA
A20 Mixture experiment: contour plot of 28day strength in water, silica fume, and coarse aggregate
A21 Mixture experiment: contour plot of 28day strength in cement, coarse aggregate, and fine aggregate
A22 Mixture experiment: normal probability plot for RCT charge passed (no transform)
A23 Mixture experiment: normal probability plot for RCT charge passed (natural log transform)
A24 Mixture experiment: residuals vs. predicted for RCT charge passed (no transform)
A25 Mixture experiment: residuals vs. run for RCT charge passed (no transform)
A26 Mixture experiment: residuals vs. predicted for RCT charge passed (natural log transform)
A27 Mixture experiment: residuals vs. run for RCT charge passed (natural log transform)
A28 Mixture experiment: Cook's distance for RCT charge passed (natural log transform)
A29 Mixture experiment: trace plot for RCT charge passed (natural log transform)
A31 Mixture experiment: contour plot of ln (RCT charge passed) in water, silica fume, and HRWRA
A32 Mixture experiment: contour plot of ln (RCT charge passed) in cement, HRWRA, and fine aggregate
B1 Factorial experiment: normal probability plot for slump
B2 Factorial experiment: raw data plot for slump
B3 Factorial experiment: scatterplot of slump vs. w/c
B4 Factorial experiment: scatterplot of slump vs. coarse aggregate
B5 Factorial experiment: scatterplot of slump vs. fine aggregate
B6 Factorial experiment: scatterplot of slump vs. HRWRA
B7 Factorial experiment: scatterplot of slump vs. silica fume
B8 Factorial experiment: means plots for slump
B9 Factorial experiment: slump vs. run sequence
B10 Factorial experiment: lag plot for slump
B11 Factorial experiment: normal probability plot for 1day strength
B12 Factorial experiment: raw data plot for 1day strength
B13 Factorial experiment: scatterplot of 1day strength vs. w/c
B14 Factorial experiment: scatterplot of 1day strength vs. fine aggregate
B15 Factorial experiment: scatterplot of 1day strength vs. coarse aggregate
B16 Factorial experiment: scatterplot of 1day strength vs. HRWRA
B17 Factorial experiment: scatterplot of 1day strength vs. silica fume
B18 Factorial experiment: means plot for 1day strength
B19 Factorial experiment: 1day strength vs. run sequence
B20 Factorial experiment: lag plot for 1day strength
B21 Factorial experiment: normal probability plot for 28day strength
B22 Factorial experiment: raw data plot for 28day strength
B23 Factorial experiment: scatterplot of 28day strength vs. w/c
B24 Factorial experiment: scatterplot of 28day strength vs. fine aggregate
B25 Factorial experiment: scatterplot of 28day strength vs. coarse aggregate
B26 Factorial experiment: scatterplot of 28day strength vs. HRWRA
B27 Factorial experiment: scatterplot of 28day strength vs. silica fume
B28 Factorial experiment: means plot for 28day strength
B29 Factorial experiment: 28day strength vs. run sequence
B30 Factorial experiment: lag plot for 28day strength
B31 Factorial experiment: normal probability plot for RCT charge passed
B32 Factorial experiment: raw data plot for RCT charge passed
B33 Factorial experiment: scatterplot of RCT charge passed vs. w/c
B34 Factorial experiment: scatterplot of RCT charge passed vs. fine aggregate
B35 Factorial experiment: scatterplot of RCT charge passed vs. coarse aggregate
B36 Factorial experiment: scatterplot of RCT charge passed vs. HRWRA
B37 Factorial experiment: scatterplot of RCT charge passed vs. silica fume
B38 Factorial experiment: means plots for RCT charge passed
B39 Factorial experiment: RCT charge passed vs. run sequence
B40 Factorial experiment: lag plot for RCT charge passed
C1 COST homepage
C2 "Response Information" form
C3 First two sections of "Mixture Factors and Information" input form
C4 Third section of "Mixture Factors..." form (mineral admixtures section)
C5 Third section of "Mixture Factors..." form (chemical admixtures section)
C6 Third section of "Mixture Factors..." form (aggregates section)
C7 Fourth section of "Mixture Factors..." form (additional information section)
C8 Portion of an experimental plan generated by COST
C9 "Run Trial Batches" screen
C10 Data entry form for the COST system
C11 Analysis menu showing individual analysis tasks
C12 Summary statistics table (output of analysis task 1)
C13 Output of analysis task 2 (counts plot matrix of factors)
C14 Output of analysis task 3 (counts plot matrix of factors)
C15 Output of analysis task 4
C16 Output of analysis task 5A
C17 Output of analysis task 5B
C18 Output of analysis task 6
C19 Output of analysis task 7A
C20 Output of analysis task 7B
C21 Output of analysis task 8 (for response RCT)
C22 Output of analysis task 9
C23 Calculator for predicting responses based on models
C24 Example summary returned by the COST system
1 Number of runs required for CCD experiment for k = 2 to 5 factors)
2 Example of ANOVA sequential model sum of squares
3 Example of ANOVA lackoffit test
4 Example of ANOVA model fitting for 1day strength
5 Material volume fraction ranges for mixture experiment
6 Mixture proportions for mixture experiment
7 Test results and costs (mixture experiment)
8 Sequential model sum of squares for 28day strength (mixture experiment)
9 Variable settings corresponding to coded values (factorial experiment)
10 Mixture proportions (per m^{3}) for factorial experiment
11 Test results and costs (factorial experiment)
12 Sequential model sum of squares for 1day strength (factorial experiment)
13 Lackoffit test for 1day strength (factorial experiment)
14 ANOVA for 1day strength model (factorial experiment)
15 Summary statistics for 1day strength model (factorial experiment)
16 Summary of analysis tasks and tools in COST
A1 Mixture experiment design in terms of volume fractions of components
A2 Mixture experiment: slump and 1day strength data
A3 Mixture experiment: 28day strength and RCT charge passed data
A4 Mixture experiment: sequential model of squares for slump
A5 Mixture experiment: lackoffit test for slump
A6 Mixture experiment: model summary statistics for slump
A7 Mixture experiment: ANOVA for slump mixture model
A8 Mixture experiment: coefficient estimates for slump mixture model
A9 Mixture experiment: adjusted effects for slump mixture model
A10 Mixture experiment: sequential model of sum of squares for 1day strength
A11 Mixture experiment: lackoffit test for 1day strength
A12 Mixture experiment: summary statistics for 1day strength
A13 Mixture experiment: ANOVA for 1day strength mixture model
A14 Mixture experiment: coefficient estimates for 1day strength mixture model
A15 Mixture experiment: sequential model of sum of squares for 28day strength
A16 Mixture experiment: lackoffit test for 28day strength
A17 Mixture experiment: model summary statistics for 28day strength
A18 Mixture experiment: ANOVA for 28day strength mixture model
A19 Mixture experiment: estimated coefficients for 28day strength mixture model
A20 Mixture experiment: adjusted effects for 28day strength mixture model
A21 Mixture experiment: sequential model of sum of squares for RCT charge passed
A22 Mixture experiment: lackoffit test for RCT charge passed
A23 Mixture experiment: model summary statistics for RCT charge passed
A24 Mixture experiment: ANOVA for RCT charge passed mixture model
A25 Mixture experiment: estimated coefficients for RCT charge passed mixture model
A26 Mixture experiment: adjusted effects for RCT charge passed mixture model
B1 Factorial experiment: design by volume fraction of factors
B2 Factorial experiment: slump and 1day strength data
B3 Factorial experiment: 28day strength and RCT charge passed data
B4 Factorial experiment: sequential model sum of squares for slump
B5 Factorial experiment: lackoffit test for slump
B6 Factorial experiment: ANOVA for slump model
B7 Factorial experiment: summary statistics for slump model
B8 Factorial experiment: coefficient estimates for slump model
B9 Factorial experiment: sequential model sum of squares for 1day strength
B10 Factorial experiment: lackoffit test for 1day strength
B11 Factorial experiment: ANOVA for 1day strength model
B12 Factorial experiment: summary statistics for 1day strength model
B13 Factorial experiment: coefficient estimates for 1day strength model
B14 Factorial experiment: sequential model sum of squares for 28day strength
B15 Factorial experiment: lackoffit test for 28day strength
B16 Factorial experiment: ANOVA for 28day strength model
B17 Factorial experiment: summary statistics for 28day strength model
B18 Factorial experiment: coefficient estimates for 28day strength model
B19 Factorial experiment: sequential model sum of squares for RCT charge passed
B20 Factorial experiment: lackoffit test for RCT charge passed
B21 Factorial experiment: ANOVA for RCT charge passed model
B22 Factorial experiment: summary statistics for RCT charge passed model
B23 Factorial experiment: coefficient estimates for RCT charge passed model
C1 Examples of components and responses
C2 Information required for different materials
C3 Description of summary statistics provided in analysis task 1