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Publication Number: FHWA-RD-03-060

Concrete Mixture Optimization Using Statistical Methods

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FOREWORD

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 Internet-based 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.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality 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.

FHWA-RD-03-060

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
Georgetown Pike, McLean, VA 22101
National Institute of Standards and Technology, Building Materials
Division, 100 Bureau Drive, Gaithersburg, MD 20899
National Institute of Standards and Technology, Statistical

10. Work Unit No. (TRAIS)

11. Contract or Grant No.

DTFH61-97-Y-30033

12. Sponsoring Agency Name and Address

Office of Infrastructure Research and Development
Federal Highway Administration
6300 Georgetown Pike
McLean, VA 22101-2296

13. Type of Report and Period Covered

Final Report
November, 1996 to July, 2003

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
and Fire Reseach Laboratory (Building Materials Division), and the NIST Information Technology Laboratory (Statistical
Engineering Division).

16. Abstract

This report presents the results of a research project whose goals were to investigate the feasibility of using statistical experiment
design and analysis methods to optimize concrete mixture proportions and to develop an Internet-based software program to
optimize concrete mixtures using these methods. Two experiment design approaches (classical mixture and factorial-based
central composite design) were investigated in laboratory experiments. In each case, six component materials were used, and
mixtures were optimized for four performance criteria (properties) and cost. Based on the experimental results, the factorialbased
approach was selected as the basis for the Internet-based system. This system, the Concrete Optimization Software Tool
(COST), employs a six-step interactive procedure starting with materials selection and working through trial batches, testing, and
analysis of test results. The end result is recommended mixture proportions to achieve the desired performance levels. COST
was developed as a tool to introduce the industry to the potential benefits of using statistical methods in concrete mixture
proportioning, and to give interested parties an opportunity to try the methods for themselves.

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
the National

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 (8-72) Reproduction of completed pages authorized

SI* (Modern Metric) Conversion Factors


TABLE OF CONTENTS

CHAPTER 1. Introduction

1.1 Statement of Problem and Project Goals

1.2 Scope of Report

CHAPTER 2. Background on Statistical Methods

2.1 Response Surface Methodology

2.2 Experiment Design

   2.2.1 Mixture Approach

   2.2.2 Factorial (MIV) Approach

2.3 Model Fitting and Validation

2.4 Optimization

CHAPTER 3. Laboratory Experiment Using Mixture Approach

3.1 Introduction

3.2 Selection of Materials, Proportions, and Constraints

3.3 Experiment Design Details

3.4 Specimen Fabrication and Testing

3.5 Results and Analysis

   3.5.1 Measured Responses

   3.5.2 Model Identification and Validation for 28-Day Strength

   3.5.3 Models for Other Responses

3.6 Optimization

   3.6.1 Graphical Optimization

   3.6.2 Numerical Optimization

   3.6.3 Accounting for Uncertainty

CHAPTER 4. Laboratory Experiment Using Factorial Approach

4.1 Introduction

4.2 Selection of Materials, Proportions, and Constraints

4.3 Experiment Design Details

4.4 Specimen Fabrication and Testing

4.5 Results and Analysis

   4.5.1 Responses

   4.5.2 Exploratory Data Analysis for 1-Day Strength

   4.5.3 Model Fitting and Validation for 1-Day Strength

   4.5.4 Models for Other Responses

4.6 Optimization

   4.6.1 Graphical Optimization

   4.6.2 Numerical Optimization

   4.6.3 Accounting for Uncertainty

CHAPTER 5. Development of Interactive Web Site (COST Program)

5.1 Introduction

5.2 Selection of Approach

5.3 Considerations in Development

5.4 Description of the Software and Web Site

   5.4.1 Introduction

   5.4.2 Overview of COST Six-Step Process

5.5 Future Considerations

ACKNOWLEDGMENTS

REFERENCES

APPENDIX A. Experiment Design and Data Analysis for Mixture Experiment

A.1 Experiment Design and Response Data

A.2 Data Analysis and Model Fitting

   A.2.1 Slump

   A.2.2 1-Day Strength

   A.2.3 28-Day Strength

   A.2.4 RCT Charge Passed

APPENDIX B. Experiment Design and Data Analysis for Factorial Experiment

B.1 Experiment Design and Response Data

B.2 Data Analysis and Model Fitting

   B.2.1 Slump

   B.2.2 1-Day Strength

   B.2.3 28-Day Strength

   B.2.4 RCT Charge Passed (coulombs)

APPENDIX C. COST User's Guide

Abstract

Section 1. Overview

C1.1 Introduction

C1.2 Scope

C1.3 System Requirements

C1.4 Disclaimer

C1.5 General Information

   C1.5.1 COST Homepage and Main Menu

Section 2. Using COST

C2.1 Background and Preliminary Planning

   C2.1.1 Responses

   C2.1.2 Factors

C2.2 Step 1-Specify Responses

C2.3 Step 2-Specify Measures

   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 Step 3-Run Trial Batches

   C2.4.1 Guidelines for Running Trial Batches

   C2.4.2 Nuisance Factors and Run Sequence Randomization

   C2.4.3 Running the Experiment

C2.5 Step 4-Input Results

   C2.5.1 Instructions for Changing Cost Information

   C2.5.2 Instructions for Entering/Editing Data

C2.6 Step 5-Analyze Data

   C2.6.1 Instructions for Changing Response Information

   C2.6.2 Analysis Tasks

C2.7 Step 6-Summarize Analysis

Section 3. References

LIST OF FIGURES

1 Example of triangular simplex region from three-component mixture experiment

2 Simplex-centroid 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 28-day strength (mixture experiment)

7 Contour plot for 28-day strength in water, cement, and HRWRA

8 Contour plot for 28-day strength in water, cement, and silica fume

9 Contour plot for 28-day strength in water, coarse aggregate, and fine aggregate

10 Contour plot for 28-day strength in silica fume, coarse aggregate, and fine aggregate

11 Desirability functions for responses in mixture experiment

12 Raw data plot for 1-day strength (factorial experiment)

13 Scatterplot showing effect of w/c on 1-day strength (factorial experiment)

14 Means plot for 1-day 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 28-day strength in w/c and silica fume (HRWRA at middle setting)

19 28-day strength in w/c and silica fume (HRWRA at high setting)

20 Overlay plot for RCT < 700 and slump = 50-100 mm

21 Overlay plot for RCT < 700, slump 50-100 mm, and 28-day strength > 51 MPa

22 Desirability functions for factorial experiment

23 Summary screen from COST

A-1 Mixture experiment: normal probability plot for slump

A-2 Mixture experiment: residuals vs. run for slump

A-3 Mixture experiment: Cook's distance for slump

A-4 Mixture experiment: trace plot for slump

A-5 Mixture experiment: contour plot for slump in water, cement, and silica fume

A-6 Mixture experiment: contour plot of slump in water, cement, and HRWRA

A-7 Mixture experiment: normal probability plot for 1-day strength

A-8 Mixture experiment: residuals vs. run for 1-day strength

A-9 Mixture experiment: trace plot for 1-day strength

A-10 Mixture experiment: contour plot of 1-day strength in water, cement, and silica fume

A-11 Mixture experiment: contour plot of 1-day strength in water, cement, and HRWRA

A-12 Mixture experiment: contour plot of 1-day strength in water, cement, and fine aggregate

A-13 Mixture experiment: contour plot of 1-day strength in silica fume, HRWRA, and fine aggregate

A-14 Mixture experiment: contour plot of 1-day strength in silica fume, coarse aggregate, and fine aggregate

A-15 Mixture experiment: normal probability plot for 28-day strength

A-16 Mixture experiment: residuals vs. run for 28-day strength

A-17 Mixture experiment: Cook's distance vs. run for 28-day strength

A-18 Mixture experiment: trace plot for 28-day strength

A-19 Mixture experiment: contour plot of 28-day strength in water, silica fume, and HRWRA

A-20 Mixture experiment: contour plot of 28-day strength in water, silica fume, and coarse aggregate

A-21 Mixture experiment: contour plot of 28-day strength in cement, coarse aggregate, and fine aggregate

A-22 Mixture experiment: normal probability plot for RCT charge passed (no transform)

A-23 Mixture experiment: normal probability plot for RCT charge passed (natural log transform)

A-24 Mixture experiment: residuals vs. predicted for RCT charge passed (no transform)

A-25 Mixture experiment: residuals vs. run for RCT charge passed (no transform)

A-26 Mixture experiment: residuals vs. predicted for RCT charge passed (natural log transform)

A-27 Mixture experiment: residuals vs. run for RCT charge passed (natural log transform)

A-28 Mixture experiment: Cook's distance for RCT charge passed (natural log transform)

A-29 Mixture experiment: trace plot for RCT charge passed (natural log transform)

A-30 Mixture experiment: contour plot of ln (RCT charge passed) in water, silica fume, and coarse aggregate

A-31 Mixture experiment: contour plot of ln (RCT charge passed) in water, silica fume, and HRWRA

A-32 Mixture experiment: contour plot of ln (RCT charge passed) in cement, HRWRA, and fine aggregate

B-1 Factorial experiment: normal probability plot for slump

B-2 Factorial experiment: raw data plot for slump

B-3 Factorial experiment: scatterplot of slump vs. w/c

B-4 Factorial experiment: scatterplot of slump vs. coarse aggregate

B-5 Factorial experiment: scatterplot of slump vs. fine aggregate

B-6 Factorial experiment: scatterplot of slump vs. HRWRA

B-7 Factorial experiment: scatterplot of slump vs. silica fume

B-8 Factorial experiment: means plots for slump

B-9 Factorial experiment: slump vs. run sequence

B-10 Factorial experiment: lag plot for slump

B-11 Factorial experiment: normal probability plot for 1-day strength

B-12 Factorial experiment: raw data plot for 1-day strength

B-13 Factorial experiment: scatterplot of 1-day strength vs. w/c

B-14 Factorial experiment: scatterplot of 1-day strength vs. fine aggregate

B-15 Factorial experiment: scatterplot of 1-day strength vs. coarse aggregate

B-16 Factorial experiment: scatterplot of 1-day strength vs. HRWRA

B-17 Factorial experiment: scatterplot of 1-day strength vs. silica fume

B-18 Factorial experiment: means plot for 1-day strength

B-19 Factorial experiment: 1-day strength vs. run sequence

B-20 Factorial experiment: lag plot for 1-day strength

B-21 Factorial experiment: normal probability plot for 28-day strength

B-22 Factorial experiment: raw data plot for 28-day strength

B-23 Factorial experiment: scatterplot of 28-day strength vs. w/c

B-24 Factorial experiment: scatterplot of 28-day strength vs. fine aggregate

B-25 Factorial experiment: scatterplot of 28-day strength vs. coarse aggregate

B-26 Factorial experiment: scatterplot of 28-day strength vs. HRWRA

B-27 Factorial experiment: scatterplot of 28-day strength vs. silica fume

B-28 Factorial experiment: means plot for 28-day strength

B-29 Factorial experiment: 28-day strength vs. run sequence

B-30 Factorial experiment: lag plot for 28-day strength

B-31 Factorial experiment: normal probability plot for RCT charge passed

B-32 Factorial experiment: raw data plot for RCT charge passed

B-33 Factorial experiment: scatterplot of RCT charge passed vs. w/c

B-34 Factorial experiment: scatterplot of RCT charge passed vs. fine aggregate

B-35 Factorial experiment: scatterplot of RCT charge passed vs. coarse aggregate

B-36 Factorial experiment: scatterplot of RCT charge passed vs. HRWRA

B-37 Factorial experiment: scatterplot of RCT charge passed vs. silica fume

B-38 Factorial experiment: means plots for RCT charge passed

B-39 Factorial experiment: RCT charge passed vs. run sequence

B-40 Factorial experiment: lag plot for RCT charge passed

C-1 COST homepage

C-2 "Response Information" form

C-3 First two sections of "Mixture Factors and Information" input form

C-4 Third section of "Mixture Factors..." form (mineral admixtures section)

C-5 Third section of "Mixture Factors..." form (chemical admixtures section)

C-6 Third section of "Mixture Factors..." form (aggregates section)

C-7 Fourth section of "Mixture Factors..." form (additional information section)

C-8 Portion of an experimental plan generated by COST

C-9 "Run Trial Batches" screen

C-10 Data entry form for the COST system

C-11 Analysis menu showing individual analysis tasks

C-12 Summary statistics table (output of analysis task 1)

C-13 Output of analysis task 2 (counts plot matrix of factors)

C-14 Output of analysis task 3 (counts plot matrix of factors)

C-15 Output of analysis task 4

C-16 Output of analysis task 5A

C-17 Output of analysis task 5B

C-18 Output of analysis task 6

C-19 Output of analysis task 7A

C-20 Output of analysis task 7B

C-21 Output of analysis task 8 (for response RCT)

C-22 Output of analysis task 9

C-23 Calculator for predicting responses based on models

C-24 Example summary returned by the COST system


LIST OF TABLES

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 lack-of-fit test

4 Example of ANOVA model fitting for 1-day 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 28-day strength (mixture experiment)

9 Variable settings corresponding to coded values (factorial experiment)

10 Mixture proportions (per m3) for factorial experiment

11 Test results and costs (factorial experiment)

12 Sequential model sum of squares for 1-day strength (factorial experiment)

13 Lack-of-fit test for 1-day strength (factorial experiment)

14 ANOVA for 1-day strength model (factorial experiment)

15 Summary statistics for 1-day strength model (factorial experiment)

16 Summary of analysis tasks and tools in COST

A-1 Mixture experiment design in terms of volume fractions of components

A-2 Mixture experiment: slump and 1-day strength data

A-3 Mixture experiment: 28-day strength and RCT charge passed data

A-4 Mixture experiment: sequential model of squares for slump

A-5 Mixture experiment: lack-of-fit test for slump

A-6 Mixture experiment: model summary statistics for slump

A-7 Mixture experiment: ANOVA for slump mixture model

A-8 Mixture experiment: coefficient estimates for slump mixture model

A-9 Mixture experiment: adjusted effects for slump mixture model

A-10 Mixture experiment: sequential model of sum of squares for 1-day strength

A-11 Mixture experiment: lack-of-fit test for 1-day strength

A-12 Mixture experiment: summary statistics for 1-day strength

A-13 Mixture experiment: ANOVA for 1-day strength mixture model

A-14 Mixture experiment: coefficient estimates for 1-day strength mixture model

A-15 Mixture experiment: sequential model of sum of squares for 28-day strength

A-16 Mixture experiment: lack-of-fit test for 28-day strength

A-17 Mixture experiment: model summary statistics for 28-day strength

A-18 Mixture experiment: ANOVA for 28-day strength mixture model

A-19 Mixture experiment: estimated coefficients for 28-day strength mixture model

A-20 Mixture experiment: adjusted effects for 28-day strength mixture model

A-21 Mixture experiment: sequential model of sum of squares for RCT charge passed

A-22 Mixture experiment: lack-of-fit test for RCT charge passed

A-23 Mixture experiment: model summary statistics for RCT charge passed

A-24 Mixture experiment: ANOVA for RCT charge passed mixture model

A-25 Mixture experiment: estimated coefficients for RCT charge passed mixture model

A-26 Mixture experiment: adjusted effects for RCT charge passed mixture model

B-1 Factorial experiment: design by volume fraction of factors

B-2 Factorial experiment: slump and 1-day strength data

B-3 Factorial experiment: 28-day strength and RCT charge passed data

B-4 Factorial experiment: sequential model sum of squares for slump

B-5 Factorial experiment: lack-of-fit test for slump

B-6 Factorial experiment: ANOVA for slump model

B-7 Factorial experiment: summary statistics for slump model

B-8 Factorial experiment: coefficient estimates for slump model

B-9 Factorial experiment: sequential model sum of squares for 1-day strength

B-10 Factorial experiment: lack-of-fit test for 1-day strength

B-11 Factorial experiment: ANOVA for 1-day strength model

B-12 Factorial experiment: summary statistics for 1-day strength model

B-13 Factorial experiment: coefficient estimates for 1-day strength model

B-14 Factorial experiment: sequential model sum of squares for 28-day strength

B-15 Factorial experiment: lack-of-fit test for 28-day strength

B-16 Factorial experiment: ANOVA for 28-day strength model

B-17 Factorial experiment: summary statistics for 28-day strength model

B-18 Factorial experiment: coefficient estimates for 28-day strength model

B-19 Factorial experiment: sequential model sum of squares for RCT charge passed

B-20 Factorial experiment: lack-of-fit test for RCT charge passed

B-21 Factorial experiment: ANOVA for RCT charge passed model

B-22 Factorial experiment: summary statistics for RCT charge passed model

B-23 Factorial experiment: coefficient estimates for RCT charge passed model

C-1 Examples of components and responses

C-2 Information required for different materials

C-3 Description of summary statistics provided in analysis task 1

 

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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