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This report is an archived publication and may contain dated technical, contact, and link information
Publication Number: FHWA-RD-03-060

Concrete Mixture Optimization Using Statistical Methods

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CHAPTER 1 Introduction

1.1 Statement of Problem and Project Goals

The purpose of this project was to investigate the use of statistical experiment design approaches in concrete mixture proportioning. These statistical methods are applied in industry to optimize products such as gasoline, food products, and detergents. In many cases, the products are, like concrete, combinations of several components. Typically, these applications optimize a product to meet a number of performance criteria (user-specified constraints) simultaneously, at minimum cost. For concrete, these performance criteria could include fresh concrete properties such as viscosity, yield stress, setting time, and temperature; mechanical properties such as strength, modulus of elasticity, creep, and shrinkage; and durability-related properties such as resistance to freezing and thawing, abrasion, or chloride penetration.

This project was sponsored by the Federal Highway Administration (FHWA) and was performed jointly by researchers from FHWA and the National Institute of Standards and Technology (NIST) Building Materials and Statistical Engineering Divisions. Both FHWA and NIST hope to facilitate the use of high-performance concrete (HPC) in both public and private construction, and are currently working to develop tools for optimizing HPC mixture proportions.

HPC has been referred to as "engineered concrete," implying that an HPC mixture is not specified in a generic recipe, but rather designed to meet project-specific needs [1]. Such a definition gives a concrete producer or materials engineer greater than usual latitude in selecting constituent materials and defining proportions in an HPC mixture, since fewer or possibly no prescriptive constraints, such as minimum cement contents or maximum water-cement (w/c) ratios, are included in specifications. HPC mixtures are usually more expensive than conventional concrete mixtures because they usually contain more cement, several chemical admixtures at higher dosage rates than for conventional concrete, and one or more supplementary cementitious materials. As the cost of materials increases, optimizing concrete mixture proportions for cost becomes more desirable. Furthermore, as the number of constituent materials increases, the problem of identifying optimal mixtures becomes increasingly complex. Not only are there more materials to consider, but there also are more potential interactions among materials. Combined with several performance criteria, the number of trial batches required to find optimal proportions using traditional methods could become prohibitive.

The general approach to concrete mixture proportioning can be described by the following steps:

  1. Identifying a starting set of mixture proportions.
  2. Performing one or more trial batches, starting with the mixture identified in step 1 above, and adjusting the proportions in subsequent trial batches until all criteria are satisfied.

Current practice in the United States for developing new concrete mixtures often relies upon using historical information (i.e., what has worked for the producer in the past) or guidelines for mixture proportioning outlined in American Concrete Institute (ACI) 211.1 [2]. Following the ACI 211.1 guidelines, an engineer would select and run a first trial batch (selecting proportions using ACI 211.1 or historical data), evaluate the results, adjust the proportions of various components, and run further trial batches until all specified criteria are met. Typically, this is performed by varying one component at a time. While both historical information and ACI 211.1 can yield a starting point for trial batches, neither method is a comprehensive procedure for optimizing mixtures. Historical information may not be valid for materials other than the particular ones used in a given project. In ACI 211.1, interactions among the concrete constituents cannot be accounted for, and there is no means to achieve an efficiently optimized mixture for a given criterion.

In contrast, statistical experimental design methods are rigorous techniques for both achieving desired properties and determining an optimized mixture for a given set of constraints. They are used widely in industry to optimize products and processes [3], and have been applied in some research studies on improving high-performance concrete [4,5]. They have not, however, been applied as a general approach to concrete mixture proportioning.

Employing statistical methods in the trial batch process does not change the overall approach, but it changes the trial batch process. Rather than selecting one starting point, a set of trial batches covering a chosen range of proportions for each component is defined according to established statistical procedures [3]. Trial batches are then carried out, test specimens are fabricated and tested, and results are analyzed using standard statistical methods. These methods include fitting empirical models to the data for each performance criterion. In these models, each response (resultant concrete property) such as strength, slump, or cost, is expressed as an algebraic function of factors (individual component proportions) such as w/c, cement content, chemical admixture dosage, and percent pozzolan replacement.

After a response can be characterized by an equation (model), several analyses are possible. For instance, a user could determine which mixture proportions would yield one or more desired properties. A user also could optimize any property subject to constraints on other properties. Simultaneous optimization to meet several constraints is also possible. For example, one could determine the lowest cost mixture with strength greater than a specified value, air content within a given range, and slump within a given range. A method for optimizing several responses simultaneously is described later in the report.

Mechanistic (or semimechanistic) models that were developed from results of fundamental and applied materials research have also been used as a basis for mixture proportioning methods [6]. An advantage of this approach is that it does not require trial batches to obtain the models; however, some trial batches most likely would be needed to adjust proportions because of differences in material properties at the local level. It is unlikely that a mechanistic model would be able to account for all possible differences in local materials. The advantage of the trial batch approach is that the project-specific materials are used and accounted for in the model.

An additional advantage of the statistical approach is that the expected properties (responses) can be characterized by an uncertainty (variability). This has important implications for specifications and for production. When an empirical model equation is used to determine mixture proportions that yield a desired strength, the model equation gives only the expected mean strength; that is, if replicate mixtures were made, the model equation would predict the mean value. This is not an appropriate target value for specifications, because in the long run, the strength would be below that value half of the time. Instead, to ensure that most of the strength test results would comply with specifications, a producer would select target values for the mean strength to account for the variability and to ensure that, for example, 95 percent of the results would be expected to meet or exceed the specified value.

A disadvantage of the statistical approach is that it requires an initial investment of time and money for planning and performing trial batches and tests. Additionally, knowledge of good experimentation procedures and some knowledge of statistical analysis is needed. Statistical computer programs are available to perform both experiment design and analysis, but knowing how to interpret and ensure the validity of statistical models is important. For this reason, the second objective of this project was to develop an interactive Web site to provide users with rudimentary knowledge and lead them step by step through a mixture proportioning process using statistical methods. The aim was not to provide a comprehensive, user-friendly software package, but rather to introduce producers and engineers to these methods and to provide sufficient results and guidance on interpretation to allow them to see potential advantages of the approach.

Although these methods require a commitment of time and money upfront, they have the potential to save money during construction. Reducing the concrete material cost by $20 per cubic meter (m3) could result in savings of $40,000 per km of 30-cm thick, two-lane concrete pavement.

1.2 Scope of Report

The report is organized as follows: Chapter 1 introduces the problem and the project goals, and describes the scope. Chapter 2 provides background on the statistical concepts used in this project, including response surface methodology (RSM) and its components: experiment design, model fitting and validation, and optimization. Chapter 3 describes the laboratory experiment using a mixture experiment design approach, and chapter 4 describes a laboratory experiment using a mathematically independent variable (MIV), or factorial, approach. Chapter 5 describes the development of the interactive Web site, the Concrete Optimization Software Tool (COST). References are provided after chapter 5. Appendices A (mixture experiment) and B (factorial experiment) contain experiment designs, test data, data analysis and model fitting (tables and graphs) from the laboratory experiments. Appendix C contains the COST User's Guide, which describes the COST system and its use in detail.


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