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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 5 Development of Interactive Web Site (COST Program)

5.1 Introduction

The goal of the second phase of this research project was to develop an interactive Web site that can be used to optimize concrete mixture proportions using the response surface approach. The purpose of this Web site is to introduce this approach to the concrete community and to give concrete practitioners an opportunity to apply the approach to their own mixture development. Because the response surface approach was likely to be unfamiliar to many practicing engineers and producers, the aim was to make it as user-friendly as possible (within budget constraints) and to provide as much guidance as possible in interpreting results.

5.2 Selection of Approach

A systematic approach is critical when optimizing a HPC mixture subject to several performance criteria. The laboratory experiments described in chapters 3 and 4 investigated two such approaches: the classical mixture experiment design and the factorial/CCD experiment design. Using either of these approaches, a trial batch and testing program can thoroughly examine the concrete properties of interest over the selected range of component proportions, and models estimated from the data can be used to identify optimal mixes.

Using a statistical approach to mixture optimization requires a significant investment in trial batches and testing. In both the mixture approach and factorial approach, 31 different trial batches were required for a 6-component mixture. The large number of runs was required to fit a full quadratic model for each response and to provide control runs and replicate runs for estimating repeatability.

If the responses are represented adequately by linear models (as opposed to quadratic), the number of trial batches can be reduced by as much as 50 percent. In the mixture experiment (chapter 3), linear models were adequate for all but one response (1-day strength). If linear model were assumed, the number of experimental runs could have been halved. However, since materials and conditions vary by location, the quadratic model is a better initial assumption.

The factorial approach has an advantage over the mixture approach in that it can be performed sequentially (see page 10 of this report). In a sequential approach, the CCD experiment is divided into two parts. The adequacy of linear models for the responses can be assessed after the initial portion of the experiment (for a 6-component mixture, the first part would consist of 19 trial batches). If linear response models are sufficient over the range of material proportions being considered, the second part of the experiment would not be necessary. If not, the second part of the experiment can be run, and quadratic models can be fit to the data.

In both approaches, the number of runs also can be reduced by holding certain variables constant. Reducing the number of components from 6 to 4 would reduce the number of runs in a factorial/CCD experiment from 31 to 19. For example, if a user is interested primarily in a property that is influenced by cement paste characteristics, he might choose to vary only the paste component proportions while holding aggregate constant.

Based on the experimental results described in chapters 3 and 4, the two approaches, mixture and factorial, were evaluated to select the best approach for an interactive Web site. Technical suitability and practical considerations (e.g., ease of understanding, ease of use) were considered in deciding which method to use for the Web site. While both methods were considered technically suitable, the factorial approach was considered to be more practical. The advantage of sequential experimentation, which could reduce the number of required trial batches, favored the factorial approach. Furthermore, materials engineers are more likely to have encountered factorial experiments than mixture experiments, and the factorial approach is more straightforward and easier to use, understand, analyze, and interpret. Finally, the statistical software to be used for the Web site (DATAPLOT) was better suited for the factorial approach.

5.3 Considerations in Development

The following are some of the considerations that shaped the development of the COST software and Web site:

5.4 Description of the Software and Web Site

5.4.1 Introduction

COST is an online interactive system developed to assist engineers, concrete producers, and researchers in optimizing portland cement concrete mixtures for their particular applications. COST applies response surface methodology (RSM), a collection of statistical experiment design and analysis methods, to the problem of optimizing concrete mixture proportions. RSM often is used in industry for product development, formulation, and improvement, and is applicable to problems such as concrete mixture proportioning where several input variables (factors) influence a performance measure (response).

COST is intended to provide an introduction to concrete practitioners who are unfamiliar with the concepts and process of applying RSM to concrete mixture proportioning. COST allows users to learn how to apply RSM to the problem of optimizing concrete mixtures.

There are two scenarios for which COST could be applied:

  1. To proportion a concrete mixture to meet a set of specifications at minimum material cost. This is probably the most common scenario.
  2. To maximize (or minimize) a particular response or responses, irrespective of cost.

COST can be used to optimize cement paste, mortar, or concrete mixtures. In all three cases, varying the mixture component proportions affects both fresh and hardened properties of the paste, mortar, or concrete. The properties (responses) depend on the proportions of the components.

In COST, w/c (or water-cementitious materials ratio, w/cm) is varied along with as many as four additional components. These are referred to as variable factors. Other factors may be included in the mixture at fixed (constant) levels, and are referred to as fixed factors. The user can designate as many as five concrete properties, or responses, (e.g., slump, strength, air content, cost, etc.) according to the requirements of the application.

COST is accessible via the Internet. The program consists of a front-end HTML interface that allows the user to enter required information. Underlying code (written in C) processes the input, generates the experiment designs and mixture proportions, calls routines for statistical analysis, and generates output. The statistical analysis routines are part of an interactive statistical software package, DATAPLOT, which was developed at NIST. COST is not intended to supplant or compete with commercially available experiment design and analysis software packages. Rather, COST's purpose is to introduce to the concrete practitioner the concepts of statistical experiment design and analysis using RSM and to explain how these concepts might be applied to concrete mixture proportioning. COST is specifically geared toward applying these methods to concrete mixture proportioning.

This section provides a brief, general overview of COST. The COST User's Guide, which describes the step-by-step approach of the Web site, is included as appendix C of this report.

5.4.2 Overview of COST Six-Step Process

The tasks required to optimize a concrete mixture using statistical methods have been assigned to the six steps listed below:

In most cases, these steps will be performed in the order listed above. Each step is described in detail in the COST User's Guide (see appendix C).

Before starting the six-step process, the user should define the overall objective of the project. Typical objectives include the following:

Step 1: Specify Responses

The first step is to specify the responses of interest. Responses are the concrete properties which the user is interested in, and are usually dictated by job requirements. The units (e.g., MPa, mm) and the allowable range of the response must also be specified. The allowable range defines the performance specification for the response. For example, a response like slump may have an allowable range between 50 and 100 mm. Another response, like strength, may have a specified minimum value greater than 40 MPa.

Step 2: Specify Mixtures

Step 2 involves specifying the concrete mixture components and their ranges. Concrete may contain a variety of component materials. Allowable material types for this version of COST include the following:

Each component, or factor, may be variable or fixed (set at a constant level). For concrete mixture proportioning, variable factors would usually be the mixture components expected to have the most significant effects on the responses. Fixed factors would be those expected to have little or no effect on the responses, allowing them to be held constant in the experiment. Any of the components included in COST may be set as variable or fixed; however, COST limits the user to a maximum of five variable factors for any one experiment (the greater the number of variable factors, the greater the number of trial batches required). Because w/c or w/cm is always considered to be one factor, as many as six material components (water, cement, and four others) may be varied.

The user must also provide information about material properties (e.g., for cement, specific gravity) and costs for each component to be included. Details on property information required can be found in the COST User's Guide (appendix C).

After the user has decided which factors to include, defined their ranges (for variable factors) or constant levels (for fixed factors), and entered required material information into the COST program, a trial batch plan is generated.

Step 3: Running the Experiment

After generating a trial batch plan, the next step is to perform the experiment. The experiment in this case is a set of trial batches from which specimens will be fabricated and tested for the responses specified in Step 1.

Step 4: Enter Results

After testing is completed, the test results are input into COST for analysis. The data are entered into a form, which is set up according to the experimental plan.

Step 5: Analyze Results

Analysis of the results consists of 10 tasks, which are performed using one or more statistical tools. Table 16 summarizes these analyses. The analysis techniques employed by COST consist of both graphical analysis and numerical analysis (modeling), which can be classified in the following groups:

Examples and details on each analysis task can be found in the COST User's Guide (appendix C).

Step 6: Summarize Analysis

The final step summarizes the analysis. The summary includes a list of the component variables, the responses, and the optimum settings based on three different perspectives: mean values, individual runs, and numerical optimization. A sample of the summary screen is shown in figure 23.

Table 16. Summary of analysis tasks and tools in COST

Task #Task DescriptionTool(s)
1Characterize response variablesSummary statistics
2Assess balance of designCounts plot matrix
3Assess optimality of design points- all responses jointlyCounts in admissible region matrix
Percentage in admissible region plots
4Assess optimality of design points- all four responses jointlyPercentage in admissible region plots
5Determine interrelationships between responsesScatterplots of response variables
Scatterplots of response variables vs. factors
6Assess relationship between response variables and factorsMeans plots of responses vs. factors
7Determine optimal settings for each factorBest settings based on mean values
Best settings based on individual runs
8Model fitting and verificationModel fitting tool
9Numerical optimizationBest settings based on maximum total score
10Response predictionResponse prediction tool

Figure 23 shows the summary screen from the COST system. The following description is from top to bottom. First, the variables examined are listed by name. Next, the responses are listed in a similar manner. The variables and responses are followed by notes describing the units used for particular variables. Underneath the notes is a table containing the best settings for each of three optimization situations: mean value, individual run, and numerical optimization. The rows of the table are the variables and the columns are the optimization options. The table contains the variable settings corresponding to each optimization scenario.

Figure 23. Summary screen from COST

5.5 Future Considerations

The current version of COST, while functional, is limited in several respects, because it is Web-based software and because of the specific architecture involved. The software runs slowly, the graphical capabilities are limited, and data is stored on the host computer instead of the user's computer. A stand-alone, Microsoft® Windows®-based version of COST could be developed in the future. However, there are commercially available statistical software packages that could be used for this application. Because these packages are general in nature (i.e., not specifically geared towards concrete mixture proportioning), some care is needed to assure that they are being used correctly.


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