U.S. Department of Transportation
Federal Highway Administration
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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: FHWA-RD-03-060
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:
As mentioned in chapter 1, commercially available statistical software packages can provide the required experiment design and analysis capabilities needed for this approach. However, these packages are not specifically geared toward concrete mixture proportioning. The purpose of the COST software is to introduce the RSM approach as a means of optimizing concrete mixtures. The COST software is not intended to be a state-of-the-art, all-inclusive, "definitive" software product.
Concrete producers want to minimize the effort (and cost) needed to identify optimal mixtures. Therefore, the maximum number of factors was limited to five, one of which is water-cement ratio or water-cementitious materials ratio. The maximum number of responses was also limited to five (one of which is cost).
The most common concrete component materials were included, and in each category of material (e.g., chemical admixtures, mineral admixtures, aggregates) a "user-defined" selection was included to accommodate unusual or new materials. Flexibility was provided so a user could, for example, optimize the cementitious matrix alone (i.e., hold aggregates constant), or optimize the entire concrete mixture.
For this reason, guidance was included for analysis and interpretation as well as actually running the experiment. For example, potential sources of error, the importance of randomization, and the importance of accuracy in batching and in following the experimental plan are discussed. Because the results and circumstances for any user will vary widely, guidance in analysis and interpretation was limited to general aspects, such as indicating strong and weak factors. More subtle statistical analysis requires human knowledge and judgment.
There were several issues to contend with. Speed was one issue-the speed of transfer to and from a user's computer over the Internet to the server housing COST, and the computational speed of DATAPLOT. Computations were minimized to reduce waiting times. Speed was also an issue in generating graphics (plots). Another limitation associated with graphics was the type and quality of graphics that could be generated and presented on the Web. DATAPLOT generates postscript plots which were converted to GIF format for the Web site.
Speed issues also prevented the use of a mathematically rigorous numerical optimization scheme. Instead, numerical optimization was achieved by calculating a score function at each point on a superimposed grid over the range of each factor. For 5 factors and 10 points per factor, this requires 105, or 100,000, calculations. To avoid excessive computation time, the grids were limited in size.
In addition to speed, there were file storage, access, and privacy issues. For example, configuration and security constraints require that files be stored on the COST server. They cannot be saved on the user's computer.
5.4 Description of the Software and Web Site
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:
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 Description||Tool(s)|
|1||Characterize response variables||Summary statistics|
|2||Assess balance of design||Counts plot matrix|
|3||Assess optimality of design points- all responses jointly||Counts in admissible region matrix |
Percentage in admissible region plots
|4||Assess optimality of design points- all four responses jointly||Percentage in admissible region plots|
|5||Determine interrelationships between responses||Scatterplots of response variables |
Scatterplots of response variables vs. factors
|6||Assess relationship between response variables and factors||Means plots of responses vs. factors|
|7||Determine optimal settings for each factor||Best settings based on mean values|
Best settings based on individual runs
|8||Model fitting and verification||Model fitting tool|
|9||Numerical optimization||Best settings based on maximum total score|
|10||Response prediction||Response prediction tool|
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.