Eric S. Lagergren
James J. Filliben
Lynne B. Hare
Statistical Engineering Division, ITL
Dale P. Bentz
Ken A. Snyder
Building Materials Division, BFRL
Federal Highway Administration (FHWA)
Optimizing high-performance concrete is currently more of an art than a science. Some guidelines are available for selecting optimal conditions, but no systematic approach is used to identify these conditions. As a result, trial and error or "one-factor-at-a-time" designs are typically used to identify best mixtures. A collaboration is underway between the FHWA and NIST's Statistical Engineering and Building Materials Divisions to investigate the feasibility of using mixture design and analysis techniques for optimizing high-performance concrete. A second objective is to develop a World Wide Web service for users to design and analyze mixture experiments for optimizing concrete mixes.
In the first phase of this work, a laboratory experiment was conducted to study six mixture components: water, cement, fine and coarse aggregate, superplasticizer, and microsilica. The first four components produce concrete. The last two enhance specific properties yielding "high-performance" concrete. The properties of interest are workability, air content, strength, and chloride ion permeability. Since the proportions of the six components were constrained to a subset of the full mixture space, standard Scheff simplex designs could not be used. Instead, a modified distance-based design was used. This design permits fitting a second-order Scheff polynomial and includes points for checking the adequacy of the fitted model and estimate repeatability.
The figure shows the contour plot of the fitted model for 28-day strength over the simplex in three components: superplasticizer (HRWRA), coarse aggregate and fine aggregate at fixed proportions of water, cement, and microsilica. The plot shows that increasing the proportion of fine aggregate (moving toward the vertex labelled fine aggregate) increases 28-day strength. Optimal conditions were identified for each property using the contour plots and numerical optimization routines. Also, a best condition across multiple responses was found using desirability functions.
There is some concern that the mixture design & analysis approach is more complicated than necessary for novice users, the customers of the proposed web service. We are currently investigating other approaches using more balanced response surface designs that would lend themselves to simpler, graphical analyses and be less reliant on model fitting.
Date created: 7/20/2001