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3.4.3 Compressive Strength Modeling for Portland Cements

Stefan Leigh
Statistical Engineering Division, ITLCurtis Spring, James Pielert
Building Materials Division, BFRLKer Chau Li
Department of Statistics, UCLA A large database of Portland cement interlaboratory test results has been generated and maintained by the Cement and Concrete Reference Laboratory (CCRL) at NIST since 1965. The database represents a rich resource inasmuch as the cements tested were produced by many different production facilities, from raw materials of different geological areas, over a long period of time. Measurements of 10 physical test properties and 11 chemical constituents for a constantly growing number of Portland cements tested is available from 120 to 200 test laboratories throughout the United States.

An initial publication, NISTIR 5387, analyzed gross trends in the database graphically using various forms of box annd profile plots. But an ultimate goal has always been to make use of the database to model 3-day and 7-day compressive strengths in terms of the other constituent variables. Such work would update considerably an older series of studies by Blaine and Arni at NIST (1965-1971), that made use of simpler regression technology as understood by engineers at that time. Regression-related methodology having progressed considerably in the last 25 years, it was expected that newer methods applied to richer data would yield interesting new results.

Novel approaches have been used in the study of this newer data. Ker-Chau Li (UCLA), Senior Research Fellow at SED, applied Sliced Inverse Regression to came up relatively quickly with a simple hypothesis comparing the 3-day and 7-day strength responses: namely that 3-day strength could be modeled adequately with a multilinear model, but that 7-day strength would require nonlinear models. This has been amply confirmed by running thousands of comparable multilinear models, using All Possible Subsets Regression (APSR) combined with Principal Components Analysis (PCA) in a novel manner, with both 3-day and 7-day strength responses. The 3-day strength models always dominate the corresponding 7-day ones in terms of $\mbox{R}^{2}$.

Further, the yoking of APSR to PCA, with judicious transformation of independent variables suggested by engineering knowledge, has produced a number of credible multilinear models for 3-day compressive strength. Models are compared post hoc on the basis of numbers of principal component variables, Mallows' $\mbox{C}_{p}$, and $\mbox{R}^{2}$, and have been selectively cross-validated against other portions of the database. It is noteworthy that multiple easily identifiable linear subunits, such as contrasts among oxide groupings (structural versus alkali), contrasts or averages of major Bogue compound constituents, either with similar or proportionate numerical coefficients, recur throughout the principal component constituents of the most important 15 models.


Figure 26: First 3 principal components for best 15 models. Row positions indicate relative significance. Brackets indicate contrasts.

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Date created: 7/20/2001
Last updated: 7/20/2001
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