National Academies Press: OpenBook
Page i
Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2010. Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. Washington, DC: The National Academies Press. doi: 10.17226/22917.
×
Page R1
Page ii
Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2010. Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. Washington, DC: The National Academies Press. doi: 10.17226/22917.
×
Page R2
Page iii
Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2010. Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. Washington, DC: The National Academies Press. doi: 10.17226/22917.
×
Page R3
Page iv
Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2010. Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. Washington, DC: The National Academies Press. doi: 10.17226/22917.
×
Page R4
Page v
Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2010. Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. Washington, DC: The National Academies Press. doi: 10.17226/22917.
×
Page R5
Page vi
Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2010. Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. Washington, DC: The National Academies Press. doi: 10.17226/22917.
×
Page R6
Page vii
Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2010. Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. Washington, DC: The National Academies Press. doi: 10.17226/22917.
×
Page R7
Page viii
Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2010. Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. Washington, DC: The National Academies Press. doi: 10.17226/22917.
×
Page R8
Page ix
Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2010. Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. Washington, DC: The National Academies Press. doi: 10.17226/22917.
×
Page R9

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

ACKNOWLEDGMENT This work was sponsored by the American Association of State Highway and Transportation Officials (AASHTO), in cooperation with the Federal Highway Administration, and was conducted in the National Cooperative Highway Research Program (NCHRP), which is administered by the Transportation Research Board (TRB) of the National Academies. COPYRIGHT INFORMATION Authors herein are responsible for the authenticity of their materials and for obtaining written permissions from publishers or persons who own the copyright to any previously published or copyrighted material used herein. Cooperative Research Programs (CRP) grants permission to reproduce material in this publication for classroom and not-for-profit purposes. Permission is given with the understanding that none of the material will be used to imply TRB, AASHTO, FAA, FHWA, FMCSA, FTA, Transit Development Corporation, or AOC endorsement of a particular product, method, or practice. It is expected that those reproducing the material in this document for educational and not-for-profit uses will give appropriate acknowledgment of the source of any reprinted or reproduced material. For other uses of the material, request permission from CRP. DISCLAIMER The opinions and conclusions expressed or implied in this report are those of the researchers who performed the research. They are not necessarily those of the Transportation Research Board, the National Research Council, or the program sponsors. The information contained in this document was taken directly from the submission of the author(s). This material has not been edited by TRB.

iii CONTENTS LIST OF TABLES .......................................................................................................................................v LIST OF FIGURES ................................................................................................................................... vi ABSTRACT……………….. ..................................................................................................................... ix CHAPTER 1- INTRODUCTION AND RESEARCH APPROACH ......................................................1 1.1 Background ............................................................................................................... 1 1.2 Effects of Cement Phase Characteristics ................................................................ 3 1.3 Previous Work on Heat of Hydration ..................................................................... 4 1.4 Problem Statement ................................................................................................... 7 1.5 Research Objectives ................................................................................................. 7 1.6 Scope of Study ........................................................................................................... 7 CHAPTER 2- STATISTICAL MODELING ............................................................................................8 2.1 The Data .................................................................................................................... 8 2.1.1 Phase Measures ............................................................................................ 8 2.1.2 Fineness Measures ..................................................................................... 11 2.1.3 Time of Setting ........................................................................................... 11 2.2 Tools of Statistical Modeling ................................................................................. 11 2.2.1 Prescreening Variables: Scatterplots ....................................................... 12 2.2.2 Transformations ........................................................................................ 15 2.2.3 Logodds Transform ................................................................................... 15 2.3 All Possible Subsets Regression (APSR) ............................................................... 18 2.3.1 Misspecification : Model Bias ................................................................... 19 2.3.2 Mallow's Cp ................................................................................................ 19 2.3.3 Ensuring Model Validity ........................................................................... 20 2.4 Principal Components Analysis ............................................................................ 22

iv 2.5 Alternating Conditional Expectation .................................................................... 23 2.6 Synergizing Clusters for ACE Analysis ................................................................ 25 2.6.1 Cluster Analysis ......................................................................................... 25 2.6.2 Explicit Parameterization of ACE outputs: an example ........................ 43 CHAPTER 3- CONCLUSIONS AND FUTURE DIRECTIONS ..........................................................52 3.1 Conclusions ............................................................................................................. 52 3.2 Future Directions .................................................................................................... 53 REFERENCES . ………………………………………………………………………………………….55 APPENDIX: CEMENTS DATA ..............................................................................................................57

v LIST OF TABLES Table 1-1- Heat of hydration values for clinker phases, and coefficients at 7 d and 28 d. From Taylor [3] ........................................................................................................... 6 Table 2-1- Predictor Variables and Classes used in the exploratory data analysis ................. 9 Table 2-2- Within-laboratory (s-within) and the between-laboratory standard deviations (s- between) and 95 % d2s values expressed as mass percents [16]. .......................... 10 Table 2-3- APSR regression results according to the untransformed var iable class combinations. ............................................................................................................. 21 Table 2-4- Selected phase clusters exhibit either a high R2 and poor quality data transforms, or a low R2 and smooth transforms. ........................................................................ 26 Table 2-5- Oxide clusters for combinations of TiO 2 and either CaO or MgO with other oxides. ......................................................................................................................... 29 Table 2-6- Total aluminate, cubic and or thorhombic plus structural phase cluster ............. 32 Table 2-7- All Possible Subsets ACE for Fineness and Phase ................................................. 34 Table 2-8- Sulfate Cluster APSACE Results ............................................................................. 36 Table 2-9- Extra var iables with phase and fineness var iables belite, bassanite, and Blaine. 41 Table 2-10- Small cluster s of var iables that provide high R2 and smooth transformations. Individual var iables and a descr iption of the transform shape are provided. ..... 44

vi LIST OF FIGURES Figure 1-1- Isothermal calor imetry curve of heat evolution based upon a single measurement for a hydrating cement for 24 h shows an initial peak of heat in the first hour , followed by a dormant per iod and then a gradual r ise before taper ing off in heat development for the following 23 h ......................................................... 2 Figure 1-2- The dependence of heat of hydration, with +- 1s uncer tainties indicated, on cement Type for a limited sampling of cements produced between 1992 and 1997 [1] .................................................................................................................................. 3 Figure 1-3- SEM backscattered electron micrograph of polished cement grains embedded in an epoxy illustrates the complicated shapes and multiphase par ticles typical of a por tland cement. Phase code is: alite = A, belite = B, aluminate = Al, ferr ite = F, alkali sulfate = Alk, and gypsum = G. Field Width = 500 µm ................................. 5 Figure 2-1- Scatterplots are a useful visualization tool to pre-screening tool to look for patterns and anomalous data. .................................................................................. 13 Figure 2-2- The cor relation matr ix is a useful data screening tool to assess both the cor relation between individual var iables and 7d heat of hydration, both for cor relations and anti-correlations (C3S and C2S) between var iables. ................. 14 Figure 2-3- Normal probability plots of raw phases and logodds phases for alite, belite, fer r ite, and aluminate indicates an improvement only for the belite phase. The Y-axis is sor ted sample data and the X-axis is Gaussian median order statistic predictions of sample data ........................................................................................ 16 Figure 2-4- Normal probability plots of raw phases and logodds phases for total aluminate, aluminate forms and per iclase show improvement for the aluminate forms and for per iclase. The Y-axis is sor ted sample data and the X-axis is Gaussian median order statistic predictions of sample data ............................................................... 17 Figure 2-5- ACE Transforms where the x-axes are the or iginal var iables and the y-axes are the transformed var iables ......................................................................................... 24 Figure 2-6- Alite and cubic aluminate provide a relatively high R2 but poor transforms, par ticular ly for alite. ................................................................................................. 26 Figure 2-7- Including the pr imary cement phases results in a high R2 (0.86), but rough transform curves for several of the constituents. ................................................... 27 Figure 2-8- Oxide cluster transforms for R2=0.96 combination of CaO, TiO 2, and SO 3 ..... 30 Figure 2-9- Oxide cluster transforms for R2=0.96 combination of MgO, TiO 2, and SO 3 ..... 30 Figure 2-10- Oxide cluster transforms for R2=0.96 combination of CaO, TiO 2, and MgO .. 31

vii Figure 2-11- Oxide cluster transforms for R2=0.93 combination of MgO and TiO 2 ............. 31 Figure 2-12- Transforms of aluminate phases plus structural phases (belite and bassanite) result in a 0.81 R2 the total aluminate, belite, and bassanite exhibiting fair ly smooth transformed curves. ..................................................................................... 33 Figure 2-13- ACE Transform for Blaine fineness that yields an R2 of 0.54 ........................... 34 Figure 2-14- ACE Transforms for Blaine fineness, alite, and bassanite that yield an R2 of 0.74 .............................................................................................................................. 35 Figure 2-15- ACE transform for anhydr ite, belite, and Blaine with an R2 of 0.60. ............... 36 Figure 2-16- ACE transform for bassanite, belite, and Blaine with an R2 of 0.69. ................ 37 Figure 2-17- ACE Transforms for gypsum, belite, and Blaine with an R2 of 0.73 are rough. ..................................................................................................................................... 38 Figure 2-18- ACE Transforms for SO 3, belite, and Blaine with an R2 of 0.72 are rough. .... 38 Figure 2-19- (bassanite + gypsum + Fe2O 3) with (belite + Blaine), giving an R2 of 0.88, illustrates the smooth bassanite ACE transform. ................................................... 39 Figure 2-20- (anhydrite + gypsum + SO3) + (belite + Blaine), also giving an R2 of 0.88, but the ACE transforms are much rougher . ................................................................. 40 Figure 2-21- The 1/Vicat ACE curve yields a relatively high R2 but exhibits a r ough structure that would be difficult to model, unless the (over laid) point(s) at 0.007 can be ignored. ........................................................................................................... 42 Figure 2-22- The belite, bassanite, Blaine var iables yield an R2 of 0.71 but a rough belite curve and a break in the Blaine curve at around 3800. ......................................... 42 Figure 2-23- Belite, bassanite, Blaine and calcite ACE output gives an R2 of 0.78 and reasonably smooth curves ......................................................................................... 43 Figure 2-24- ACE transforms for aluminate, Blaine, 1/Vicat with an R2 of 0.78. ................. 45 Figure 2-25- ACE transforms for ferr ite, Blaine, and 1/Vicat yields a combination of a smooth transform and high R2 of 0.88. This is the combination chosen to illustrate explicit parameter ization. ......................................................................... 45 Figure 2-26- ACE transforms for ferr ite, aluminate, Blaine, and 1/Vicat yields an R2 of 0.90 but the curves for fer r ite and aluminate appear rough. ........................................ 46 Figure 2-27- ACE transforms for aluminate, ferr ite, bassanite, Blaine, and 1/Vicat yields an R2 of 0.86. ................................................................................................................... 47 Figure 2-28- Ferr ite ACE transform is approximately descr ibed by a simplified cubic function. ..................................................................................................................... 48

viii Figure 2-29- Transformed Blaine fineness can be descr ibed by a mixed x-(1/x) quadratic. 48 Figure 2-30- Transformed 1/Vicat results in an almost linear structure. .............................. 49 Figure 2-31- The roughness of the ACE(HOH7) transform (upper-r ight) precludes a simple inver tible parameter ization ...................................................................................... 51

ix ABSTRACT The heat of hydration of hydraulic cements results from the complex sets of phase dissolution and precipitation activity accompanying the addition of water to a cement. This process generates heat, as well as an increased potential for thermal cracking in some concrete structures. The potential heat of this hydration process is measured in two ways: 1) through an acid dissolution of the raw cement and a hydrated cement after seven days, or 2) isothermal calorimetry. In principal, the heat of hydration should be predictable from knowledge of the cement composition, and perhaps some measure of the cement fineness or total surface area. The improved mineralogical estimates provided by quantitative X-ray powder diffraction, together with improved statistical data exploration techniques that examine nonlinear combinations of candidate constituents, are used to explore alternative predictive models for 7-day heat of hydration (HOH7) based on a set of more complete and more accurate characterizations of portland cements. In the modeling described in this report we make essential use of the groupings, or classes, of potential explanatory variables of phase, fineness, and other physical parameters. An All Possible Alternating Conditional Expectations (APACE) exploratory tool, created by combining All Possible Subsets Regression with the Alternating Conditional Expectation (ACE), is used to determine which variables within an explanatory variable class and which subsets of variables across explanatory variable classes exhibit the highest potential predictive power for additive nonlinear models for HOH7. While a single, strong candidate model for HOH7 did not emerge from these analyses, some general conclusions did result. Good fitting models include a key structural mineralogical phase (belite preferred), a calcium sulfate phase (bassanite preferred), a total fineness or surface area component (Blaine fineness preferred), and ferrite in conjunction with Fe2O3, or aluminate, or cubic aluminate. Surprisingly, TiO2 recurs as a component in good-fitting models.

Next: Chapter 1: Introduction and Research Approach »
Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables Get This Book
×
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

TRB’s National Cooperative Highway Research Program (NCHRP) Web-Only Document 167: Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables explores alternative predictive models for seven-day cement heat of hydration.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!