NISTIR 7135

Final Report for: 

EPA: IAG No. DW-13-93903501-0 Expanding a tool for predicting chloride 

diffusivity in concrete so it can be used by manufacturers to evaluate the durability 

of concrete made with blended cements. Part I: Characterizing blended cement 

materials. 

X. Feng*, NIST and Northwestern University 

E.J. Garboczi, J.W. Bullard, D.P. Bentz, K.A. Snyder, and P.E. Stutzman, NIST 

T.O. Mason, Northwestern University 

NISTIR 7135

Final Report for: 

EPA: IAG No. DW-13-93903501-0 Expanding a tool for predicting chloride 

diffusivity in concrete so it can be used by manufacturers to evaluate the durability 

of concrete made with blended cements. Part I: Characterizing blended cement 

materials. 

X. Feng*

, NIST and Northwestern University 

E.J. Garboczi, J.W. Bullard, D.P. Bentz, K.A. Snyder, and P.E. Stutzman, NIST 

T.O. Mason, Northwestern University 

August 2004

U.S. DEPARTMENT OF COMMERCE

Donald L. Evans, Secretary

TECHNOLOGY ADMINISTRATION

Phillip J. Bond, Under Secretary of Commerce for Technology

 v 

Final Report for: 

EPA: IAG No. DW-13-93903501-0 Expanding a tool for predicting chloride 

diffusivity in concrete so it can be used by manufacturers to evaluate the durability 

of concrete made with blended cements. Part I: Characterizing blended cement 

materials. 

by 

X. Feng*

, NIST and Northwestern University 

E.J. Garboczi, J.W. Bullard, D.P. Bentz, K.A. Snyder, and P.E. Stutzman, NIST 

T.O. Mason, Northwestern University 

Cover: Processed scanning electron microscopic image of the fly ash-blended cement (256 μm 

by 200 μm) studied in this report. The orange particles are fly ash, and the rest are cement 

constituents. Some of the orange fly ash particles are not particularly round, as is usual for fly 

ash, which may be a result of the fly ash-cement intergrinding process.

 

*

 Present address: Department of Civil Engineering, University of New Brunswick, New Brunswick, Canada 
 vi 

Table of Contents 

Preface................................................................................vii 

Introduction............................................................................1 

1. Materials........................................................................4 

2. Paste preparation..............................................................5 

3. Detailed experimental procedures and results.............................7 

3.1 Chemical shrinkage..........................................................7 

3.2 Degree of hydration by LOI and SEM...................................10 

3.3 Pore solution press and conductivity measurement....................11 

3.4 Bulk conductivity...........................................................17 

4. Modeling......................................................................20 

4.1 3-D microstructures for cement clinkers.................................20 

4.2 Degree of hydration and fly ash reaction modeling....................22 

4.3 Conductivity modeling.....................................................26 

4.3.1 Determination of the conductivity of regular C-S-H 

 for T-1 and T-L cements................................................26 

4.3.2 Results of conductivity modeling for T-1 cement..................26 

4.3.3 Results of conductivity modeling for T-L cement..................28 

5. Conclusions..................................................................30 

6. Acknowledgements.........................................................30 

7. References....................................................................31
 vii 

Preface: The Virtual Cement and Concrete Testing Laboratory 

and the Nature of This Project

The Virtual Cement and Concrete Testing Laboratory (VCCTL) Consortium was formed in 

January 2001. The overall goal of the consortium is to develop a virtual testing system that will 

reduce the amount of physical cement and concrete testing needed and expedite the research and 

development process in the cement and concrete industry. This will result in substantial time and 

cost savings to all aspects of the concrete construction industry. Headquartered in the Building 

and Fire Research Laboratory (BFRL) at the National Institute of Standards and Technology 

(NIST), at present, June, 2004, the consortium consists of two NIST laboratories: the Building 

and Fire Research Laboratory (BFRL) and the Information Technology Laboratory (ITL), and 

nine industrial members: (cement companies) Holcim (US) Inc. and the Portland Cement 

Association (PCA); (chemical admixture companies) Master Builders Technologies Inc. (MBT), 

W.R. Grace & Co, and Sika Technology AG; (aggregate companies) International Center for 

Aggregates Research (ICAR); (ready-mixed concrete companies) National Ready-Mixed 

Concrete Association (NRMCA); and the French and German portland cement associations, 

Association Technique de l’Industrie des Liants Hydrauliques (ATILH), and Verein Deutscher 

Zementwerke e.V. (VDZ). In the United States, we estimate that 80 % of the cement market, 90 

% of the chemical admixture market, 75 % of the aggregate market, and 80 % of the readymixed concrete market are represented in the VCCTL consortium either through direct 

participation or through the participation of the relevant trade association. 

The VCCTL software package consists of fundamental models of microstructure formation and 

physical property prediction for cement-based materials (cement paste, mortar, and concrete). 

But without meticulous characterization of the starting materials, it is practically impossible to 

formulate fundamental microstructure models of the hydration and properties of a cement paste, 

mortar, or concrete. One of the signature features and strengths of the VCCTL cement hydration 

model is its incorporation of microstructural information with unprecedented levels of detail. 

Proper characterization of cement-based materials is not a trivial task. The starting powders 

typically consist of a wide distribution of particle sizes, each particle of which is composed of 

multiple phases with variable chemical compositions. Many products of hydration are 

amorphous or poorly crystalline, and these may be finely intermixed. An additional 

complication is that some microstructural characteristics have not been rigorously defined. In 

some cases it has not been possible even to properly calibrate measurements, like those of 

particle size distribution (PSD), because of the absence of an accepted reference material or 

standard methodology. 

Recognizing the critical importance of materials characterization for predictions of 

microstructure development, physical properties, and durability, the consortium has continually 

sought to achieve greater accuracy and detail in these types of measurements, and to supply 

robust, calibrated measurement techniques where those have been lacking. Doing this for wastestream materials that are often added to concrete to improve performance and reduce 

environmental waste generation, like fly ash or blast-furnace slag, is an especially difficult task.

This report summarizes a project that dealt with the characterization of a fly ash and fly-ash 
 viii 

blended cement material, so that these could be incorporated into the VCCTL software. The 

information generated from this project will be transferred to the members of the consortium, 

who represent all parts of the concrete materials community – cement production, chemical 

admixtures, aggregates, and ready-mixed concrete manufacture. Other members of the cement 

and concrete industry are welcome to join the VCCTL consortium, to take advantage of this 

software. Eventually, all the VCCTL software will be publicly accessible, but since new features 

developed by the consortium are not released to the public for three years, joining the VCCTL 

consortium will allow quicker access to the software (for more information, contact 

jeffrey.bullard@nist.gov). 

Products of this partially EPA-funded project include: a method for predicting the conductivity 

of pore solutions where the concentration of [Na]+

 and [K]+ ions are known, unique experimental 

data on the hydration of cement and the consumption of fly ash in a fly ash blended cement, 

experimental data on the electrical conductivity of blended cement pastes made from these 

materials, and model modifications that allow for more quantitative modeling of blended cement 

hydration and microstructure formation. We are pleased that this project has turned out products 

that will allow much greater progress in the future in the area of modeling blended cements. 

A link is currently being explored between VCCTL, which is materials science-based and 

oriented towards performance predictions and the BEES (Building for Environmental and 

Economic Sustainability) software (found at http://www.bfrl.nist.gov/oae/software/bees.html). 

This link has not been developed enough to be able to described in this report, however. BEES 

was developed by the NIST (National Institute of Standards and Technology) Building and Fire 

Research Laboratory, with support from the United States EPA Environmentally Preferable 

Purchasing Program, to be a powerful technique for selecting cost-effective, environmentallypreferable building products. Linking VCCTL with BEES will give an economic and 

environmental component that will add to the power of physical performance prediction. 

BEES measures the environmental performance of building products by using the life-cycle 

assessment approach specified in ISO 14000 standards. All stages in the life of a product are 

analyzed: raw material acquisition, manufacture, transportation, installation, use, and recycling 

and waste management. Economic performance is measured using the ASTM standard life-cycle 

cost method, which covers the costs of initial investment, replacement, operation, maintenance 

and repair, and disposal. Environmental and economic performance are combined into an overall 

performance measure using the ASTM standard for Multi-Attribute Decision Analysis. For the 

entire BEES analysis, building products are defined and classified according to the ASTM 

standard classification for building elements known as UNIFORMAT II. 
Introduction

The models developed by NIST to predict the microstructure and ionic diffusivity of cementbased materials require experimental information in order to operate successfully. This 

information is not for providing empirical fits, but is for (1) measuring the fundamental 

properties of materials needed to accurately simulate the microstructural development, and for 

(2) validating model predictions of ionic diffusivities. The project summarized in this report is 

the Environmental Protection Agency (EPA) project on a fly ash (FA) blended cement material. 

A similar project on a blast furnace slag material, partially funded by the Center for Advanced 

Cement-Based Materials (ACBM), was simultaneously carried out in one experimental program. 

Since both programs were small monetarily (and had to be supplemented by NIST funds), this 

also allowed a single post-doctoral researcher to be hired to do both sets of work simultaneously. 

This report, however, only summarizes the work on a fly ash blended cement, as that was the 

goal of the EPA funding. The title states “Part I,” since there is clearly more work needed, as will 

be made clear throughout the report and in the conclusions. 

The EPA project, “Expanding a tool for predicting chloride diffusivity in concrete so it can be 

used by manufacturers to evaluate the durability of concrete made with blended cements,” grew 

out of the EPA ClimateWise program. This program at EPA was working with cement 

manufacturers to help encourage control of CO2 emissions. Cement manufacturers have been 

pursuing the option of using fly ash as a replacement for some of the portland cement in 

concrete. By partially funding the experimental work needed to help incorporate and test the use 

of a fly ash in the Virtual Cement and Concrete Testing Laboratory (VCCTL), EPA would help 

encourage the expanded use of fly ash by users of the VCCTL software. A secondary goal of the 

project was to compare a cement interground with a fly ash at the cement plant with the same 

cement and same fly ash simply mixed in the laboratory. The term “a fly ash” is used rather than 

“fly ash,” since every fly ash differs from each other. Characterizing a single fly ash does not 

finish the job for all the classes of fly ash found across the country. The ASTM fly ash 

classifications, class C and class F, are very generic, so that just stating that a fly ash material is 

class F, for example, does not in any way completely characterize its properties when used in a 

cement system. The challenge of characterizing fly ashes across the United States so that they 

can be used reliably is an outstanding problem. 

Simulating the hydration of portland cement requires detailed knowledge of cement chemistry, 

and of the chemical and physical makeup of the portland cement being considered. Detailed 

work to gather this information has been done in the past for portland cement [1]. To incorporate 

a new material into the model requires the same kind of information on the identity and density 

of products and the details of the chemical interactions with portland cement constituents. Some 

of this information for a fly ash was obtained in earlier work [2,3], although some new 

information had to be obtained for this study. In particular, chemical shrinkage measurements 

and degree of hydration measurements were made in this study to understand each material’s 

reactions with water and to check with the model, since the fly ash part of CEMHYD3D had not 

been thoroughly validated before. 

It has recently been shown that the rate of ionic transport under diffusion and electrical field 

gradients can be determined by two parameters – the porosity, φ, and the formation factor, F, 
 2 

along with information about the concentration of all types of ions in the water-filled pore space 

[4-6]. The formation factor is defined simply by the following - for a porous material, assume 

that the pore space is totally evacuated, without altering the solid part of the material, which has 

zero conductivity. Fill the pores with a fluid of some known conductivity, σf, again without 

changing the solid part at all. Measure the bulk conductivity, σb, assuming that the material is 

uniform. Just from stereology alone [7,8], the value of σb is at most σb = φσf, and is usually less 

due to the tortuosity of the pore space [7,8]. The ratio F = σf /σb isthen defined as the formation 

factor, and is always greater than unity. Using these two parameters, F and φ, along with 

knowledge of other ion concentrations in the pore space, the entire ionic transport response can 

be determined [4,5]. 

F is defined by the above thought experiment. In principle, it can be experimentally determined 

in cement paste, with some measure of uncertainty, measuring σf by pressing out the pore 

solution and measuring the bulk conductivity of a companion sample with nominally the same 

pore solution. Their ratio then gives the value of F. This is the procedure carried out in this 

paper. There is some experimental uncertainty, as one is not quite sure that one is not changing 

the pore fluid by causing some pressure-induced dissolution. Also, the amount of pore fluid so 

expressed is small, leading to the possibility of statistical fluctuations. In fact, it was found as a 

result of this experimental work that the ionic concentration in the expressed cement paste pore 

solutions was systematically too high, above even an estimate of the maximum concentration 

possible. Upon review of the literature, this problem was found in other studies as well. 

Therefore, we concentrated on only comparing bulk conductivities as predicted by the model to 

those measured by experiment, as will be described later. 

The use of mineral admixtures like fly ash (FA) and ground granulated blast furnace slag 

(GGBFS) is known to change ionic transport properties. The formation factors of cement pastes 

with these materials have not, however, been measured before. In order to fundamentally 

understand ionic transport in these materials, the value of F is needed. For example, a popular 

test called the Rapid Chloride Permeability Test only measures the bulk resistance (reciprocal of 

conductance), and so cannot distinguish between materials that alter the pore solution 

conductivity and materials that alter the pore space characteristics [6]. As was mentioned above, 

and as will be detailed later, it proved not possible to accurately measure the formation factor of 

the materials used in this study, so that only the bulk conductivity was compared to model 

predictions. As the bulk electrical conductivity is a direct analogue of the ionic diffusivity, this is 

also an important transport parameter and gives insight into what the fly ash does to the 

microstructure. 

The CEMHYD3D model, also as embodied in the VCCTL consortium software [1,9], can 

predict cement paste microstructure and compute the value of F. In the year 2001 version, the 

effect on the microstructure of mineral admixtures like FA and slag could also be simulated to 

some approximation. There were, however, no quantitative measures of the degree of reaction 

vs. time of the mineral admixtures and measurements of F against which to compare the 

predictions of the model and check for any systematic errors. A recent result coming from the 

present project, using scanning electron microscopy-based point counting, allowed 
 3 

measurements to be made of the degree of reaction of FA and GGBFS, along with portland 

cement, as a function of time [10]. These measurements, along with a new model capability to 

predict the pore solution concentrations and thus the pore solution conductivity, allow one finally 

to check the model’s predictions when FA is present along with portland cement. The 

comparison with these data highlighted several shortcomings in the model. Modifications that 

were made to correct these limitations are also briefly described in this report. 

What follows first is a detailed listing of experimental procedures, experimental data, and graphs 

showing that data. These experimental results pointed out some inadequacies in our hydration 

model, as regards mainly to fly ash. New model results are then used to compare to the 

experimental data, showing that the models give generally accurate results for experimental 

parameters, allowing one, with some degree of confidence, to replace experiments with models. 
 4 

1. Materials 

An ASTM Type I Portland cement, provided by Holcim* (designated as T-1); one blended 

cement (designated as T-1P) made with 80 % T-1 cement and 20 % fly ash, interground by a 

Holcim cement plant; and the same fly ash, also supplied by Holcim, were selected in the current 

study. The Blaine surface area for cements T-1 and T-1P were 343 m2

/kg and 400 m2/kg, 

respectively (uncertainty of 1 %). The chemical compositions of the materials used are given in 

Table 1. The particle size distributions of T-1 and T-1P are shown in Figure 1, as measured by 

laser diffraction and numerically processed, so that the point at 1 μm includes the mass of all 

particles with particle size less than 1 μm, the point at 3 μm includes the mass of all particles 

with particle size between 1 and 3 μm, etc. Figure 1 indicates that T-1P is finer than T-1, 

probably because of the extra intergrinding carried out at the cement plant to adequately blend 

the fly ash and portland cement. In cement T-1P, the particle size measurement does not 

distinguish between the cement and fly ash particles, so we do not know how the fly ash and the 

cement separately contribute to the different parts of the size distribution. The cement particle 

size distribution is an important piece of information necessary for understanding how a cement 

will perform in practice, and must be measured quite carefully in order to obtain valid results 

[11]. 

It should be emphasized again that this characterization work was done for a single fly ash 

material. In general, all fly ashes are different from each other. It may be, that if this kind of 

characterization was done for a broad range of fly ash materials, trends would be seen so that fly 

ash performance could be related quantitatively to fly ash chemical composition and particle 

microstructure and size distribution. 

Table 1. Chemical Compositions of Cement and the fly-ash used (mass fraction in percent, 

uncertainty in any number in table is about + 0.1) 

 T-1 T-1P Fly ash 

SiO2 20.1 29.8 61.3 

Al2O3 5.6 9.26 19.4 

Fe2O3 2.5 3.32 4.5 

CaO 64.7 53.5 9.1 

MgO 0.8 1.11 2.3 

SO3 3.4 3.19 0.2 

K2O 0.76 0.84 1.06 

Na2O 0.14 0.19 0.3 

L.O.I. 1.2 1.07 0.1 

 

*

 Certain commercial equipment and/or materials are identified in this report in order to 

adequately specify the experimental procedure. In no case does such identification imply 

recommendation or endorsement by the National Institute of Standards and Technology, nor 

does it imply that the equipment and/or materials used are necessarily the best available for the 

purpose. 
 5 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 10 20 30 40 50 60 70 80

T-1

T-1P

Mass Fraction

Diameter (μm)

Figure 1. Differential particle size distributions of T-1 and T-1P cements. 

2. Paste preparation 

A fly ash blended cement designated as T-L, similar to T-1P blended cement, also consisting of 

20 % (mass fraction) fly ash and 80 % T-1 cement, was mixed in the laboratory. The purpose to 

make this T-L cement was an attempt to see any differences in properties obtained between 

intergrinding a blended cement at the cement plant vs. simply adding fly ash in the laboratory or 

at a ready-mix plant. When making the blended cement pastes, the solid materials were premixed 

in a large beaker and then added to the mixing bowl with the water needed, to obtain a 

homogeneous paste. Overall, six different kinds of cement pastes were studied, three types (T-1, 

T-1P, T-L) and two w/s ratios, 0.4 and 0.5. “w/s” means the ratio of the mass of water to the 

mass of solid materials (cement, fly ash, etc.) used in a particular mix, while “w/c” is defined the 

same way but where the solid materials are portland cement only. 

Before substantial research could progress and samples be made, the bleeding characteristics of 

each cement needed to be checked. It is very hard to control the w/c ratio in a sample that bleeds 

heavily (separation of water and cement, instead of staying intimately mixed). The bleeding 

properties of the three cements are given in Table 2. The uncertainty in these measurements is 

about 1 %, as measurement of mass is very precise. The T-1 cement pastes have the largest 

bleeding capacity at any w/c tested, which means adding fly ash in cement can significantly 
 6 

improve the bleeding properties of cement pastes. Simply blending in fly ash (T-L) improved 

the bleeding properties somewhat. The T-1P cement, interground at the cement plant, has the 

smallest bleeding capacity of all three cements, clearly showing the benefits of extra grinding at 

the cement plant. Note that the T-1P cement had finer particles, and therefore a larger surface 

area, which means it can “hold on” to water more effectively, thus reducing bleeding. 

Table 2. Bleeding capacities (mL/g binder) of cement (1 % uncertainty) 

w/s T-1 T-1P T-L 

0.3 0.40 0.06 0.52 

0.35 1.42 1.16 1.57 

0.4 2.69 1.62 2.03 

0.45 4.75 2.42 3.39 

Based on the bleeding test results, at the first stage of the project, 0.3 and 0.45 w/s ratios were 

chosen to be used for further study for the two blended cement systems. The 0.3 w/s samples did 

not require any special treatment, as their bleeding was minimal. However, when we progressed 

to making samples for conductivity measurements, we found many air bubbles were trapped 

when casting paste samples at w/s=0.3, which of course made determining the true conductivity 

difficult to impossible. Therefore, the w/s ratios studied were chosen to be 0.4 and 0.5. In order 

to prevent substantial bleeding at these w/s ratios and to also effectively eliminate entrapped air 

bubbles, house vacuum was employed during the mixing and casting processes, as well as a 

vibration table during casting (Fig. 2). The samples were cast in sealed plastic molds and slowly 

rotated on a roller for 5 h. By constantly changing the orientation of the samples with respect to 

the direction of gravity, bleeding was minimized. After this, the pastes were kept in the molds 

and put in sealed plastic bags and maintained at 20 °C and 100 % RH until the testing age was 

reached. 

Figure 2. House vacuum container and vibrator used in paste preparation 
 7 

3 Detailed experimental procedures and results 

3.1 Chemical shrinkage

Cement pastes were prepared for chemical shrinkage tests. The water to binder mass ratio was 

controlled at w/s = 0.3. This is lower than is typically used in the field, but is sometimes used for 

high performance concrete. Cement and the needed water were mixed in the mixer as specified 

in ASTM C305 (C305-99e1 Standard Practice for Mechanical Mixing of Hydraulic Cement 

Pastes and Mortars of Plastic Consistency). Pastes were then placed in glass vials, and 1 mL of 

limewater was placed on top of the paste to minimize the leaching of calcium hydroxide from the 

paste. The vials were filled to the top using vegetable oil, to keep out air. Rubber stoppers with 

0.01 mL graduated cylinders encased in the centers were used to seal the vials. This experimental 

arrangement was placed in a water bath at a temperature of 25 °C. Two replicate specimens were 

prepared using the same paste. The consumption of water could be followed by the lowering of 

the water/vegetable oil meniscus in the graduated cylinders. The uncertainty in these 

measurements is estimated to be about 10 %. 

Results are shown in Figs. 3 and 4 (20 % FA means T-L). In Fig. 3, under the same conditions, 

the T-1 cement shows the largest chemical shrinkage, followed by the T-1P cement. The T-L 

cement had the smallest chemical shrinkage. However, if the chemical shrinkage data (volume) 

are expressed in milliliter per gram of cement, as shown in Fig. 4, the chemical shrinkage of the 

T-1 cement is the smallest, with the T-1P cement the largest. Part of the reason for this is that the 

T-1P cement is finer than the T-1 cement and also the fly ash contained in the T-1P cement can 

accelerate the cement hydration process. Due to the fineness and homogeneous distribution, the 

fly ash in the T-1P cement could be more active than in the T-L cement. 

0

0.01

0.02

0.03

0.04

0.05

1 10 100 1000

T-1

T-1P

T-L

Chemical shrinkage (mL/g binder)

Time, log(h)

Figure 3. Chemical shrinkage results for various cements, w/c=0.3 
 8 

0

0.01

0.02

0.03

0.04

0.05

0.06

1 10 100 1000 104

T-1

T-1P

T-L

Chemical shrinkage (mL/g cement)

Time, log(h)

Figure 4. Chemical shrinkage results shown as mL per gram of cement. 

The v2.0 VCCTL software was used to simulate the chemical shrinkage results of the T-1 and T1P cement pastes. (Note that the fly ash experimental data was used to build the fly ash results 

into the VCCTL software, providing the required software tool of this project.) Results are 

provided in Figs. 5 and 6. The values of the parameter B used to convert from computational 

hydration cycles to real time were in both cases equal to 0.00032 [1]. However, after about 50 h 

of hydration, the experimental results begin to fall below the model predictions in both cases, 

suggesting only the early-time chemical shrinkage can be employed in evaluating the goodness 

of fit between model and experiment. This was also an indication to us that the implementation 

of fly ash consumption in the CEMYD3D model was possibly overreacting the fly ash. The 

chemical shrinkage results lumped all the chemical shrinkage together, so it was not possible to 

use these data to elucidate this possible problem. However, using SEM-based point counting 

enabled us to zero in on this problem by being able to measure individual phase consumption 

rates. 
 9 

0

0.01

0.02

0.03

0.04

0.05

0.06

0.1 1 10 100 1000

Exp

Sealed (mod)

Sat/sealed (mod)

Chemical shrinkage (mL/g cement)

Time (h)

Figure 5. Experimental results (data points) and model predictions (lines) 

for w/c = 0.3 T-1 cement. 

0

0.02

0.04

0.06

0.08

0.1

0.1 1 10 100 1000 104

Exp

Sat urated (mod)

Sat/sealed (mod)

Chemcial shrinkage (mL/g cement)

Time (h)

Figure 6. Experimental results (data points) and model predictions (lines) 

for w/s = 0.3 T-1P cement. 
 10 

3.2 Degree of hydration by LOI and SEM 

A simple way to measure the degree of hydration of portland-cement-only cement pastes is 

performed using loss on ignition (LOI). A mass difference is measured between a sample dried at 

100 o

C, and the same sample ignited at 1000 oC in an oven. The mass difference is attributed to 

chemically bound water loss. Knowing the relevant reactions, and the full amount of chemically 

bound water at 100 % hydration, allows one to extract a value of α, the degree of hydration, from 

the LOI measurement. The uncertainty in this measurement comes mainly from computing the 

full amount of chemically bound water at 100 % hydration and is estimated at 2 %. 

Measuring the degree of hydration of portland cement in the presence of a mineral admixture 

like fly ash is not an easy task. The amount of water loss at full hydration is not known, and the 

equations of reaction are not precise enough to be able to extract a value of α for the LOI 

measurements. In order to quantitatively compare to model results, however, a value of degree of 

hydration is needed. In addition, the CEMHYD3D model can give the extent of reaction of any 

phase present in the cement. So if the extent of reaction of the fly ash phase, along with the 

degree of hydration of the portland cement could be measured, it would provide a very sensitive 

check on model predictions, as well as providing the information needed to eventually be able to 

compare predictions for the formation factor. 

Therefore a SEM-based point counting technique was developed. Details, including estimates of 

uncertainty, can be found elsewhere [10]. The basic idea of the method is simple: to measure the 

amount of cement and fly ash left after a given time of hydration. Knowing how much should 

have been there before hydration started allows one to quantitatively calculate how much has 

been consumed. 

To test this technique, the degree of hydration of the plain portland cement paste (T-1) was 

determined by both the LOI measurement and the SEM-based point-counting technique. After 

this technique was validated, the degree of hydration of the cement in the blended cement pastes 

and the extent of reaction of the fly ash could then be estimated by the point-counting technique. 

The results for the fly ash system are shown in Table 3. The top portion of the table shows the 

comparison between LOI and point counting results for the plain cement. The lower half of the 

table shows the degree of hydration of the cement phase in the blended cement pastes, as 

measured by point counting, and the extent of reaction of the fly ash phase (actually more than 

one phase but treated as one phase in this measurement) measured the same way (Frac. Reacted 

FA means the volume fraction of the fly ash phase). In this case, the regression equations relating 

LOI and point counting results in the plain cement data were also used to convert the degree of 

hydration of the cement phase in the blended cement pastes to the equivalent LOI results. This 

converted LOI data will be used as the input for modeling. Further discussion of these results is 

found in [10]. We want to emphasize that the lower half of Table 3, containing the fly ash 

consumption results, is unique (and very useful) data, the collection of which was made possible 

by this project. 
 11 

Table 3. Degree of hydration for plain cement and fly ash blended cement system 

 T-1 w./c=0.4 T-1 w/c=0.5 

age α LOI α SEM α LOI α SEM 

3 d 0.5386 0.5218 0.5771 0.5521 

7 d 0.6000 0.5481 0.7083 0.6608 

14 d 0.6428 0.6286 0.7412 0.6992 

28 d 0.6684 0.6418 0.7708 0.7461 

60 d 0.6858 0.6870 0.7707 0.7723 

90 d 0.7156 0.6722 0.8015 0.7836 

 T-L w/s=0.4 T-L w/s=0.5 

age α cement α LOI equiv. Frac reacted FAα cementα LOI equiv.Frac. Reacted FA 

3 d 0.5594 0.5897 0.0347 0.5560 0.5952 0.0380 

7 d 0.6293 0.6535 0.0636 0.6559 0.6860 0.0741 

14 d 0.7289 0.7443 0.0723 0.7425 0.7648 0.0971 

28 d 0.7426 0.7568 0.1099 0.7750 0.7943 0.1431 

60 d 0.7628 0.7752 0.1532 0.8195 0.8348 0.1857 

90 d 0.7861 0.7964 0.2053 0.8400 0.8534 0.2416 

 

3.3 Pore solution press and conductivity measurement 

Concrete and cement paste are porous materials, with pores ranging from nanometer to 

millimeter sizes. The left over mixing water, which partially or fully saturates these pores, is full 

of ions from dissolved cement chemical species. In fact, it is very alkaline, with a pH of around 

13. Any diffusive transport of chloride ions through concrete must go through these pores. The 

composition of the ions already present in the pore fluid will greatly affect the speed at which the 

dissolved chlorides will diffuse through the pores. Therefore, as part of the model-building 

process, it is crucial that the actual composition of the ions in the pore fluid be measured so that 

the hydration and transport models can be properly calibrated. 

To get water out of a saturated sponge, one simply squeezes the sponge and the water oozes out. 

Cement paste is essentially a sponge, but with a much more rigid solid backbone and pores that 

are much smaller and less well-connected than in a typical sponge. So to squeeze out the pore 

fluid requires a pressure of over 690 MPa (100 000 psi), which can only be supplied by a 

mechanical loading machine [12]. A special jig is needed to hold and confine the cement paste 

under such high pressures. The setup for pore solution extraction is shown in Fig. 7. Samples 

made for the pore solution press were diameter 50 mm × height 100 mm cylinders. Samples were 

cast following the same procedures described in the previous section. After being cured for 

various ages, the samples were used for pore solution extraction. Figure 8 shows two such 

cylindrical samples after pore fluid extraction. Notice the shortened height, since the samples 
 12 

were axially compressed under very high load. The 7 d sample is shorter than the 28 d sample, 

because the 7 d sample has a lower stiffness and lower confined compressive strength. After 

extraction, the pore solutions were immediately diluted by deionized water and then analyzed by 

ion chromatography, shown in Fig. 9. 

Figure 7. Setup for the pore solution extraction 

Controls 

for 

mechanical 

loading 

machine 

Special 

sample jig 

Mechanical 

loading 

machine 

Receptacle

for pore 

solution 
 13 

Figure 8. Showing one cylinder before pore extraction, and two cylinders (7 d and 28 d) after 

pore fluid extraction. 

Before 7 d 28 d 

After 
 14 

Figure 9. Ion Chromatography system 

The test machine shown in Fig. 7 was not able to apply a high enough load to force the pore 

solution out at later ages, with a maximum load of only 440 kN, so a larger testing machine was 

used, with loads up to 1.5 MN. This higher load was successful in forcing out enough pore 

solution at later ages so that an ion chromatography measurement of the ionic concentrations in 

the pore solution could be made. 

Ion chromatography was used only to measure the [Na+

] and [K+] concentrations, along with the 

associated [OH-] concentration. To avoid carbonation problems, and to give enough fluid for an 

accurate measurement, the conductivity of artificial pore fluid, with the same [Na+

] and [K+] 

concentrations, was measured. Previous work had shown this to be an accurate method [13], so 

that only knowledge of the [Na+

] and [K+] concentrations, and corresponding [OH-] 

concentration, is enough to accurately predict the pore solution conductivity. The data in Table 4 

include the age of the cement paste at pore solution extraction, the [Na+

] and [K+] concentrations, 

and the conductivity of the pore fluid, σf. Note that these are sealed systems, so they tend to have 

higher ionic concentrations than saturated systems. Also note that the T-1P and T-L cements give 

similar results. 
 15 

Table 4. Conductivity and compositions of pore solutions for fly ash system 

 (ion concentrations are given in mol/L) 

T-1 w/c=0.5 T-1 w/c=0.4 

Age [Na] [K] C sol (S/m) Age [Na] [K] C sol (S/m)

3 d 0.0935 0.4048 10.35 3 d 0.1327 0.6306 15.09 

7 d 0.1112 0.4575 11.63 7 d 0.1588 0.7300 17.21 

14 d 0.1163 0.4873 12.26 14 d 0.1716 0.7410 17.59 

28 d 0.1198 0.4929 12.42 28 d 0.1918 0.7629 18.08 

56 d 0.1208 0.5203 12.94 56 d 0.1975 0.7838 18.7 

90 d 0.1242 0.5279 13.13 90 d 0.2094 0.7994 19.14 

T-1P w/s=0.5 T-1P w/s=0.4 

Age [Na] [K] C sol (S/m) Age [Na] [K] C sol (S/m)

3 d 0.0987 0.3445 9.29 3 d 0.1322 0.5003 12.76 

7 d 0.1129 0.3768 10.15 7 d 0.1318 0.5716 14.03 

14 d 0.1079 0.3527 9.61 14 d 0.1383 0.5868 14.41 

28 d 0.1211 0.3987 10.7 28 d 0.1406 0.5989 14.66 

60 d 0.1238 0.4163 11.08 60 d 0.1495 0.6427 15.56 

90 d 0.1266 0.4419 11.6 90 d 0.1549 0.6637 16.01 

T-L w/s=0.5 T-L w/s=0.4 

Age [Na] [K] C sol (S/m) Age [Na] [K] C sol (S/m)

3 d 0.0787 0.3136 8.35 3 d 0.1011 0.4307 10.97 

7 d 0.0874 0.3478 9.16 7 d 0.1347 0.4449 11.79 

14 d 0.0941 0.3526 9.37 14 d 0.1217 0.4618 11.88 

28 d 0.1057 0.3645 9.8 28 d 0.1255 0.4844 12.36 

56 d 0.1205 0.3961 10.64 56 d 0.1304 0.5263 13.2 

90 d 0.1234 0.4264 11.26 90 d 0.1355 0.5612 13.91 

The uncertainty in both ionic concentrations and measured conductivity is less than + 1 in the 

last digit. The main component of uncertainty lies in the actual pore fluid extraction process. The 

question is – are we getting the actual pore fluid that is in the interior of the specimen? Is the 

pore fluid that we collect the same as the pore fluid that was squeezed out of the sample? These 

are very real questions, and we have come to the conclusion that the pore fluid that we extract is 

not the same as the pore fluid that is in the specimen. Consider the plain cement pastes made 

with T-1 cement, no fly ash. Figures 10 and 11 show the concentration of potassium and sodium 

vs. time as measured by experiment, and as predicted by the CEMHYD3D (VCCTL) hydration 

model. More importantly, the curves marked “sealed” and “saturated” are theoretical estimates 

based on the known total amount of alkalis (sodium and potassium minerals) in the cement. The 

total amount of alkalis present, along with a calculation of the porosity present in the cement 

paste, give an upper bound estimate for the pore solution concentrations. “Saturated” means 

saturated curing, with the sample embedded in water that can supply the amount used up in 

hydration. “Sealed” means sealed curing, where the only water available to the hydrating cement 

is that mixed originally with the cement. Our samples underwent sealed curing, so these curves 

are the more appropriate for comparison with the experimental results. Note that in Fig. 10, both 
 16 

the [K+] and [Na+] ion concentrations are at or above the theoretical maxima for sealed curing. 

In Fig. 11, at a higher w/c value, the experimental values are slightly below the theoretical 

maxima. So the w/c = 0.4 values are definitely not trustworthy. After careful analysis, we 

reached the conclusion that the experiments were done properly, but the technique as performed 

in this study was inadequate, especially at lower w/c values where the amount of fluid collected 

is very small because of a combination of the stiffness of the sample and its lower porosity. 

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

T-1 0.4 w/c

K+ sat'd

K+ sealed

K+ exp

K+ mod

Na+ sat'd

Na+ sealed

Na+ exp

Na+ mod

Ionic concentrations, (mol/L)

Age, d

Figure 10: Concentration of [K+] and [Na+] ions vs. time for the T-1 cement, w/c = 0.4, using 

experimental measurements (exp), theoretical maximum estimates (saturated and sealed curing 

conditions), and direct predictions from the CEMHYD3D software (mod) for sealed curing 

conditions. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100

T-1 0.5 w/c

K+ sat'd

K+ sealed

K+ exp

K+ mod

Na+ sat'd

Na+ sealed

Na+ exp

Na+ mod

Ionic concentrations, (mol/L)

Age, d

Figure 11: Concentration of [K+] and [Na+] ions vs. time for the T-1 cement, w/c = 0.5, using 

experimental measurements (exp), theoretical maximum estimates (saturated and sealed curing 
 17 

conditions), and direct predictions from the CEMHYD3D software (mod) for sealed curing 

conditions. 

3.4 Bulk conductivity 

Samples for bulk conductivity measurements were diameter 37.5 mm × height 37.5 mm 

cylinders. Samples were cast following similar procedures as above. The reason for the sealed 

curing conditions was to protect the samples from ions leaching from the samples and changing 

the pore solution concentrations. We desired the pore solution samples and the bulk conductivity 

samples to have the same pore solution, and different leaching conditions for the two sets of 

samples would destroy this equality. Sealed curing conditions seemed like the only possible 

solution. Unfortunately, especially for the w/c = 0.4 samples, sealed curing created unsaturated 

conditions in the pore space, so that subsequent exposure to water will draw water into the pore 

space. Up to 25 % of the pore space can be unsaturated under these conditions. After being cured 

for various ages, samples were cut into thin slices approximately 3 mm to 4 mm thick. Three 

discs at the same age were cut from three different cylinders cast at the same time. The bulk 

conductivity of a paste at a given age was calculated as the average of the three discs. In order to 

reduce the loss of the pore solution during the cutting process, an alkali solution with 0.1 mol/L 

KOH and 0.05 mol/L NaOH was used instead of methanol as a cutting lubricant. Exposure to 

this solution will also change the pore solution by the drawing in of this solution into the pore 

space. After cutting, the specimens were washed by the same cutting solution and kept in a 

sealed plastic bag to keep in the moisture. The thickness was measured by using a digital caliper 

before the bulk conductivity measurement, taking at least eight readings around the diameter, 

and the average was used as the disc thickness. 

The bulk conductivity was measured by the divided-cell method (see Fig. 12). Two cells with 

different lengths were employed in the project. Both divided cell effective diameters were 25.4 

mm (1 in), and thus the specimen area tested was 5.0654 .

 10-4 m

2

. But before the cell could be 

used to measure bulk conductivity, the cell constant for each cell had to be measured. To 

measure the cell constant, two standard KCl solutions, at 0.1 mol/L and 0.01 mol/L 

concentration, were prepared. The conductivities of the two solutions were 12.8246 S/m and 

1.40823 S/m. The cells were filled with the solution and clamped together (without any sample 

in the middle), and connected to an impedance spectrometer to measure the true DC resistance 

(Fig. 13). The cell constant was calculated as follows: 

where L/A is the cell constant, in m-1, σ is the conductivity of the solution in the cell, in S/m, and 

R is the measured resistance, in ohms. The cell constant of the longer divided-cell was found to 

be 505.78 m-1, and a value of 317.976 m-1 was found for the shorter one used. 

Cement paste sample discs were clamped between the two cells. The cells then were filled with 

R

A

L =σ ×
 18 

0.1 mol/L KOH and 0.05 mol/L NaOH solutions, with a total conductivity of 3.414 S/m. The 

cell was connected to the impedance spectrometer, which was used to determine the true DC 

resistance of each disc. The bulk conductivity was calculated as follows: 

R b = R t ─ R 0

where L/A is the cell constant (m-1), σ0 = 3.414 S/m is the conductivity of the solution in the cell, 

R0 is the resistance of the solution-filled, which varies from cell to cell (Ω), Rt is the measured 

resistance from impedance spectroscopy (Ω), Rb is the resistance for the bulk cement paste (Ω), 

σb is the bulk conductivity of the cement paste (S/m), Lb is the thickness of the cement paste disc 

(m), and A is the effective specimen area tested (5.0654 . 10-4 m

2

 in the current study). Since 

sealed curing created unsaturated conditions in the pore space, the exposure to the ionic solution 

serving as electrodes in the divided cell apparatus will draw this fluid into the pore space. Up to 

25 % of the pore space can be unsaturated under these conditions, so up to this amount could 

have the conductivity of the divided cell apparatus solution. This will be taken into account in 

subsequent modeling predictions. The saturated curing, which was found to be necessary in order 

to avoid pore fluid leaching during curing, unfortunately complicated the actual pore fluid 

solution during bulk conductivity measurement. Some work was carried out to see whether or 

not the samples could all be independently saturated with a known ionic solution, but this was 

found to be impractical – it took too long and was unreliable. 

If the measured pore solution conductivity was a reliable indication of the pore solution actually 

present inside the sample, the formation factor for each cement paste disc would be calculated by 

dividing the conductivity of pore solution by the bulk conductivity: 

where F = formation factor, σb = conductivity of the bulk cement paste in S/m, and σp = pore 

solution conductivity in S/m. 

0

0

100

σ

 × 

 





= A

L

R

R A

L

b

b

b

×

σ =

b

p F

σ

σ

=
 19 

We limit ourselves to bulk conductivity measurements. Table 5 contains all the experimental 

data, averaged over three samples each, for the bulk conductivity of the T-1 and T-L systems. 

Based on the findings that the T-1P system was not much different from the T-L system, except 

for finer particle size, we only carried out conductivity measurements on the T-L and T-1 

systems. 

Table 5: Bulk conductivity, σb , for T-1 and T-L systems 

T-1 w/c = 0.4 T-1 w/c = 0.5 

age σb (S/m) Age σb (S/m)

3 d 0.1404 3 d 0.2239 

7 d 0.1195 7 d 0.1537 

14 d 0.1150 14 d 0.1402 

28 d 0.0955 28 d 0.1274 

60 d 0.0895 60 d 0.1307 

90 d 0.0770 90 d 0.0923 

T-L w/s = 0.4 T-L w/s = 0.5 

age σb (S/m) Age σb (S/m)

3 d 0.2514 3 d 0.2916 

7 d 0.1500 7 d 0.2604 

14 d 0.1367 14 d 0.2296 

28 d 0.1110 28 d 0.1814 

60 d 0.0732 60 d 0.1231 

90 d 0.0564 90 d 0.0759 
 20 

Figure 12. Divided-cell apparatus used for the bulk conductivity measurement. 

Figure 13. Setup for the bulk conductivity measurement (impedance spectrometer) 

4 Modeling 

4.1 Three dimensional microstructures for cement clinkers

The T-1, T1-P, and fly ash were analyzed using scanning electron microscope (SEM) techniques 
 21 

that NIST has developed [14]. These techniques go beyond simple particle size distribution 

measurements, by showing how the different chemical phases of cement are distributed among 

the different size particles. To prepare a polished specimen for viewing in the SEM, 

approximately 25 g of the powder to be imaged is blended with an epoxy resin to form an 

extremely viscous paste. The resin/powder mixture is pressed into a small cylindrical mold and 

cured at 60 °C for 24 h. The cured specimen is then cut and polished to obtain a plane surface for 

imaging. The composite X-ray images for the various materials are shown in Figs. 14 and 15. 

These images will be used in generating 3-D microstructures and model predictions for cement 

properties in later research. 

Figure 14. Processed image of the T-1 cement (500X- 256 μm by 200 μm). Red is C3S, aqua is 

C2S, green is C3A, yellow is C4AF, and pale green is gypsum (the main minerals found in 

portland cement). 
 22 

Figure 15. Processed image of the T-1P blended cement (500X - 256 μm by 200 μm). Red is 

C3S, aqua is C2S, green is C3A, yellow is C4AF, and pale green is gypsum (the main minerals in 

portland cement). The orange particles are fly ash, although some of the orange particles are not 

particularly round, as is usual for fly ash, which may be a result of the intergrinding process. 

White is free lime, dark green is silica, and dark blue is calcium aluminosilicate. 

4.2 Degree of hydration and fly ash reaction modeling 

 

The cement and particle size distribution (PSD) files in the prediction of degree of hydration can 

be reached at the following files in VCCTL Version 2: 

Cement Cement file Particle 

microstructure file 

T-1 w/c=0.4 T1h040b Pt1h040a.img 

T-1 w/c=0.5 T1h050b T1h050.psd 

T-L w/s=0.4 T1hfa040c Pt1hfa040.img 

T-L w/s=0.5 T1hfa050c Pt1hfa050.img 

The cement hydration model works via cycles of dissolution, diffusion, and reaction – see Ref. 

[1] for more details. The number of model cycles is related, nonlinearly, to the actual time of 

reaction. 
 23 

Table 6: Age, number of model cycles, and model degrees of hydration for T-1 cements. The 

number of model cycles were chosen so as to closely match the experimentally determined 

degree of hydration. 

w/c=0.4 Cycles α (model) 

3 388 0.539 

7 529 0.6 

14 770 0.643 

28 1042 0.668 

60 1370 0.686 

90 2347 0.716 

w/c=0.5 Cycles α (model) 

3 354 0.5771 

7 604 0.7083 

14 711 0.7412 

28 839 0.7708 

60 839 0.7707 

For orientation purposes, Table 6 shows the amount of model hydration cycles needed to achieve 

a certain level of cement hydration in the T-1 plain cement system. The point of this project was 

to be able to extend this model into fly-ash blended cements. For that reason, the following 

figures, as well as Table 7, show the degree of hydration vs. time, both model and experiment, 

for the cement in the fly ash systems, as well as the fraction reacted of the fly ash vs. the cement 

degree of hydration for the same systems. This experimental data for the fly ash system is 

unique. By checking against it, we found that the model was definitely overreacting fly ash 

phases – at a given degree of cement hydration, the model had much too large of an extent of 

reaction of the fly ash phases compared to experiment. The scientific details of what was done to 

improve the model and make it more realistic (reaction theory, etc.) are to be found elsewhere 

[15]. In the following graphs, which display results of the corrected model, one sees both the 

reasonably good fit of model vs. experiment for the degree of hydration of the cement vs. time, 

which we had before, and the extent of reaction of the fly ash vs. the degree of hydration of the 

cement phase, which is now much improved from earlier work. There is not perfect agreement 

between model and experiment, but one must remember that the uncertainty in the experimental 

data points is about + 0.04 (absolute), so that there is approximate agreement within 

experimental uncertainty. Having good agreement with both the degree of hydration of the 

cement simultaneously with the extent of reaction of the mineral admixture means that the model 

is more likely producing an accurate blended cement paste microstructure. 

 
 24 -0.2 0 0.2 0.4 0.6 0.8 1

0.1 1 10 100

w/c=0.4 Mod

w/c=0.4 Exp

Degree of hydration

Log(time), d

Figure 16. Degree of hydration of the cement in T-L, w/s=0.4 0 0.2 0.4 0.6 0.8 1

0.1 1 10 100

w/c=0.5 Mod

w/c=0.5 Exp

Degree of hydration

Log(time), d

Figure 17. Degree of hydration of the cement phase in T-L, w/s=0.5 
 25 

0

0.05

0.1

0.15

0.2

0.25

0.55 0.6 0.65 0.7 0.75 0.8

T-L w/s = 0.4

Exp Model

Fraction Reacted Fly Ash

Degree of cement hydration

Figure 18. Fraction reacted of the fly ash phase in T-L, w/s = 0.4 

0

0.05

0.1

0.15

0.2

0.25

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

T-L w/s = 0.5

Exp

Mod

Fraction Reacted Fly Ash

Degree of cement hydration

Figure 19. Fraction reacted of the fly ash phase in T-L, w/s=0.5 

 
 26 

Table 7: Age, number of model cycles, and model degrees of cement hydration and fraction 

reacted of fly ash for T-L cements. The number of model cycles was chosen so as to closely 

match the experimentally determined degree of hydration. 

w/c=0.4 Cycles α (model) 

Fraction Reacted 

(exp) 

Fraction Reacted 

(model) 

3 398 0.5897 0.0347 0.0346 

7 519 0.6535 0.0636 0.05101 

14 926 0.7443 0.0723 0.11007 

28 1046 0.7568 0.1099 0.1179 

60 1272 0.7752 0.1532 0.1303 

90 1663 0.7964 0.2053 0.1443 

w/c=0.5 Cycles α (model) 

Fraction Reacted 

(exp) 

Fraction Reacted 

(model) 

3 386 0.5952 0.038 0.035 

7 556 0.686 0.0741 0.0492 

14 812 0.7648 0.0971 0.0856 

28 955 0.7943 0.1431 0.1134 

60 1230 0.8348 0.1857 0.1564 

90 1397 0.8534 0.2416 0.1751 

4.3 Conductivity modeling 

 

4.3.1 Determination of the conductivity of regular CSH for 

 T-1 and T-L cements

A relative conductivity for regular C-S-H of 0.005 provides the best fit to the experimental data, 

for the T-1 cement, in the absence of fly ash. This was determined by running the conductivity 

code, for a range of cement paste microstructures, with different conductivity values for the C-SH phase. It was scaled so that the pore solution conductivity in the capillary pores was 1. The 

uncertainty in the conductivity value for the C-S-H phase is probably of the order of 100 %, as 

its value can vary widely without changing the predicted bulk conductivity that much for w/c = 

0.4 and w/c = 0.5 cement pastes. This same value of 0.005 was found to hold, within a similarly 

large uncertainty, for the pozzolanic C-S-H that was formed from reaction of the silica in fly ash 

with the calcium hydroxide phase in the cement paste. 

4.3.2 Results of conductivity modeling for T-1 

A fitted value of relative conductivity (relative to the pore solution) for the regular C-S-H that 

comes from cement hydration is enough to proceed to compute values of the bulk conductivity 

for the plain (T-1) cement pastes and compare them to experimental data. Table 8 shows the 

modeling results for the bulk conductivity for the T-1 cement systems. There is reasonably good 
 27 

agreement, within uncertainty, between experiment and model results. Note that model computes 

the cement paste conductivity relative to the pore solution having a conductivity of unity. A 

separate part of CEMHYD3D computes the principal ionic concentrations ([K+], [Na+], and 

[OH-]), from which a prediction of pore solution conductivity, σp, is made [13]. Then, following 

the equation for F, the formation factor, one gets the bulk conductivity by σb = (1/F) σp. 

0

0.05

0.1

0.15

0.2

0.5 0.55 0.6 0.65 0.7 0.75

T-1 w/c = 0.4

Exp

Model

Conductivity, (S/m)

Degree of cement hydration

Figure 20. The experimental and modeling values of the bulk conductivity found for the T-1 

w/c = 0.4 cement pastes. 

0

0.1

0.2

0.3

0.4

0.5

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

T-1 w/c = 0.5

Exp

Model

Conductivity, (S/m)

Degree of cement hydration

Figure 21. The experimental and modeling values of the bulk conductivity found for the T-1 

w/c = 0.5 cement pastes. 
 28 

Table 8: Bulk conductivity data, experiment and model, for T-1 cement. The uncertainty in the 

bulk conductivity is about + 1 in the least significant figure. The uncertainty in the model data is 

larger, about 10 % of the total value. 

Degree of 

cement 

hydration 

Bulk 

conductivity – 

exp 

Bulk 

conductivity – 

model 

T-1 w/c = 0.4 

0.539 0.1404 0.187 

0.600 0.1195 0.117 

0.643 0.1150 0.0858 

0.668 0.09550 0.0719 

0.686 0.08950 0.0681 

0.716 0.07700 0.0533 

T-1 w/c = 0.5 

0.577 0.2239 0.396 

0.708 0.1537 0.177 

0.741 0.1402 0.142 

0.771 0.1274 0.122 

0.771 0.1307 0.122 

0.802 0.09230 0.102 

4.3.3 Results of conductivity modeling for T-L 

Table 9 shows the modeling results for the bulk conductivity for the T-L cement/fly ash systems. 

Note that model computes the cement paste conductivity relative to the pore solution having a 

conductivity of unity. A separate part of CEMHYD3D computes the principal ionic 

concentrations ([K+], [Na+], and [OH-]), from which a prediction of pore solution conductivity, 

σp, is made [13]. Then, following the equation for F, the formation factor, one gets the bulk 

conductivity by σb = (1/F) σp. Conductivities were only computed when the predicted value of 

fly ash reaction was within 25 % of the experimental measurement, which explains some of the 

missing data points in the third column of Table 9. Figures 22 and 23 display the same 

information graphically. There is rough agreement between experiment and model results, 

although probably not within uncertainty. It is difficult to tell what the model uncertainties are, 

although they have been estimated at 10 %. 
 29 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.55 0.6 0.65 0.7 0.75 0.8

T-L w/s = 0.4

Exp

Mod

Conductivity, (S/m)

Degree of cement hydration

Figure 22. The experimental and modeling values of the bulk conductivity found for the T-L 

w/s = 0.4 cement pastes. 

0

0.1

0.2

0.3

0.4

0.5

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

T-L w/s = 0.5

Exp

Model

Conductivity, (S/m)

Degree of cement hydration

Figure 23. The experimental and modeling values of the bulk conductivity found for the T-L 

w/s = 0.5 cement pastes. 
 30 

Table 9: Bulk conductivity data, experiment and model, for T-L cement 

Degree of 

cement 

hydration 

Bulk 

conductivity - 

exp 

Bulk 

conductivity – 

model 

T-L w/s = 0.4 

0.590 0.2514 0.239 

0.654 0.1500 0.149 

0.744 0.1367 

0.757 0.1110 0.0470 

0.775 0.07320 0.0393 

0.796 0.05640 

T-L w/s = 0.5 

0.595 0.2916 0.487 

0.686 0.2604 

0.765 0.2296 0.197 

0.794 0.1814 0.152 

0.835 0.1231 0.0982 

0.853 0.07590 

5 Conclusions 

This project was designed to systematically incorporate a fly ash into the CEMHYD3D model 

and therefore into the VCCTL software. This would be a start to allowing cement manufacturers, 

and others, to virtually see how this waste-stream material affects the properties of concrete 

made with this material. The complex chemistry of these materials necessitated a unique 

experimental approach to be able to so incorporate them. Because of this project, which involved 

novel work never done before for these materials, we ended up with: (1) a new SEM-based point 

counting technique for measuring how fly ash (and other materials like slag), and cement in their 

presence, reacted over time; (2) a unique data set of individual phase reactions vs. time that can 

be used to check model refinements for a particular fly ash and cement; (3) greatly improved 

models of how these materials reacted with water and cement over time; (4) bulk conductivities 

vs. degree of hydration and fly ash reaction extent for cement pastes that included these 

materials, and (5) model predictions in reasonable agreement with experiment for cement pastes 

that included one kind of fly ash material. 

The uncertainties found in the experimental measurements certainly propagate into the model 

results in the formation factor work, as the experimental formation factors were used to calibrate 

the conductivity assigned to the regular C-S-H and the extra C-S-H formed from the mineral 
 31 

admixture. This calibration is only necessary because we do not have a nano-scale model for the 

actual nano-pore structure and nano-adsorption qualities of C-S-H, from which we could 

accurately predict the conductivity. 

However, the improved models give us a useful tool with which to address hydration up to 90 d. 

The reactions of the fly ash were only measured up to 90 d. The formation factors of the blended 

cements were not that much different from the plain cement pastes. It is possible that the mineral 

admixtures go on reacting strongly after 90 d, so that the formation factor of the blended cement 

pastes would eventually be much larger than that of the plain cement pastes. This would be 

useful data to collect. 

Doing the experimental work necessary to properly characterize one fly ash material showed us 

how much improved characterization techniques are necessary to be able to handle the many 

kinds of cement/fly ash in use in the United States today. This will be the focus of future 

research. 

6 Acknowledgements 

We would like to thank the EPA for partial support of this project, and specifically the direction 

of Heather Tansey and Vincent Camobreco of the EPA. We would also like to thank Dr. Clarissa 

Ferraris and Dr. Arnold Rosenberg, of NIST, for useful comments on the manuscript. 

7 References 

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 32 

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