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NIST Technical Note 1405

Computational Materials Science of

Cement-Based Materials: An Education Module

Dale P. Bentz, Edward J. Garboczi, and R. Tate Coverdale

—QC100

,U5753

#1405

1993

'•\-r
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NIST Technical Note 1405

Computational Materials Science of

Cement-Based Materials: An Education Module

Dale P. Bentz, Edward J. Garboczi, and R. Tate Coverdale *

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

* Northwestern University, Evanston, IL

August 1 993

^f^TES o* ^

9"

U.S. Department of Commerce

Ronald H. Brown, Secretary

Technology Administration

Mary L Good, Under Secretary for Technology

National Institute of Standards and Technology

AratI Prabhakar, Director
National Institute of Standards

and Technology

Technical Note 1405

Natl. Inst. Stand. Technol.

Tech. Note 1405

43 pages (Aug. 1993)

CODEN: NTNOEF

U.S. Government Printing Office

Washington: 1993

For sale by the Superintendent

of Documents

U.S. Government Printing Office

Washington, DC 20402
ABSTRACT

An education module demonstrating the principles of computational materials science has

been developed. The module consists of: software that executes on a personal computer, and

this NIST Technical Note, which provides documentation and instructions for using the computer

software. The computer programs are available for both DOS-compatible PC and Macintosh

computing environments. Four separate computer programs illustrate the development of

microstructure during cement hydration, mercury intrusion porosimetry, percolation of

overlapping ellipses and rectangles as a function of aspect ratio, and percolation of nonoverlapping hard cores each encompassed by a soft overlapping shell. All of the programs

operate on two-dimensional microstructures due to the space and time limitations imposed by

a personal computer environment. The computer software is interactive and highly graphicsoriented. To date a preliminary version of the computer module has been utilized in a variety

of undergraduate and graduate level civil engineering classes. Feedback from faculty and

students has been used to revise and enhance the capabilities of the computer programs.

Ill

TABLE OF CONTENTS

ABSTRACT iii

LIST OF FIGURES vii

LIST OF TABLES vii

1. INTRODUCTION 1

2. INTRODUCTION TO COMPUTATIONAL MATERIALS SCIENCE OF CEMENTBASED MATERIALS 2

3. COMPUTER PROGRAM DESCRIPTIONS AND SAMPLE EXERCISES 3

3.1 Simulation of Interfacial Zone Microstructure 3

3.1.1 Introduction 3

3.1.2 Hydration Model Description 3

3.1.3 Interfacial Zone Simulation 4

3.1.4 Use of mineral admixtures 5

3.1.5 Use of lightweight absorptive aggregate 5

3.1.6 Use of cement clinker as aggregate 5

3.1.7 Exercise #1- Interfacial Zone Microstructural Development

Exercise 5

3.1.7. 1 Description of Main Menu Options for HYDRA2D.EXE . 6

3.1.7.2 Exercise la: Effect of Cement Particle Size 9

3.1.7.3 Exercise lb: Effect of Mineral Admixture Particle Size . . 10

3.1.7.4 Exercise Ic: Effect of Aggregate Characteristics 12

3.2 Percolation Theory 14

3.2.1 Introduction 14

3.2.2 Exercise #2- Continuum Percolation Exercise 16

3.2.3 Exercise #3- Hard Core/ Soft Shell Percolation Exercise 20

3.3 Simulation of Mercury Porosimetry in 2-D 23

3.3.1 Introduction 23

3.3.2 Exercise #4- Mercury Porosimetry Exercise 24

4. FEEDBACK FROM USERS 25

5. REFERENCES 27

6. APPENDIX A- GUIDE TO USE OF EDUCATION MODULE ON MACINTOSH . 29

6.Description of HYDRA2D on Macintosh 29

6.2 Description of PERSHAPE on Macintosh 31

6.3 Description of PERSHELL on Macintosh 32

6.4 Description of MERCURY on Macintosh 33
TABLE OF CONTENTS (continued)

7. APPENDIX B- SURVEY ON USE OF EDUCATION MODULE 36

VI
LIST OF FIGURES

Figure 1. Examples of Ellipse Continuum Percolation 18

Figure 2. Schematic of Hard Core/Soft Shell Model 21

Figure 3. Examples of Hard Core/Soft Shell Percolation 22

Figure 4. Effect of Line Length on Pore Size 24

LIST OF TABLES

Table la. Parameters for Hydration Model 10

Table lb. Cement and Mineral Admixture Required 12

Table Ic. Cement Particle and Aggregate Characteristics 14

Table 2. Ellipse and Rectangle Area in Pixels for Various Aspect Ratios 19

Table 3. Hard Core (2b) and Total (2a) Particle Diameters 21

Vll

1. INTRODUCTION

Under the auspices of the National Science Foundation Science and Technology Center

for Advanced Cement-Based Materials (ACBM), an education module has been developed to demonstrate the principles of computational materials science applied to cement-based materials.

Based on computer exercises originally developed for the computer modelling workshop,

supported by ACBM, that has been held annually since 1990 in the Building Materials Division

at the National Institute of Standards and Technology (NIST), the module consists of this

documentation and computer software covering the topics of microstructure development during

cement hydration, simulation of mercury intrusion porosimetry, and the application of

percolation theory to material microstructure. The computer software is PC-based, interactive,

and highly graphics-oriented. Both DOS and Macintosh-compatible versions of the programs

have been completed and are available for distribution. To date, portions of the module have

been incorporated into a number of undergraduate and graduate-level classes in civil engineering

and materials science departments at several universities throughout the United States. The goal

of the module is to demonstrate how microstructure can be simulated, quantified, and its relationship to properties analyzed, so that students will obtain a greater appreciation of cementbased materials as systems whose properties can be engineered.

This NIST Technical Note provides the documentation necessary for using the

ACBM/NIST Education Module. Following a brief introduction to the computational materials

science of cement-based materials, background information and detailed example computer

exercise descriptions are provided for each technical area covered by the module. Feedback on

the use of the models in the classroom environment is presented and separate appendices detail

the usage of the programs on a Macintosh-based system and provide a sample feedback survey

form.

The DOS compatible versions of the software require a personal computer with EGA or higher graphics. An 80386 or faster processor-based machine is recommended for executing the

programs; an 80286-based machine is adequate but somewhat slow. The computer programs

and executable files are available for distribution via the NIST Cementitious Materials Modelling

Laboratory (CMML). Individuals interested in obtaining copies of the distribution diskette may

contact:

Mr. Dale P. Bentz

Building 226 Room B-348

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

(301) 975-5865

E-mail: bentz@enh.nist.gov
2. INTRODUCTION TO COMPUTATIONAL MATERIALS SCIENCE OF CEMENTBASED MATERIALS

Cement-based materials exhibit very complex structures over many length scales. For

example, concrete is a composite material, containing rocks and sand (coarse and fine

aggregates) as inclusions in a cement paste matrix. The effective properties of this composite

material are complicated, even if we consider the cement paste matrix to be a simple,

homogeneous material. Coarse aggregate size is on the order of 1 to 20 millimeters, while the

fine aggregate size typically ranges from 0.2 to 2.0 millimeters. Thus the aggregates alone span

two orders of magnitude in size.

Now consider the cement paste matrix. It is not a simple, homogeneous material.

Instead, cement paste is formed from an original watericement particle mixture, which forms

a dense suspension with complex viscoelastic properties. The cement particles cover a size

range of about 0.001 to 0.1 millimeters, and each particle is itself a complex agglomeration of

several different calcium, silicate, aluminate, ferrite, and sulfate phases. When the cement

particles are suspended in water, hydration reactions begin, forming both crystalline and

amorphous reaction products that fill in the pore space and eventually change the viscoelastic

suspension into a rigid solid. When hydration is essentially complete, pores exist on length

scales ranging from 10"^ millimeters (1 nm) in one of the amorphous reactants, up to 0.0001-

0.01 millimeters in the capillary pore space. Therefore, the important length scales in concrete

range from about 10'^ millimeters up to about 20 millimeters—7 orders of magnitude!

The fundamental idea of materials science is the triad of processing, microstructure, and

properties, and their interrelationships. For a given material, experimental and theoretical

understanding of this triad is necessary in order to have true control of the material and its properties. The complexity of cement-based materials rule out much hope of using analytical

methods to achieve theoretical understanding of, say, microstructure-property relationships. This

forces us to consider how computational materials science techniques can be used.

In the context of cement-based materials, computational materials science means: 1)

using a computer to build, via computer simulation, a numerical microstructure that is realistically based on individual cement particles and their hydration products, and 2) operating on the completed microstructure with various algorithms to exactly compute, within numerical

precision, the physical properties of interest (electrical conductivity, elastic moduli, fluid

permeability, etc.). The computed properties are then compared to experimental results. Agreement leads to new understanding of microstructure-property relationships, since the

numerical microstructure model is available for analysis. Disagreement leads to refinement of

the microstructure model, to try to find where it does not agree with real microstructures.

For such an approach, some general unifying ideas for random systems are extremely

important. For example, the ideas of percolation theory have proven to be extremely useful in describing and understanding microstructural development and microstructure-property
relationships in cement-based materials [1,2].

In light of the above discussion, the computer exercises that will be described below

cover both microstructure models and percolation theory. In addition, there is one simple

application exercise that performs a computation on a given microstructure. Most of the

algorithms that compute properties require very fast workstations or supercomputers to execute

in a reasonable amount of time. As these exercises have been designed to be executed on

microcomputers, the simulation exercises have been scaled down in order to run more quickly.

There are four exercises described in this module, which have been adapted from the exercises

used at the 3rd ACBM/NIST Computer Modelling Workshop held in 1992.

3. COMPUTER PROGRAM DESCRIPTIONS AND SAMPLE EXERCISES

3.1 Simulation of Interfacial Zone Microstructure

3.1.1 Introduction

As a composite material, concrete's performance can be expected to depend on the

properties of the interfaces between its two major components, aggregate and cement paste. The

general consensus is that the interfacial zone is a region, up to 50 /xm wide around each

aggregate, containing more porosity and larger pores than the bulk cement paste, and often

containing large calcium hydroxide crystals. Due to these features, the interfacial zone is often

considered to be the weak link in concrete with respect to mechanical performance and

durability.

In this exercise, a digital-image-based cement microstructural model is applied to simulate

interfacial zone microstructural development. Reasons for the differences between interfacial zone and bulk paste microstructure and methods for improving the structure of this weak link

will be explored.

3.1.2 Hydration Model Description

Detailed descriptions of the NIST digital-image-based cement hydration model are

available [3,4]. In the model, two-dimensional (2-D) area or three-dimensional (3-D) volume

is represented by a set of pixels each identified as a particular phase of concrete. For this

exercise, relevant phases are anhydrous cement (assumed to be pure tricalcium silicate- C3S),

calcium hydroxide (CH), calcium silicate hydrate (C-S-H), porosity, aggregate, and mineral

admixtures. Thus a cement particle is represented as a collection of contiguous pixels assigned

to be C3S. In this manner, real cement particle shapes may be utilized, as well as circles and

spheres, in generating simulated cement microstructures.

Hydration is simulated by operating on all the pixels present in the cement paste volume

or area. The two reactions considered are the hydration of C3S to form CH and C-S-H and the
pozzolanic reaction between CH and silica (found in silica fume or fly ash) to form secondary

or pozzolanic C-S-H. The assumed reaction stoichiometrics are as follows:

C^S + 5 .3H - Cx .iSH, .0 + 1.2CH

s + 1. ICH + 2. 3H q,.l^^i.O

In terms of volumes or areas, each unit of dissolved C3S produces 1.7 units of C-S-H and 0.61

units of CH. Regarding the pozzolanic reaction, each unit volume of silica is capable of reacting

with 2.08 units of CH to produce 4.6 units of pozzolanic C-S-H. The value 2.08, corresponding

to the number of volume units of CH which may be consumed by one volume unit of silica

fume, is called the pozzolanic reactivity factor throughout this exercise.

Hydration is executed in discrete cycles consisting of dissolution, diffusion, and reaction

phases. During dissolution, all C3S pixels in contact with water-filled porosity are given a chance to dissolve and produce diffusing CH and C-S-H species. The dissolution probability is based on the amount of C3S surface in contact with water. During diffusion, the C-S-H and CH

diffusing species execute random walks within the available pore space until reaction occurs. C-S-H forms on the surfaces of the original cement particles or on previously formed solid

C-S-H. CH forms crystals by a nucleation and growth mechanism within the pore space.

Additionally, if amorphous silica is present, the CH diffusing species react at silica surfaces to form pozzolanic C-S-H. When all diffusing species generated from one dissolution have reacted, a hydration cycle is complete and a new dissolution is begun. By monitoring how much cement

remains after any number of hydration cycles, the degree of hydration, a, of the system can be

determined. As in real systems, the hydration is ultimately self-limiting as the surfaces of the

remaining cement become totally surrounded by hydration products, preventing further

dissolution. However, typically 80-90% hydration can be achieved before this situation occurs.

3.1.3 Interfacial Zone Simulation

There are two basic mechanisms that have been found to underlie interfacial zone

formation [5]. Bleeding may also contribute, but we are ignoring this gross effect in the model

presented here. The two mechanisms are the wall effect and the one-sided growth effect.

The wall effect is a packing effect. An aggregate surface acts as a wall, against which

the packing of cement particles is inefficient, and results in an originally high porosity, low

cement region around each aggregate. The one-sided growth effect is different. Consider a

small volume of space in the bulk cement paste. On the average, hydration products are growing into this region from all directions. Now consider the region close to an aggregate

surface. Growth only occurs from the cement paste side, not the aggregate side, which will also

contribute to a higher porosity in this region. The wall effect is the more important effect, but

the one-sided growth effect also contributes. To simulate an interfacial zone in concrete, a

single aggregate is first placed in the hydration volume (area) and then the cement particles are randomly placed such that no particles overlap one another or the aggregate. The hydration

algorithm is then executed as described previously.
3.1.4 Use of mineral admixtures

The microstructural model allows for both the size and reactivity of mineral admixtures

such as silica fume and fly ash to be varied [6]. Since in the model, a pixel is typically 1 fim on a side, well dispersed silica fume can be represented by small particles one pixel in size.

Conversely, fly ash or agglomerated silica fume is "large," and is assigned the same size as cement particles. Pozzolanic activity is varied by specifying a pozzolanic reactivity factor,

corresponding to how many units of CH each unit of mineral admixture may consume via the

pozzolanic reaction. According to the reaction given earlier, pure silica would be able to consume 2.08 units of CH. Fly ash must be assigned a lower reactivity as it is typically only

about 50% silica. Thus 1 .04 might be a reasonable maximum activity to be expected for fly ash,

while 0.47 appears to be a more likely value to be achieved in practice [7].

3.1.5 Use of lightweight absorptive aggregate

Recently, Zhang and Gjorv [8] have characterized the microstructure of the interfacial zone in lightweight concrete as being more dense and homogeneous than that found in normal

weight concrete. One possible reason for this observation is the rearrangement of the cement

particles in the vicinity of an aggregate due to water absorption by the aggregate. To simulate a lightweight absorptive aggregate using the model, the original distribution of cement particles

around the aggregate may be modified by moving all particles toward the aggregate surface to simulate water absorption by the (dry) aggregate. This results in the aggregate acting somewhat

as a filter, drawing in water and pulling cement particles towards its surface [9].

3.1.6 Use of cement clinker as aggregate

Berger [10] has investigated the use of cement clinker aggregate in concrete. He

attributed the increased strengths of these systems to an improved cement paste-aggregate bond.

More recently, Yang et al. have experimentally addressed the issue of engineering an optimum

aggregate for concrete, consisting of an inert core and a reactive surface layer [11]. To model

cement clinker aggregate, the aggregate is assigned a phase identifier of C3S so that it is eligible

for dissolution and reaction just like the smaller cement particles. Due to its small surface-tovolume ratio, only a thin layer on the outer surface of the clinker aggregate will undergo

significant hydration.

3.1.7 Exercise #1- Interfacial Zone Microstructural Development Exercise

Program: HYDRA2D.EXE

In this exercise, the goal is to examine development of microstructure in the interfacial zone as a function of cement particle size, or presence of mineral admixtures, or aggregate

characteristics. Please feel free to investigate your own variations as time permits.

The program, HYDRA2D.EXE, is included on the distribution diskette. Simply switch
to the appropriate disk drive and type HYDRA2D at the DOS prompt to begin execution. The

program is menu-driven and uses a square unit cell that is 200*200 pixels in dimension.

Periodic boundaries are used for both particle placement and subsequent hydration. This means

that if a portion of a cement particle extends beyond the 2-D box boundaries, the extending piece

is "wrapped around" to the other side of the box. As the diffusing species move at random

throughout the pore space, they may exit one side of the box and enter into the opposite side.

Periodic boundaries help to eliminate artificial edge effects typically present in a small scale

model.

The color code for the model on the PC is as follows:

C3S - red

C-S-H - light yellow

CH - light cyan

Inert filler - dark grey

Reactive (pozzolanic) filler - dark yellow

Pozzolanic C-S-H - dark yellow

Inert Aggregate - magenta

Reactive Aggregate - light blue

Diffusing CH - cyan

Diffusing C-S-H - green.

The colors for the non-diffusing phases are also indicated by color bars placed on the left side

of the PC monitor screen during hydration and measurement of phase fractions.

3.1.7.1 Description of Main Menu Options for HYDRA2D.EXE

While explicit instructions for using HYDRA2D for each of the exercises are provided

below, this section describes the functionality of each of the main menu options. This

information will be useful for individuals who want to explore their own variations of the

exercises or other topics using the HYDRA2D program. The main menu options are:

0) Exit the program

1) Add cement particles or large fillers 2) Add an aggregate particle

3) Add an inert or reactive filler 4) Run the hydration model

5) Measure phase fractions

6) Measure phase fractions as a function of distance from aggregate surface

7) Move all cement particles towards aggregate surface (absorption)

8) Reset system by clearing microstructure

0) Exit the program

This option simply exits the HYDRA2D program and returns the user to DOS. The last microstructure generated will appear on the screen and the user may press any key to exit to DOS.
1) Add cement particles or large fillers

This option allows the user to add cement particles or filler particles to the starting

microstructure. If the user wishes to add filler particles which are one pixel in size, menu

option 3 should be used. The user will be prompted to enter the number, size (diameter), and

phase (cement, inert, or reactive filler) of the particles to be placed in the microstructure. If reactive filler particles are selected, the user must also specify the pozzolanic reactivity factor

to be user for the pozzolanic reaction between the filler and calcium hydroxide. If an aggregate

is to be added to the microstructure, it should be placed before any cement or filler particles are

placed. Additionally, when multiple size cement and filler particles are desired, they should be

added in order of largest to smallest. (If the smaller particles are placed at random first, there

may not be any spaces remaining that are large enough for the random location of the larger

particles). There is a limit of 999 total particles which may be added using this menu

selection. The program will advise the user of this limit if any attempts are made to exceed it.

2) Add an aggregate particle

This option allows the user to add a flat plate aggregate to the center of the twodimensional microstructure. The user must specify the half thickness of the aggregate and the

phase to be assigned to the aggregate (inert or reactive). The aggregate extends throughout the

height of the two-dimensional system. If an aggregate is desired, it should be added before any

of the cement or filler particles.

3) Add an inert or reactive filler

This option allows the user to add one-pixel filler particles to the microstructure. The

user must specify the type (inert or reactive) of filler to be added and the number of filler particles to add. Additionally, if a reactive filler is selected, the user must specify the

pozzolanic reacUvity factor to be used for the filler. The one-pixel filler particles should

generally be added after all of the cement and large filler particles have been added to the

microstructure.

4) Run the hydration model

This option allows the user to execute the cement hydration model. The user will be

prompted as to whether they wish to execute a specific number of hydration cycles or hydrate

the system to a specific degree of hydration. In the former case, the user must supply the

number of hydration cycles to execute, while in the latter, the desired degree of hydration (e.g.,

0. 1-0.9) must be specified. It should be noted that the degree of hydration is calculated with

respect to the cement present in the microstructure when menu item #4 is selected (and not

necessarily the amount of cement present in the initial microstructure, i.e., if some

hydration has already been executed). The user must also provide three parameters for the

hydration process: 1) the maximum number of diffusion steps to be taken in any one cycle

before all product pixels spontaneously nucleate into solid hydration product, 2) an exponential

7
prefactor for the nucleation probability for calcium hydroxide, and 3) an exponential scale factor

for this nucleation. Suggested values for these parameters are provided in parentheses when the

program prompts the user for input. The hydration algorithm will then execute until the desired

final condition (number of cycles or degree of hydration) is met. If an error in an input

parameter has been made or the user becomes impatient, they may press the Escape key to exit

the hydration algorithm immediately. Pressing the Escape key, however, may require that the

microstructure currently being generated be erased and that the user start over with particle

placement, etc. During hydration, two advancing lines at the top of the screen indicate the

progress of the hydration with respect to number of cycles and degree of hydration respectively.

This allows the user to gauge how much more time will be required for a given microstructure

to be produced.

5) Measure phase fractions

This option reports the number of pixels of each phase present in the microstructure.

The numerical values are first listed, followed by a bar graph showing the relative fracfions of

all phases. This is useful for verifying the original water-to-cement (w/c) ratio or observing the

effects of hydration on the phase fractions.

6) Measure phase fractions as a function of distance from aggregate surface

As with menu selection 5, this option determines the phase fractions, but as a function

of distance from the aggregate surface. The results are output to a datafile which can be easily

imported into a spreadsheet package for further analysis. The phase fractions will be in the

order porosity, C3S, C-S-H, CH, inert, and pozzolanic material in the output datafile. The first five times that this menu item is selected during a single execution of HYDRA2D, the output

file is called aggphase.OO$ where $ ranges from 1 to 5. For all subsequent selections, the

output file is called aggphase.lst, and this file will be overwritten when menu item 6) is selected

for the seventh time, etc. After the results are written to disk, a line graph is displayed showing

the porosity and (C3S + C-S-H -I- pozzolanic filler) phase fractions vs. distance from the

aggregate surface.

7) Move all cement particles towards aggregate surface (absorption)

This option is utilized to simulate the effect of a lightweight absorptive aggregate. The

user must specify how many pixels to move each cement and large filler particle towards the

aggregate. This option cannot be executed if no aggregate is present in the system or if onepixel filler particles have already been added to the microstructure.

8) Reset system by clearing microstructure

This option allows the user to clear out any existing microstructure and start over without

exiting the HYDRA2D program.
3.1.7.2 Exercise la: Effect of Cement Particle Size

For this exercise, monosize cement particles of three different sizes will be used to create

random starting microstructures, each of which will be hydrated to 70% hydration. A constant

w/c ratio (= 0.45) will be used for all three cases.

To begin a simulation for a particular case, select menu item #2 to place a flat aggregate

in the middle of the 2-D microstructure. Enter 10 for the half thickness of the aggregate,

followed by a 1 to select an inert aggregate. Next, add the cement particles by selecting menu

item #1 and entering the appropriate values for number and diameter of particles as given in

Table la. Input a value of 4 for the phase to be assigned to the particles to generate C3S

(cement) particles. At this point, the user may want to select menu item #5 to determine the

volume fractions of porosity (water filled) and cement, and verify that the w/c ratio is correct. The equation to compute w/c from the volumetric phase counts is:

IV _ Number of pore pixels

c 3.2* Number of C^S pixels

assuming a value of 3.2 for the specific gravity of cement. When item #5 is selected, the phase

counts in pixels will first be output to the screen, followed by the generation of a bar chart,

graphically showing the relative amounts of the phases present.

To execute the hydration, select item #4 from the main menu and input the following

parameters:

Select hydration to a defined degree of hydration - 1 Maximum degree of hydration - 0.7

Max. # steps per cycle - 5000

Max. prob. for CH nucleation - 0.01

Exp. scale factor for CH nucleation - 10000.

If necessary, the user may abort the hydration process by pressing the ESCape key. However,

the microstructure will be cleared and the user will have to start over at the beginning (i.e.,

adding an aggregate). The two advancing lines at the top of the monitor screen indicate the

progress of the hydration with respect to number of cycles and degree of hydration respectively.

When the hydration is complete, select menu item #6 to measure the phase fractions as a

function of distance from the aggregate surface. This selection will create a file, aggphase.xxx, on the distribution diskette which will contain a tabular list of the phase counts as distance from

the aggregate surface increases in increments of one pixel. Here, xxx is a three-digit number

(e.g., 001) which starts at 001 and is incremented every time menu item #6 is selected during

a single program execution. After five selections of #6 have been made during a single run, all future output will be written to aggphase.lst. Once this file has been produced, a graph of

phase fractions (for porosity and C3S-l-C-S-H+pozzolanic material) vs. distance from the

aggregate surface will be displayed on the screen. These plots can be viewed to estimate the
thickness of the interfacial zone. Finally, the user may select item #0 to exit the main program.

The file aggphase.xxx may be copied to a new name for preparation to be imported into a

spreadsheet to generate hardcopy graphs of the results (aggphasl.prn for example).

The phase fractions will be in the order porosity, C3S, C-S-H, CH, inert, and pozzolanic

material (reactive filler and pozzolanic C-S-H) in the file the user imports into the spreadsheet

package. For this exercise, the user should graph porosity vs. distance from the aggregate

surface for the three cement particle sizes on one graph and C3S-I-C-S-H vs. distance on another.

Porosity should be indicative of the durability of the composite while C3S-I-C-S-H should be an

indication of strength. These curves can then be utilized to estimate the thickness of interfacial zone. Averaging of results (i.e., phase fractions) over multiple random configurations would

remove much of the "noise" present in these plots. Thus, the user should complete multiple (3 or more) runs as time permits.

Questions:

Given that a finer cement produces a more uniform microstructure, what are some of the

disadvantages of using a finer cement? Can you think of any way of possibly offsetting these

disadvantages by modifying the normal mix procedures for concrete?

Does the use of a finer cement affect the wall effect, the one-sided growth effect, or both?

Table la. Parameters for Hydration Model

Number of

Particles

Particle

Diameter

152 11

42 21

20 31

3.1.7.3 Exercise lb: Effect of Mineral Admixture Particle Size

For this exercise, mineral admixture size and content will be varied to create three

different starting microstructures as outlined in Table lb, each of which will be hydrated to 70%

hydration. A constant water-to-solids (w/s) ratio (= 0.45) will be used for all three cases. The

control case will consist of cement particles only, while the two other cases will consist of small

and large mineral admixture (silica fume) particles added at a 10% weight replacement for

cement, respectively. Because we assume a specific gravity of 2.2 for the mineral admixture

as opposed to 3.2 for cement, a 10% weight replacement is equivalent to a volume fraction of

13.9%. Menu selection Ml will be used to add the large cement and reactive mineral admixture

10
particles while #3 will be used to add the small one-pixel mineral admixture particles. In all cases, when prompted by the program, the user should set the mineral admixture pozzolanic

reactivity factor at 2.08 (this parameter could be varied to model less reactive mineral

admixtures such as fly ash).

The program HYDRA2D should be executed once for each of the three cases specified

in Table lb. To begin a simulation for a particular case, select menu item #2 to place a flat aggregate in the middle of the 2-D microstructure. Enter 10 for the half thickness of the

aggregate, followed by a 1 to select an inert aggregate. Next, add the cement (and large mineral

admixture) particles by selecting menu item #1 and entering the appropriate values for number

and diameter of particles as given in the Table lb. Use a value of 4 to select C3S particles or

a value of 6 to select reactive filler (pozzolanic) particles. If small one-pixel mineral admixture

particles are required, select menu item #3 and enter the type (e.g., reactive) and number (Table

lb) of admixture particles to be added to the two-dimensional system. In all cases, add the

cement first, followed by the mineral admixtures if any. At this point, the user may want to select menu item #5 to determine the volume fractions of porosity (water filled) and cement, and

verify that the w/s ratio and admixture volume fraction are correct. When item §5 is selected,

the phase counts in pixels will first be output to the screen, followed by the generation of a bar

chart, graphically showing the relative amounts of the phases present. For these systems,

w_ Number of pore pixels

s 3.2 * Number of C^S pixels + 2.2 * Number of Min. Adm. pixels

To execute the hydration, select item #4 from the main menu and input the following

parameters:

Select hydration to a defined degree of hydration - 1 Maximum degree of hydration - 0.7

Max. # steps per cycle - 5000

Max. prob. for CH nucleation - 0.01

Exp. scale factor for CH nucleation - 10000.

If necessary, the user may abort the hydration process by pressing the ESCape key. However,

the microstructure will be cleared and the user will have to start over at the beginning of the

simulation process. The two advancing lines at the top of the monitor screen indicate the

progress of the hydration with respect to number of cycles and degree of hydration respectively.

When the hydration is complete, select menu item #6 to measure the phase fractions as a function of distance from the aggregate surface. This selection will create a file, aggphase.xxx, on the distribution diskette which will contain a tabular list of the phase counts as distance from

the aggregate surface increases in increments of one pixel. Here, xxx is a three-digit number

(e.g., 001) which starts at 001 and is incremented every time menu item #6 is selected during

a single program execution. After five selections of #6 have been made during a single run, all future output will be written to aggphase.lst. Once this file has been produced, a graph of

11
phase fractions (for porosity and C3S + C-S-H+pozzolanic material) vs. distance from the

aggregate surface will be displayed on the screen. These plots can be viewed to estimate the

thickness of the interfacial zone. Finally, the user may select item #0 to exit the main program.

The file aggphase.xxx may be copied to a new name for preparation to be imported into a spreadsheet to generate hardcopy graphs of the results (aggphasl.prn for example).

The phase fractions will be in the order porosity, C^S, C-S-H, CH, inert, and pozzolanic

material (reactive filler and pozzolanic C-S-H) in the file the users imports into the spreadsheet

package. For this exercise, the user should graph porosity vs. distance from the aggregate

surface for the three cases on one graph and C3S 4- C-S-H -I- pozzolanic material vs. distance on

another. Porosity should be indicative of the durability of the composite while

CgS + C-S-H-f-pozzolanic material should be an indication of strength. These curves can then

be utilized to estimate the thickness of interfacial zone. Averaging of results over multiple

random configurations would remove much of the "noise" present in these plots. Thus, the user should complete multiple (3 or more) runs as time permits.

Questions:

The model assumes a certain stoichiometry for the reaction between CH and pozzolanic

material. How would you modify the model to alter this stoichiometry to produce C-S-H of a

different Ca/Si molar ratio? What information (physical properties, etc.) would you need to do

this?

Does the addition of mineral admixtures affect the wall effect, the one-sided growth

effect, or both?

Table lb. Cement and Mineral Admixture Required

Number of

Cement

Particles

Cement

Particle

Diameter

Number of

Coarse

Min. Adm.

Coarse

Min. Adm.

Diameter

Number of

One Pixel

Min. Adm.

42 21 — — —

37 21 6 21 —

37 21 — — 2094

3.1.7.4 Exercise Ic: Effect of Aggregate Characteristics

For this exercise, aggregate characteristics will be varied to create three different starting

microstructures, each of which will be hydrated to 70% hydration. A constant w/c ratio

(=0.45) will be used for all three cases. The base case will consist of cement particles and an

inert aggregate, while the two other cases will consist of a reactive (cement clinker) aggregate

12
and an absoq^tive reactive aggregate, respectively.

To begin a simulation for a particular case, select menu item #2 to place a flat aggregate

in the middle of the 2-D microstructure. Enter 10 for the half thickness of the aggregate,

followed by a 1 to select an inert aggregate or a 2 to select a reactive aggregate (see Table Ic),

Next, add the cement particles by selecting menu item #1 and entering the appropriate values

for number and diameter of particles as given in Table Ic. Input a value of 4 for the phase to be assigned to the particles to place C3S particles. For the third case, select menu item #7 to simulate the absorption of water by the aggregate and input a value of 10 for the number of

pixels to move the cement particles inward. At this point, the user may want to select menu

item #5 to determine the volume fractions of porosity (water filled) and cement, and verify that

the w/c ratio is correct. When item #5 is selected, the phase counts in pixels will first be output

to the screen, followed by the generation of a bar chart, graphically showing the relative

amounts of the phases present. For these systems,

w_ Number of pore pixels

c 3.2* Number of C-^S pixels

assuming a specific gravity of 3.2 for cement.

To execute the hydration, select item #4 from the main menu and input the following

parameters:

Select hydration to a defined degree of hydration - 1 Maximum degree of hydration - 0.7

Max. # steps per cycle - 5000

Max. prob. for CH nucleation - 0.01

Exp. scale factor for CH nucleation - 10000.

If necessary, the user may abort the hydration process by pressing the ESCape key. However,

the microstructure will be cleared and the user will have to start over at the beginning. The user should note that in the case of a reactive aggregate, the 0.7 degree of hydration corresponds to hydration of the bulk cement and does not include hydration of the aggregate, as dissolution of

the reactive aggregate and cement particles are tabulated separately. The two advancing lines

at the top of the monitor screen indicate the progress of the hydration with respect to number

of cycles and degree of hydration respectively. When the hydration is complete, select menu

item #6 to measure the phase fractions as a function of distance from the aggregate surface.

This selection will create a t~ile, aggphase.xxx, on the distribution diskette which will contain a tabular list of the phase counts as distance from the aggregate surface increases in increments

of one pixel. Here, xxx is a three-digit number (e.g., 001) which starts at 001 and is incremented every time menu item #6 is selected during a single program execution. After five

selections of #6 have been made during a single run, all future output will be written to aggphase.Ist. Once this file has been produced, a graph of phase fractions (for porosity and

CjS+C-S-H+pozzolanic material) vs. distance from the aggregate surface will be displayed on

13
the screen. These plots can be viewed to estimate the thickness of the interfacial zone. Finally,

the user may select item #0 to exit the main program. The file aggphase.xxx may be copied

to a new name for preparation to be imported into a spreadsheet to generate hardcopy graphs

of the results (aggphasl.prn for example).

The phase fractions will be in the order porosity, C3S, C-S-H, CH, inert, and pozzolanic

material (reactive filler and pozzolanic C-S-H) in the file the user imports into the spreadsheet

package. For this exercise the user should graph porosity vs. distance from the aggregate

surface for the three cases on one graph and C3S-I-C-S-H vs. distance on another. Porosity

should be indicative of the durability of the composite while C3S + C-S-H should be an indication

of strength. These curves can then be utilized to estimate the thickness of interfacial zone. Averaging of results over multiple random configurations would remove much of the "noise"

present in these plots. Thus, the user should complete multiple (3 or more) runs as time

permits.

Questions:

Does the use of a reactive (nonabsorptive) aggregate affect the wall effect, the one-sided

growth effect, or both? What about a lightweight absorptive reactive aggregate?

If you were going to choose a reactive aggregate composed of only one phase of Portland

cement (C3A, C3S, C2S, or C4AF), which would you choose? Why?

Table Ic. Cement Particle and Aggregate Characteristics

Aggregate

Reactivity

Number of

Cement

Particles

Cement

Particle

Diameter

Number of

Pixels To

Move

Cement

Particles In

Inert 42 21 —

Reactive 42 21 —

Reactive 38 21 10

3.2 Percolation Theory

3.2.1 Introduction

Percolation theory was developed to mathematically deal with disordered media, in which

the disorder is defined by a random variation in degree of connectivity [12,13]. The main

concept of percolation theory is the existence of a percolation threshold, defined in the following

14
way. Suppose p is a parameter that defines the average degree of connectivity between various

sub-units of some arbitrary system. When p = 0, all sub-units are totally isolated from every

other sub-unit. When p = 1, all sub-units are connected to some maximum number of

neighboring sub-units. At this point, the system is connected from one side to the other, since

there are paths that go completely across the system, linking one sub-unit to the next along the

spanning cluster. Now suppose, starting at p = 1, connections are randomly broken, so that p, the measure of average connectivity, decreases. The percolation threshold is that value of p, usually denoted p,,, at which there is no longer an unbroken path from one side of the system

to the other. Alternately, if we start out at p = 0, and randomly create connections, so that p

increases, p^ is defined as the point at which a spanning cluster first appears . For p less than

Pc, only isolated, nonspanning clusters can exist. For p

greater than p,, there is always a spanning cluster, although some isolated, nonspanning clusters can still be present.

A typical lattice example of a percolation problem is that of site percolation on a simple twodimensional square lattice. The lattice starts off empty, with all sites unoccupied. The sites of

the lattice are then randomly occupied, one at a time. If two occupied sites are nearest

neighbors, a connection is made between them. When a critical fraction, p, = 0.593, of the

sites are present, a spanning cluster will come into existence, and the occupied sites will

percolate.

A more complex continuum percolation problem is defined by the following. Take a white

piece of paper, and randomly throw down equal-sized circular blobs of paint, studying the

critical paint fraction needed to have a continuous path of paint from one side of the paper to the other. In this case, the critical threshold is expressed as a paint area fraction, with the value

pj"^' = 0.68.

The percolation properties of a digital-image-based model are easy to compute. The

percolation of any phase of interest may be determined by the use of a "burning" algorithm [12].

This algorithm is a simple way of identifying all pixels that are part of a spanning cluster, if such a cluster exists, and works as follows. Conceptually, all the pixels belonging to the phase

of interest are classified to be "combustible." A "fire" is started on one side of the model's unit

cell, and allowed to propagate only along these combustible pixels. If any pixels on the opposite

side of the model cell are found to have been "burned," then a spanning cluster of the phase of

interest must exist.

Another percolation model that arises in the study of cement-based composites is the hard

core/ soft shell (concentric particle) model introduced by Torquato [14]. Like the overlapping

circle (paint) percolation problem discussed above, objects are randomly placed in a continuum,

and their connectivity is studied as a function of how many have been placed, or of what area or volume fraction is occupied. In the hard core/soft shell (hcss) model, the objects, for

example circles in 2-D or spheres in 3-D, are made up of an inner core of radius b, and an outer

shell of thickness a-b, so that the total radius is a. Hard cores may not overlap each other, but

soft shells may overlap anything freely. When b is zero, in two dimensions, then we recover

the overlapping circle problem mentioned earlier. When b = a, we have the problem of random

15
close-packing of circles or spheres. For intermediate values of b/a, the percolation threshold,

expressed as number of objects per unit area or volume, or the area (volume) fraction of soft

shells, will depend on b/a.

The hcss model has been used to examine the percolation of interfacial zones in concrete

by Winslow et al [15]. In this model, the 3-D hard core spheres represent the aggregates while

the soft shells represent the interfacial zones surrounding each aggregate. As shown in computer

exercise #1, the interfacial zone regions are more porous and contain larger pores than the bulk

cement paste. If enough aggregates are present in a mortar or concrete, these interfacial zones

(soft shells) will interconnect and provide a path of lesser resistance (than the bulk paste) for the

ingress of deleterious species such as chloride ions. This phenomena has been verified

experimentally by a series of mercury intrusion porosimetry experiments [15].

Recently, the hcss model has been successfully applied to two other material systems.

The first is a three-dimensional model of the microstructure of MDF (Macro-defect-free)

cements [16], where the hard cores represent the unhydrated cement particles and the soft shells

represent the interphase region (polymer + hydration products) surrounding each cement

particle. Here, the model has been used to examine the percolation characteristics of both the

interphase regions and the bulk polymer phase. The second is a two-dimensional model for the

microstructure of chemical-vapor-infiltrated ceramic tlbers. Here, the hard cores represent the

original impenetrable fibers and the soft shells represent the deposition product, and thus

increase in size during the course of the reaction. Researchers at NIST and Northwestern

University are using the generated microstructures to compute thermal conductivities and

permeabilities of these composite microstructures as a function of porosity. These physical

properties will then be utilized in a macro-level processing model to provide a better

understanding of the relationships between processing variables (temperature, pressure, etc.) and

resultant structure,

3.2.2 Exercise #2- Continuum Percolation Exercise

Program: PERSHAPE.EXE

This exercise is designed to apply percolation theory to a real percolation problem. It will allow the user to see, in a simple way, the effect of microstructure on percolation

properties, and will familiarize them with the computational tools and methods useful in analyzing the percolation properties of computer simulation models.

In the introduction to this section on percolation theory, the problem of overlapping

circles in the plane was presented. This was just an idealized version of the more general

problem of randomly building up a structure out of individual particles, and determining where

the percolation threshold is in terms of the number of particles used or the volume fraction

occupied by the structure. For example, the degree of hydration required for setting of a cement

paste is a percolation problem, since connections are being randomly built up, via the formation

of reaction products, between the initially isolated (disconnected) cement particles.

16
This exercise will address the problem of building up structures out of randomly-oriented

and placed ellipses or rectangles, and studying the effect of the shape of the individual particles on the percolation threshold, the point at which the structure becomes continuous. The shape

of the particles is quantified by the aspect ratio, which is defined as the ratio b/a of the semiminor axis b to the semi-major axis a. The particles are allowed to freely overlap, just as in the

circle model discussed earlier. The particles will be oriented randomly either horizontally or

vertically, which has been shown to give comparable results to random orientations of all possible angles.

The program is included on the distribution diskette and is called PERSHAPE.EXE.

Simply switch to the appropriate disk drive and type PERSHAPE at the DOS prompt to begin

its execution. The program is interactive, and is set up for randomly placing ellipses or

rectangles on a square unit cell that is 300x300 pixels in dimension. Periodic boundary

conditions are used, which means that a particle that sticks out on one side is wrapped around

and brought back in on the other side. Initially, the program will ask whether the user wishes

to place ellipses or rectangles and prompt them for the values of 2a (major axis dimension),

which should always be 21 for this exercise, and of 2b (minor axis dimension), which can range

from 3 to 21. When entering the values of 2a and 2b, they should be entered on the same line

separated by a single space. The goal is to execute the program for the values of 2a and 2b

given in Table 2. At each step, the program will ask the user for the number of additional

particles they wish to place. After placing the particles, the program will determine the

connectivity of the system structure from top to bottom, and from left to right utilizing periodic

boundaries on the sides parallel to the direction of the burning. A fiag variable (burnt) will be

output, taking a value of I if a percolated pathway exists, and otherwise. The program will

also report the area fraction covered by the particles in terms of a pixel count.

As an example, microstructures for overlapping ellipses (with 2a=21 and 2b=5) are shown in Figure 1. The top left corner figure shows a system containing 550 ellipses which is not percolated from top to bottom as shown in the top right corner figure. Here, the burning

algorithm has been executed and all ellipses accessible from the top of the system are shown in bright white. The bottom two figures are for the same system to which an additional 150

ellipses have been added, for a total of 700 ellipses. Now, the system is percolated from top

to bottom and all accessible ellipses are once again shown in bright white in the lower right corner figure.

The user's task is to compute the dependence of the percolation threshold p^, the area

fraction of particles needed for the solid structure to become continuous, on the aspect ratio b/a.

The quantity n^,, the number of particles per unit area at the percolation threshold will also need

to be recorded. Averaging results over several separate executions will increase the accuracy

of these numeric values so multiple runs should be executed if possible.

The output from this assignment will be a graph (use a spreadsheet or graphics package

to create it), showing p^ vs. particle aspect ratio, for both ellipses and rectangles. The user should prepare a table of n^ vs. b/a, and consider the quantities n^,(a+b)^ for ellipses and

17
Figure 1. Percolation of Overlapping Ellipses

18
(4/-;r)n<,(a+b)^ for rectangles. Try to see if there is anything interesting about these quantities

for various values of b.

Table 2. Ellipse and Rectangle Area in Pixels for Various Aspect Ratios

2a 2b Ellipse area (pixels)

Rectangle

area (pixels)

21 3 51 63

21 5 85 105

21 7 119 147

21 9 149 189

21 11 183 231

21 13 217 273

21 15 247 315

21 17 281 357

21 19 315 399

21 21 349 441

Tips.(l) The best value for p, for a given run is the average of the critical values for left- right and top-bottom percolation. In an infinite system, these are always the same, but for a

finite-size system like the one here, they are often somewhat different. (2) There is a formula

that gives, for completely randomly-placed overlapping objects, the area fraction occupied by

them as a function of the number placed. This formula is

Area fraction occupied = p = 1 - exp(-Na/A)

where N is the number of objects placed, a is the area of one object, and A is the total area of

the region where they are being placed. In our exercise, A = 300' = 90,000 pixels, and a is the

particle area in pixels, which is given in Table 2 for both ellipses and rectangles. This formula

will not be perfectly accurate for this finite-size system, but will be accurate enough for the user

to estimate how many particles will be needed to attain a given area fraction for a specific area

particle. The user should check the actual value of p, averaged over several realizations at a

fixed number of particles, against the formula. They should agree within a percent or so. (3)

Since the program asks for the number of additional particles to be added, the user must start out below the percolation threshold, so that they can add particles to achieve the threshold. (4)

To start, for 2a=21 and 2b = 3, the user should place 500 ellipses or rectangles and then add

more according to their best judgement to approach percolation. The user should try to determine n„ to -I- 10%.

19
3.2.3 Exercise #3- Hard Core/ Soft Shell Percolation Exercise

Program: PERSHELL.EXE

In this exercise, the user will examine the percolation characteristics of a variety of hard

core/ soft shell two-dimensional systems consisting of monosize circles, as illustrated in figure

2. Hopefully, the exercise will provide some insight into what happens to the interfacial zones

in mortar and concrete as more sand and rocks are added to the mix. As stated in the

introduction, we think of the aggregates as the hard cores, and the interfacial zones as the soft

shells. If the interfacial zones percolate, that may have important implications for transport and

strength properties, as the biggest pores tend to be in the interfacial zones.

The major variable the user will be examining is b/a, the ratio of the hard core diameter

to the total (hard core + soft shell) diameter. For a given value of b/a, the user will be

computing the number of circles, and area fractions of hard cores and soft shells necessary for

the soft shells to form a percolating pathway across the 2-D microstructure (both top to bottom

and left to right).

The program is called PERSHELL.EXE. Simply switch to the appropriate disk drive

and type PERSHELL at the DOS prompt to begin execution. The program is interactive, and

is set up for randomly placing circular particles on a square unit cell that is 300*300 pixels in dimension. Periodic boundary conditions are used during particle placement and during

percolation assessment (in the appropriate directions). Initially, the program will request values

for the hard core (2b) and total (2a) diameters of the circles. The user should enter the two

values on the same line separated by a single space. The goal is to execute the program for the

values of 2b and 2a given in Table 3. After inputting values for b and a, the program requests

how many additional particles should be placed this round. If the user requests more particles

(hard cores) than can be randomly parked in a non-overlapping arrangement, the placement

routine will exit after 10,000 random attempts are made to place a single particle. After placing

the particles, the program determines the connectivity of the soft shells from left to right, and

from top to bottom and outputs a flag variable (burnt) which is 1 if a percolated pathway is present and otherwise. It also reports the hard core and soft shell areas and the total number

of particles placed so far. The user should record these values for when percolation is first achieved in each direction for each set of (2b) and (2a) values.

As an example, microstructures for monosize circles (with 2b= 13 and 2a =21) are shown

in Figure 3. The top left corner figure shows a system with 160 hcss particles. The hard cores

are shown in dark grey and the soft shells are in light grey. As seen in the upper right corner

figure, the soft shells are not yet percolated from top to bottom; here, the soft shells which are connected to the top of the system are shown in white. By adding 40 more hcss particles to the

system, for a total of 200 particles, percolation from top to bottom is achieved as shown in the

two bottom figures. Even at percolation, there still exist some hcss particles which are not

accessible from the top of the system as exemplified by the light grey soft shells in the lower

right corner figure.

20
The output of this exercise will be a graph of the various area fractions occupied (hard

core, soft shell, and total particle) at the onset of percolation as a function of b/a. Averaging

results over several separate executions will increase the accuracy of these graphs so multiple runs should be executed if possible.

Figure 2. Schematic of Hard Core/Soft Shell Model.

Table 3. Hard Core (2b) and Total (2a) Particle Diameters

2b 2a b/a

21

1 21 0.0476

3 21 0.1429

5 21 0.2381

7 21 0.3333

9 21 0.4286

11 21 0.5238

13 21 0.6190

15 21 0.7143

17 21 0.8095

Tips (1) The best value for p, for a given run is the average of the critical values for left- right and top-bottom percolation. (2) Since the program requires additional particles to be

21
Figure 3. Hard Core/ Soft Shell Percolation Example,

22
added, the user must start out below the percolation threshold and approach it slowly by adding

fewer new particles as the percolation point is neared.

3.3 Simulation of Mercury Porosimetry in 2-D

3.3.1 Introduction

Mercury porosimetry is a widely used method of approximately measuring the pore-size

distribution of porous materials [17]. Samples are first evacuated, and then surrounded by a mercury bath. Mercury is a non-wetting fluid for most porous materials of interest, so increasing pressure is required to force the mercury into smaller and smaller pores. In the

porosimeter, an increase in pressure is made, and the additional volume of mercury that goes

into the sample is monitored. This volume of mercury is then associated with a pore diameter

that is determined by assuming a circular cylindrical pore geometry. As the pressure is increased, a wide range of pore sizes can be explored.

The algorithm for mercury, or non-wetting fluids in general, injection is a geometric

method that works only for completely non-wetting fluid injection, in 2D, with a contact angle

of 180°. The algorithm, described in detail by Garboczi and Bentz [18], begins by surrounding

a porous image with a bath of fluid pixels. A pressure is implicitly chosen, via the Washburn

equation, by selecting a diameter that is the smallest channel through which the fluid will be

allowed to go. The fluid is then successively intruded from the outside by trying to place fluid

circles of the chosen diameter, centered at previously intruded fluid pixels. The circular

intruding shape gives approximately the correct meniscus, and the chosen diameter guarantees

that the fluid will only go into allowed regions. By keeping track of how much pore area is intruded with each choice of pressure/pore diameter, an approximate pore-size distribution can be traced out.

An important quantity is the pore diameter, denoted d,, that is intruded just at the point

when the mercury becomes continuous across the sample, or percolates. This parameter can be

measured experimentally using commercial porosimeters. In the mercury intrusion algorithm,

the value of d^. is determined directly by intruding from one direction (top or left) only and

finding if the intruded fluid has percolated to the other side (bottom or right). The value of d^

is then the intruding fluid circle diameter at percolation, averaged between the left-right and updown thresholds, which are not always the same due to finite-size effects.

Physically, the length scale d^ can be thought of as the smallest member of a subset of

the pore space containing the largest pores that form a continuous pathway through the pore

space. The parameter d,. is a key quantity in the Katz-Thompson fluid permeability theory [19],

and basically sets the scale for permeability. Roughly, the permeability of a porous material is propordonal to d^^.

23
3.3.2 Exercise #4- Mercury Porosimetry Exercise

Program: ^C>' MERCURY.EXE

In this exercise, the dependence of the critical pore diameter, d^, on microstructure, will

be studied, using the 2-d mercury porosimetry algorithm. The user will examine models of

porous materials, constructed in the following way. Equal-size circles are placed at random

inside a square 200*200 cell with periodic boundary conditions, but are not allowed to overlap

each other. This creates a model with a continuous pore space at any porosity, where the pore

space is composed of the "capillary" regions consisting of the leftover space between solid

circular particles.

At a fixed porosity, one might expect that the value of d, would change as the solid

particles that define the pore space are varied in size. For example, in one dimension, if a line

segment of unit length is covered with two smaller segments of length 1/4, then the space

between them is 1/4, and the covered length fraction is 1/2. If, instead, five segments, each of

length 1/10 are used, the covered length fraction will still be 1/2, but now the empty spaces will

only be of length 1/10 as shown in figure 4. Therefore one might expect, since average pore

sizes will certainly change with the fineness of the solid particles that define the pore structure,

that d^ would change as well.

1/4 1/4

> 1/4 < > 1/4

1/10 1/10 1/10 1/10 1/10

< > 1/10 < > 1/10 < > 1/10 < > 1/10 < > 1/10

Figure 4. Effect of line length on pore size.

In this exercise, the user will create pore spaces at a fixed porosity of about 70%, by

randomly placing circles of diameters 7, 13, and 19 pixels. The areas in pixels occupied by

these circles are 37, 137, and 293 pixels respectively. The mercury porosimetry program will

intrude mercury from all sides, from top to bottom, and finally from left to right, in order to check for continuity in both directions. As you will recall, d, is defined as that pore diameter

corresponding to the injection pressure at which continuity is achieved. The value found should

be averaged over the two different directions. Note that when percolation is first achieved for a given direction, intrusion in that direction will not be executed for any smaller meniscus

diameters.

24
The program is called MERCURY.EXE. Simply switch to the appropriate disk drive

and type MERCURY at the DOS prompt to begin execution. The program will ask you initially

how many and what diameter circles to use to generate the microstructure. (Although not

required for this exercise, the user may add multiple size circles as this option will appear

iteratively until a value of is entered for the number of circles to add. The user should always

add multi-size circles in order of largest to smallest.) The diameter of the circles must be an odd integer so that the circles may be centered on a pixel. The user will have to calculate the

number of monosize circles needed for each diameter to achieve a porosity of about 70% . Next,

the program will ask what range of menisci diameters to evaluate (3 to 17 for example). The

program will also ask whether to run a complete intrusion or only check for percolation and the user may choose the latter by entering a 1 (to save time) or choose both by entering a 2 to produce a complete intrusion curve. When intruding from one side only, if the mercury reaches

the opposite side from where it started, then the intrusion is stopped before completion, and the

connectivity is recorded. During all intrusions, the previous intrusion image is left on the screen

as the pressure is increased, so that the user may study how pore accessibility changes as pressure increases. Each pressure is color coded, so that the user may determine for any pixel

in the pore space, the lowest pressure (highest meniscus diameter) at which this pore would be

accessible from the exterior. When the program is finished executing for all the chosen intrusion

diameters and directions, the user must press the ESCape key to remove the final image. At this

point, if option or 2 has been selected for execution, a graph of the area intruded vs. meniscus

diameter will be produced on the screen. Finally, the user may press any key to exit the

program.

The results of this exercise should be expressed in the form of a graph plotting d^ vs. the

particle size used to generate the microstructure [18].

Tips. (1) Try to get at least three realizations at each circle size, and average d^ over

them. (2) For a given direction, d^ is the average of two menisci sizes: the first being the

largest value for which the mercury reaches the opposite side and the second being the smallest

value for which the mercury doesn't reach the opposite side (e.g., if the mercury does not

percolate for d=9 but does for d=7, then d, = (9+7)/2 = 8).

4. FEEDBACK FROM USERS

User feedback has been important to the development of this education module. The PC

programs have been used at the past two NIST/ACBM Computer Modelling Workshops and

attendees have provided many valuable comments and suggestions, resulting in significant

modifications and enhancements to the education module. It is anticipated that this pattern will

continue in the future, with improvements being incorporated into future releases of the

software.

As of early 1993, the software has been utilized by four faculty members in teaching both

undergraduate and graduate level civil engineering classes. To provide a mechanism for gaining

25
feedback from these professors, a survey form was developed and distributed to those who had

obtained copies of the PC software. A sample survey form is provided in Appendix B.

Comments received from the faculty this year have been incorporated into the latest version of

the software and this documentation. In general, professors have found the education module

useful for visually demonstrating underlying physical phenomena. The hydration and mercury

intrusion programs are somewhat time consuming and students sometime lose patience with these

exercises. This can be improved by executing the programs on an 80486-based computer to speed up execution or by shortening the number of configurations and variations included in the

example assignments.

Several of the professors have modified the computer exercises given in Section 3 and

come up with new uses for some of the computer programs. For instance, in one case, the

Macintosh version of the hard core/soft shell percolation program has been utilized to study the

effects of particle size distribution on particle placing density by setting the total and hard core diameters to be equal and observing the maximum obtainable volume fraction for different

particle size distributions (monosize, three different sizes, etc.). It is envisioned that other uses

for the programs will be developed over time. It is planned that the survey will be conducted

annually to determine needed improvements for the software programs and provide information on the impact of this education module in the college classroom.

26
5. REFERENCES

[I] Bentz, D.P., and Garboczi, E.J., "Percolation of Phases in a Three-Dimensional Cement

Paste Microstructural Model," Cement and Concrete Research, 21 (2), 325-344, 1991.

[2] Garboczi, E.J., and Bentz, D.P., "Computer Simulation of the Diffusivity of Cement-Based

Materials," Journal of Materials Science, 27, 2083-2092, 1992.

[3] Bentz, D.P., and Garboczi, E.J., "Guide to Using HYDRA3D: A Three-Dimensional

Digital-Image-Based Cement Microstructural Model," NISTIR 4746, U.S. Department of

Commerce, January 1992.

[4] Bentz, D.P., Coveney, P., Garboczi, E.J., Kleyn, M., and Stutzman, P.E., "Cellular

Automaton Simulations of Cement Hydration and Microstructure Development," accepted

by Modelling and Simulation in Materials Science and Engineering.

[5] Garboczi, E.J., and Bentz, D.P., "Digital Simulation of the Aggregate-Cement Paste

Interfacial Zone in Concrete," Journal of Materials Research, 6 (1), 196-201, 1991.

[6] Bentz, D.P., and Garboczi, E.J., "Simulation Studies of the Effects of Mineral Admixtures on the Cement Paste-Aggregate Interfacial Zone," ACI Materials Journal, 88 (5), 518-529,

1991.

[7] Hooton, R.D., "Permeability and Pore Structure of Cement Pastes Containing Fly Ash, Slag,

and Silica Fume," Blended Cements . STP 897, Ed. Geoffrey Frohnsdorff, ASTM,

Philadelphia 1986, pp. 128-143.

[8] Zhang, M.H., and Gjorv, O.E., "Microstructure of the Interfacial Zone between Lightweight

Aggregate and Cement Paste," Cement and Concrete Research, 20, 610-618, 1990.

[9] Fagerlund, G., "Frost Resistance of Concrete with Porous Aggregate," Report of the Cement

and Concrete Institute in Sweden, 1978.

[10] Berger, R.L., "Properties of Concrete with Cement Clinker Aggregate," Cement and

Concrete Research, 4, 99-112, 1974.

[II] Yang, S. et al "A New Method for Enhancing Cement-Aggregate Interfaces I. Ideal

Aggregate and Its Effects on Interfacial Microstructures," Cement and Concrete Research,

22, 612-620, 1992.

[12] Stauffer, D., Introduction to Percolation Theory (Francis and Taylor, London, 1985).

27
[13] Zallen, R., The Physics of Amorphous Solids (Wiley, New York, 1983), Ch. 4.

[14] Torquato, S., Journal of Chemical Physics, 81, 5079, 1984.

[15] Winslow, D.N., Cohen, M.D., Bentz, D.P., Garboczi, E.J., and Snyder, K.A.,

"Percolation and Pore Structure in Mortars and Concrete," Cement and Concrete Research,

in press.

[16] Lewis, J. A., Boyer, M., and Bentz, D.P., "Binder Distribution in Macro-Defect-Free

Cement: Relation Between Percolative Properties and Moisture Absorption Kinetics,"

submitted to Journal of the American Ceramic Society.

[17] van Brakel, J. (ed.), "A Special Issue Devoted to Mercury Porosimetry," Powder

Technology, 29, 1-209, 1981.

[18] Garboczi, E.J., and Bentz, D.P., "Digitized Simulation of Mercury Intrusion Porosimetry,"

Advances in Cementitious Materials , Ceramic Transactions, 16, 365-379, 1992.

[19] Katz, A.J., and Thompson, A.H., Physical Review B, 34, 8179, 1986; and Journal of

Geophysics Research, 92, 599, 1987.

28
6. APPENDIX A- GUIDE TO USE OF EDUCATION MODULE ON MACINTOSH

The four programs contained within the education module also have versions that execute on Macintosh computers. The programs require a Mac II or higher processor, and a color

monitor.

The Macintosh user interface is driven by a mouse and pointer combination which is used

to access different programs and data files stored on the computer's storage device (e.g., hard

disk). One may access the education module by either selecting the folder labelled ACBM-EducModule with the mouse and choosing Open from the FILE menu, or by simply double clicking on that same folder. Within the ACBM-Educ-Module folder, there are four other folders and

an instructional note giving some general details. Each folder contains one of the four programs

described in this document as indicated by the folder label, and may be opened in the same

manner as described above. Inside each of these folders, there is an executable program as well

as a detailed description of the menu items used in that program (also provided in sections 6.1-

6.4). The programs may be executed in the same manner in which the folders were opened.

The models were developed so that the user interfaces are as consistent with other

Macintosh programs as possible. The programs are all menu driven, with inactive menus

appearing in gray, and active menus appearing in black. Since some of the program processes

take quite some time to execute, the user may interrupt and return to the menus by clicking the

mouse at any time during execution.

6.1 Description of HYDRA2D on Macintosh

The following briefly describes the menus for the Macintosh version of the HYDRA2D

application.

The program may be interrupted at any time by clicking the mouse button.

FILE:

Open : not available in this version.

Save: not available in this version.

Quit: exits program.

Microstructure:

Add C^ S Particles : adds the number and size of C3S particles as designated by the

Number and Size menus

29
Add Filler (reactive) : adds single pixel reactive filler particles with reactivity designated

by the Pozz menu. The number of particles added is designated

by the selection from the Number menu.

Add Filler (inert) : adds single pixel inert filler particles. The number of particles added

is designated by the selection from the Number menu.

Add Aggregate (reactive) : places a single reactive aggregate particle in the center of the

image with width from the Size menu. Note: a size selection of

1 will not produce an aggregate.

Add Aggregate (inert) : places a single inert aggregate particle in the center of the image

with width from the Size menu. Note: a size selection of 1 will

not produce an aggregate.

Move Particles : allows the movement of C^S particles toward the aggregate. Particles are moved pixel amounts designated by the selection in the Size menu.

Measure Phase Fractions : displays the volume fractions of all phases present in the

image.

Measure Phase Fractions vs. Distance from Agg : writes the area fractions of all the

phases present in the image to a file. The data is written in

column format and can be imported into a spreadsheet for graphical

analysis.

Clear Image: erases current image and allows the user to start over without quitting the

program.

Number:

Number of particles to be placed the next time Add C^ S Particles or Add Filler is chosen

from the Microstructure menu.

Size:

This selection is used for several operations in the Microstructure menu. It is used to determine the size of the C^S particles, the size of the aggregate, and the number of

pixels that particles are moved in the Move procedure.

Hydrate:

This menu initiates the hydration simulation. The upper half of the menu will hydrate

the image the selected number of cycles, while the lower half of the menu will hydrate

the image to the selected degree of hydration.

30
Steps:

This menu selects the number of diffusion steps that are allowed in the hydration process

before automatic nucleation is enforced. A high number will take longer to run and

produce a more realistic microstructure.

Prob:

Prefactor for exponential probability for CH nucleation. A low number will take longer

to run and produce a more realistic microstructure.

Scale:

Scale factor for exponential probability for CH nucleation. A high number will take

longer to run and produce a more realistic microstructure.

Pozz:

Pozzolanic reactivity factor of the reactive tiller (e.g., 2.08).

6.2 Description of PERSHAPE on Macintosh

The following briefly describes the menus for the Macintosh version of the PERSHAPE

continuum percolation application.

The program may be mterrupted at any time by clicking the mouse button.

FILE:

Open : read in file saved as a continuous line of single byte integers representing either

porosity (0) or particle (1).

Save : saves current image in the same format as described above.

Quit : exits program.

Execute:

Add Particles : adds the number, size, and shape of particles as designated by the Shape. Number. Size a . and Size b menus.

Burn from top : performs the burning algorithm from the top of the image.

Burn from left : performs the burning algorithm from the left of the image.

Clear Image: erases current image and allows the user to start over without quitting the

program.

31
Volume Fraction : displays the number of particles and the volume (area) fraction,

currently present in the image. This command will accurately

describe the volume fraction of an image read from disk, but not

the number of particles.

Shape:

Allows selection of either ellipses or rectangles for the shape of the particles to be used

in the simulation. The selection will remain in effect until changed by the user.

Number:

Number of shapes to be placed the next time Add Particles is chosen from the Execute menu.

Size a: Size for major axis of ellipse or rectangle.

Size b:

Size for minor axis of ellipse or rectangle.

Seed:

The random number generator is originally seeded from the computer's internal clock.

Repeatable exercises are possible by selecting one of the three seeds provided under this menu. Each selection of Seed will reset the random generator to either the clock, or one

of the three optional seeds provided.

6.3 Description of PERSHELL on Macintosh

The following briefly describes the menus for the Macintosh version of the PERSHELL

hard core/soft shell percolation application.

The program may be mterrupred at any time by clicking the mouse button.

FILE:

Open : read in file saved as a continuous line of single byte integers representing either

porosity (0) or particle (1).

Save: saves current image in the same format as described above.

Quit : exits program.

Execute:

Add Particles : adds the number, size, and shape of particles as designated by the Shape, Number, Outer diameter , and Inner diameter menus.

32
Bum from top : performs the burning algorithm from the top of the image.

Burn from left : performs the burning algorithm from the left of the image.

Clear Image: erases current image and allows the user to start over without quitting the

program.

Volume Fraction : displays the number of particles and the volume (area) fraction,

currently present in the image. This command will accurately

describe the volume fraction of an image read from disk, but not

the number of particles.

Shape:

Allows selection of circles only for the shape of the particles to be used in the simulation.

Number:

Number of shapes to be placed the next time Add Particles is chosen from the Execute menu.

Outer diameter:

Overall diameter of the hard core and soft shell.

Inner diameter:

Diameter of the inner hard core. This length must be less than the Outer diameter value.

Seed:

The random number generator is originally seeded from the computer's internal clock.

Repeatable exercises are possible by selecting one of the three seeds provided under this menu. Each selection of Seed will reset the random generator to either the clock, or one

of the three optional seeds provided.

6.4 Description of MERCURY on Macintosh

The following briefly describes the menus for the Macintosh version of the MERCURY

two-dimensional intrusion application.

The program may be interrupred at any time by clicking the mouse button.

FILE:

Open : read in file saved as a continuous line of single byte integers representing either

porosity (0) or particle (1).

Save: saves current image in the same format as described above.

33
Quit: exits program.

Execute:

Add Particles : adds tiie number and size of particles as designated by the Number and

Size menus.

Volume Fraction : displays the volume fraction of particles currently present in the image.

Intrude from top : performs the intrusion algorithm from the top of the image. Intrusion

is performed from the maximum meniscus to the minimum

meniscus as selected by the respective menus.

Intrude from left : performs the intrusion algorithm from the left of the image. Intrusion

is performed from the maximum meniscus to the minimum

meniscus as selected by the respective menus.

Intrude Full : performs a complete intrusion from all four sides of the image. Intrusion

is performed from the maximum meniscus to the minimum

meniscus as selected by the respective menus.

Return Microstructure : after intruding an image, the original particle image may be

returned by selecting this item.

Clear Image: erases current image and allows the user to start over without quitting the

program.

Number:

Number of particles to be placed the next time Add Particles is chosen from the Execute menu.

Particle Size:

Size of particles to be placed the next time Add Particles is chosen from the Execute menu.

Min meniscus:

Minimum intrusion diameter.

Max meniscus:

Maximum intrusion diameter.

Seed:

The random number generator is originally seeded from the computer's internal clock.

Repeatable exercises are possible by selecting one of the three seeds provided under this

34
menu. Each selection of Seed will reset the random generator to either the clock, or one

of the three optional seeds provided.

35
7. APPENDIX B- SURVEY ON USE OF EDUCATION MODULE

1) Has the education module been used in any of the classes you have taught?

Yes No

If no, do you plan to use the module in the future? After answering this, you do not need to complete the remainder of this questionaire.

2) Please list the specific courses in which the module(s) have been used (both course number

and title, indicating if graduate or undergraduate level if not obvious). For each course, also

list which of the four assignments (mercury intrusion, hydration, etc.) were used.

3) In what type of assignment(s) were the modules used (mandatory or optional homework

assignment, in class laboratory, etc.)?

4) Did you use the assignments as provided, modify them, or create your own (if modified or

created, could you please enclose a copy of the assign ment(s) you used)?

36
5) How would you characterize the students' response to the assignments?

6) Will you continue to use this education module in the future?

7) Please list any suggestions/improvements that you have for the education module (including

documentation, graphics displays, specific assignments, etc.)?

*U.5. G.P.0.:1993-341-832:81067 37



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