Generation of spherical particles following measured PSD

The program genpartnew.c, whose listing is provided in Appendix B, is used to place digitized spherical particles of a user specified PSD into a three-dimensional computational volume, typically 100 pixels on a side. Periodic boundaries are employed such that a particle that extends outward through one or more faces of the 3-D microstructure is completed extending inward through the opposite face(s). Digitized spherical particles are used to approximate the complex three-dimensional shapes of actual cement particles; previous results have indicated that this approximation is adequate if the actual cement PSD and phase volume and surface fractions are maintained in the 3-D spherical particle image [1,2,10]. Initially, the user must provide a negative integer to be used as the random number seed. Following this, the program is menu driven with the following main menu options:

• 1) Exit: Exit the program
• 2) Add spherical particles (cement, mineral admixtures, and calcium sulfate) to microstructure: allows the user to specify the discretized particle size distribution that should be used, the number of particles to place, the proportion of particles that should be calcium sulfate (gypsum, hemihydrate, and/or anhydrite) as opposed to cement, and whether the particles should be dispersed. The particle size distribution should be on a number basis. Since most particle size analyzers provide the distribution on a mass basis (see Table 2 for example), a mass to number basis conversion (easily implemented in a spreadsheet) may be required. An example Excel spreadsheet is provided in Appendix A of this manual and is available for downloading from the anonymous ftp site as cem133.xls. For genpartnew, as input, the user must specifically supply the number of different size spheres to use (program parameter NUMSIZES determines the maximum number of different sizes allowed), a dispersion factor (0, 1, or 2) that specifies the minimum pixel separation to be maintained between all pairs of particles, a probability (0.0 to 1.0) for the generation of calcium sulfate particles instead of cement, and probabilities (0.0 to 1.0) for the hemihydrate and anhydrite versions of calcium sulfate (as opposed to gypsum/dihydrate). Following this, the user, for each different size class of spheres, provides the number, radius (size), and phase identifier characterizing that size class. The user should always begin with the largest particles and proceed consecutively to the smallest particles. Otherwise, after placing some of the smallest particles, no spaces where the largest particles can fit may remain in the 3-D microstructure. The dispersion capability has been included to simulate the effects of adding a superplasticizer or high range water reducer to the cement paste. However, it should be noted that for lower water-to-cement ratios (w/c <0.45), it may not be possible to place all of the requested particles in a dispersed configuration. In this case, the program will exit after parameter MAXTRIES unsuccessful attempts at finding a random location for a particle. Table 3 provides a listing of the number of pixels contained in spheres of various diameters in pixels, that should prove useful in creating user specific PSDs. It should be noted that the diameter=2*radius+1, so that all spheres may be centered exactly on a pixel. One pixel (or 1 µm) particles are typically added in the program disrealnew, just prior to executing the hydration, to significantly reduce the memory needed to execute the genpartnew program.
• 3) Flocculate system by reducing number of particle clusters: allows the user to create any desired number of flocs (clusters) by randomly moving each particle (cluster) centroid in one-pixel increments and aggregating any particles (clusters) that contact one another during this process. The only input required is the user requested number of clusters (flocs) to be present at the end of execution of the routine. Typically, if no superplasticizer or water reducing agent is used, the cement particles will have a great tendency to flocculate together [ 11], perhaps into a single floc structure.

  
  

  Table 3: Volume in Pixels Occupied by Spheres of Various Diameters

  
  

  Diameter (pixels)	Pixels per sphere
  3	19
  5	81
  7	179
  9	389
  11	739
  13	1189
  15	1791
  17	2553
  19	3695
  21	4945
  23	6403
  25	8217
  27	10395
  29	12893
  31	15515
  33	18853
  35	22575
  37	26745
  39	31103
  41	36137
  43	41851
  45	47833
  47	54435
  49	61565
  51	69599
  61	119009
  73	203965

  
  
  
  
  

• 4) Measure phase fractions: outputs the number of pixels of porosity, cement, the three forms of calcium sulfate, pozzolan (silica fume), inert filler, fly ash, and aggregate present in the 3-D microstructure. This selection is useful for checking the calcium sulfate volume fraction and the initial w/c ratio of the 3-D cement microstructure (neglecting the one-pixel particles that will be added at disrealnew execution time).
• 5) Add an aggregate to the microstructure: allows the user to add a single flat plate aggregate to the 3-D microstructure for studying the development of microstructure in the interfacial transition zone [12]. The only required input is the thickness of the aggregate to be placed, which must be an even integer. Typically, the user should place an aggregate (if desired) into the microstructure before placing any of the cement particles. Otherwise, the aggregate will simply overlap and replace any solid particle pixels contained within its boundaries.
• 6) Measure single phase connectivity: allows the user to employ a burning algorithm [13] to determine the percolation characteristics of either the porosity or the solids present in the 3-D microstructure. The user must specify the phase in which they are interested and the routine returns the number of pixels of that phase which are accessible from the top of the 3-D microstructure along with the number of pixels that are contained in pathways that traverse (span) the microstructure.
• 7) Measure phase fractions vs. distance from aggregate: outputs a listing of the number of pixels of each phase (cement, gypsum, porosity, etc.) present in parallel planes at various fixed distances (one pixel increments) from the aggregate surface. When this menu selection is executed, the results are reported to the standard output (screen) and are also written in a datafile named agglist.out. If the user wishes to preserve this output file, they must rename it to a name of their choosing immediately upon leaving the genpartnew program.
• 8) Output microstructure to file: allows the user to save the created microstructure to files. The user must supply two filenames, one for the storage of the actual microstructure (cement, calcium sulfates, fillers, and porosity), and the second for storage of the individual particle IDs (to be used in assessing the setting of the cement during hydration using the disrealnew program).

When adding calcium sulfate to the cement, the user has basically two choices. If only the composite PSD for the cement and gypsum (sulfate) is known, the user can simply specify the volume fraction of particles that should be randomly assigned to be calcium sulfate. Conversely, if the actual separate PSD of the calcium sulfate is known, the user can use a value of 0.0 for this randomly-assigned volume fraction and specify the actual numbers of each size calcium sulfate particle to be placed, in a manner analogous to that used for cement. When the separate cement and calcium sulfate PSDs are "merged" in this fashion, the user should be sure to add all the largest radius particles (e.g., first the cement, then the calcium sulfate) first before proceeding to the next smaller radius particles. If this second option is to be utilised, in the program genpartnew, a phase ID of 1 corresponds to cement, 5 to calcium sulfate (dihydrate), 6 to hemihydrate, and 7 to anhydrite, as shown in the program listing in Appendix B.

An annotated example datafile for using genpartnew (with random calcium sulfate assignment) is as follows:

-3402                   random number seed
2                       menu choice to place spherical particles
16                      number of size classes to place
0                       dispersion distance in pixels
0.055                   calcium sulfate volume fraction
0.0 0.0          fractions of calcium sulfate that are hemihydrate and anhydrite
1                       number of spheres of size class 1
17                      radius of spheres of size class 1
1                       phase ID of spheres of size class 1 (cement=1)
1                       number of spheres of size class 2
15                      radius of spheres of size class 2
1                       phase ID of spheres of size class 2 (cement)
1                       number of spheres of size class 3
14                      radius of spheres of size class 3
1                       phase ID of spheres of size class 3 (cement)
1                       number of spheres of size class 4
13                      radius of spheres of size class 4
1                       phase ID of spheres of size class 4 (cement)
2                       number of spheres of size class 5
12                      radius of spheres of size class 5
1                       phase ID of spheres of size class 5 (cement)
2                       number of spheres of size class 6
11                      radius of spheres of size class 6
1                       phase ID of spheres of size class 6 (cement)
3                       number of spheres of size class 7
10                      radius of spheres of size class 7
1                       phase ID of spheres of size class 7 (cement)
4                       number of spheres of size class 8
9                       radius of spheres of size class 8
1                       phase ID of spheres of size class 8 (cement)
8                       number of spheres of size class 9
8                       radius of spheres of size class 9
1                       phase ID of spheres of size class 9 (cement)
12                      number of spheres of size class 10
7                       radius of spheres of size class 10
1                       phase ID of spheres of size class 10 (cement)
21                      number of spheres of size class 11
6                       radius of spheres of size class 11
1                       phase ID of spheres of size class 11 (cement)
41                      number of spheres of size class 12
5                       radius of spheres of size class 12
1                       phase ID of spheres of size class 12 (cement)
93                      number of spheres of size class 13
4                       radius of spheres of size class 13
1                       phase ID of spheres of size class 13 (cement)
243                     number of spheres of size class 14
3                       radius of spheres of size class 14
1                       phase ID of spheres of size class 14 (cement)
692                     number of spheres of size class 15
2                       radius of spheres of size class 15
1                       phase ID of spheres of size class 15 (cement)
4063                    number of spheres of size class 16
1                       radius of spheres of size class 16
1                       phase ID of spheres of size class 16 (cement)
4                       menu selection to report phase counts
8                       menu selection to output current microstructure to file
cem133wc030n1.img       filename to save image to
pcem133wc030n1.img      filename to save particle IDs to
1                       menu selection to end program

The output created by executing the program genpartnew with the above input datafile is as follows:

Enter random number seed value (a negative integer) 
-3402 
 
 Input User Choice 
1) Exit 
2) Add spherical particles (cement,gypsum, pozzolans, etc.) to microstructure 
3) Flocculate system by reducing number of particle clusters 
4) Measure global phase fractions 
5) Add an aggregate to the microstructure 
6) Measure single phase connectivity (pores or solids) 
7) Measure phase fractions vs. distance from aggregate surface 
8) Output current microstructure to file 
2 
Enter number of different size spheres to use(max. is 30) 
16 
Enter dispersion factor (separation distance in pixels) for spheres (0-2) 
0 corresponds to totally random placement 
0 
Enter probability for gypsum particles on a random particle basis (0.0-1.0) 
0.055000 
Enter probabilities for hemihydrate and anhydrite forms of gypsum (0.0-1.0) 
0.000000 0.000000
Enter number, radius, and phase ID for each sphere class (largest radius 1st) 
Phases are 1- Cement and (random) calcium sulfate, 5- Gypsum, 6- hemihydrate 
7- anhydrite 8- Pozzolanic, 9- Inert, 25- Fly Ash 
Enter number of spheres of class 1 
1 
Enter radius of spheres of class 1 
(Integer <=25 please) 
17 
Enter phase of spheres of class 1 
1 
Enter number of spheres of class 2 
1 
Enter radius of spheres of class 2 
(Integer <=25 please) 
15 
Enter phase of spheres of class 2 
1 
Enter number of spheres of class 3 
1 
Enter radius of spheres of class 3 
(Integer <=25 please) 
14 
Enter phase of spheres of class 3 
1 
Enter number of spheres of class 4 
1 
Enter radius of spheres of class 4 
(Integer <=25 please) 
13 
Enter phase of spheres of class 4 
1 
Enter number of spheres of class 5 
2 
Enter radius of spheres of class 5 
(Integer <=25 please) 
12 
Enter phase of spheres of class 5 
1 
Enter number of spheres of class 6 
2 
Enter radius of spheres of class 6 
(Integer <=25 please) 
11 
Enter phase of spheres of class 6 
1 
Enter number of spheres of class 7 
3 
Enter radius of spheres of class 7 
(Integer <=25 please) 
10 
Enter phase of spheres of class 7 
1 
Enter number of spheres of class 8 
4 
Enter radius of spheres of class 8 
(Integer <=25 please) 
9 
Enter phase of spheres of class 8 
1 
Enter number of spheres of class 9 
8 
Enter radius of spheres of class 9 
(Integer <=25 please) 
8 
Enter phase of spheres of class 9 
1 
Enter number of spheres of class 10 
12 
Enter radius of spheres of class 10 
(Integer <=25 please) 
7 
Enter phase of spheres of class 10 
1 
Enter number of spheres of class 11 
21 
Enter radius of spheres of class 11 
(Integer <=25 please) 
6 
Enter phase of spheres of class 11 
1 
Enter number of spheres of class 12 
41 
Enter radius of spheres of class 12 
(Integer <=25 please) 
5 
Enter phase of spheres of class 12 
1 
Enter number of spheres of class 13 
93 
Enter radius of spheres of class 13 
(Integer <=25 please) 
4 
Enter phase of spheres of class 13 
1 
Enter number of spheres of class 14 
243 
Enter radius of spheres of class 14 
(Integer <=25 please) 
3 
Enter phase of spheres of class 14 
1 
Enter number of spheres of class 15 
692 
Enter radius of spheres of class 15 
(Integer <=25 please) 
2 
Enter phase of spheres of class 15 
1 
Enter number of spheres of class 16 
4063 
Enter radius of spheres of class 16 
(Integer <=25 please) 
1 
Enter phase of spheres of class 16 
1 
 
 Input User Choice 
1) Exit 
2) Add spherical particles (cement,gypsum, pozzolans, etc.) to microstructure 
3) Flocculate system by reducing number of particle clusters 
4) Measure global phase fractions 
5) Add an aggregate to the microstructure 
6) Measure single phase connectivity (pores or solids) 
7) Measure phase fractions vs. distance from aggregate surface 
8) Output current microstructure to file 
4 

 Phase counts are: 
Porosity= 569660 
Cement= 406682 
Gypsum= 23658 
Anhydrite= 0 
Hemihydrate= 0 
Pozzolan= 0 
Inert= 0 
Fly Ash= 0 
Aggregate= 0 
 
 Input User Choice 
1) Exit 
2) Add spherical particles (cement,gypsum, pozzolans, etc.) to microstructure 
3) Flocculate system by reducing number of particle clusters 
4) Measure global phase fractions 
5) Add an aggregate to the microstructure 
6) Measure single phase connectivity (pores or solids) 
7) Measure phase fractions vs. distance from aggregate surface 
8) Output current microstructure to file 
8 
Enter name of file to save microstructure to 
cem133wc030n1.img
Enter name of file to save particle IDs to 
pcem133wc030n1.img
 
 Input User Choice 
1) Exit 
2) Add spherical particles (cement,gypsum, pozzolans, etc.) to microstructure 
3) Flocculate system by reducing number of particle clusters 
4) Measure global phase fractions 
5) Add an aggregate to the microstructure 
6) Measure single phase connectivity (pores or solids) 
7) Measure phase fractions vs. distance from aggregate surface 
8) Output current microstructure to file 
1

The user can easily calculate that the achieved calcium sulfate volume fraction
(23658)/(23658+406682)=0.054975 is very close to the requested value of 0.055. A two-dimensional (postscript) image slice from the microstructure created using this datafile with genpartnew is shown in the left side of Fig. 3. The 2-D raw image file (ppm format) was created using the program oneimage.c, whose listing is also provided in Appendix B. The file created by this program can be easily read into an imaging program, resized, and output in a variety of file formats (gif, jpeg, postscript, etc.).

  

Figure 3: Two-dimensional slices from 3-D microstructures for cement 133 with w/c ratios of 0.30 (left) and 0.45 (right). At this point, only particles greater than 2 pixels (µm) in diameter have been placed in these microstructures. Color assignments are black- porosity, red- cement, and grey- gypsum. Gypsum volume fraction is approximately 5.5 %. Images are 100 pixels x 100 pixels.