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Generation of spherical particles following measured PSD

The program genpart3d.c, whose listing is provided in Appendix B, is used to place digitized spherical particles of a user specified particle size distribution into a three-dimensional computational volume, typically 100 pixels on a side. 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 and gypsum) 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 which should be gypsum 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, a mass to number basis conversion (easily implemented in a spreadsheet) may be required. As input, the user must specifically supply the number of different size spheres to use (parameter NUMSIZES determines the maximum number of different sizes allowed), a dispersion factor (0, 1, or 2) which specifies the minimum pixel separation to be maintained between all pairs of particles, and a probability (0.0 to 1.0) for the generation of gypsum particles instead of cement. Following this, the user, for each different size class of spheres, provides the number and radius (size) 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 to the cement paste. However, it should be noted that for lower water-to-cement ratios (< 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 2 provides a listing of the number of pixels contained in spheres of various diameters in pixels, which should prove useful in creating user specific PSDs. It should be noted that the diameter = 2 x radius + 1 so that all spheres may be centered exactly on a pixel.
• 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) which 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 [9], perhaps into a single floc.

  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

  
  Table 2: Volume in Pixels Occupied by Spheres of Various Diameters
  

• 4) Measure phase fractions: outputs the number of pixels of cement, gypsum, and aggregate present in the 3-D microstructure.
• 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 [10]. 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 cement particle or gypsum pixels contained within its boundaries.
• 6) Measure single phase connectivity: allows the user to employ a burning algorithm [11] 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 which 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) present in parallel planes at various fixed distances (one pixel increments) from the aggregate surface.
• 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, gypsum, and porosity), and the second for storage of the individual particle IDs (to be used in assessing the setting of the cement during hydration).

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