Statistical repeatability and calculation of“porosity volume fraction”

The geometry for the models was created using a Python script. Python is the underlying language for the Abaqus CAE tool (the pre-processor for the Abaqus package), so this programme enabled much of the geometry creation and meshing activity for the finite element models to be undertaken automatically.
While it is reasonably possible to create large numbers of example models, it is less reasonable to analyse each of them and present all of those results, but it is reasonable to question the statistical variation between results. To do this efficiently, the Python script was modified, to remove the Abaqus specific instructions, and to carry out some additional calculations for number of pores, total area of pores, and the “porosity volume fraction” defined as being the total area of the pores divided by the defined zone area.
Because the calculation for porosity volume fraction was based on the area of the defined zone for pore centres, it is clear that this definition is inadequate, because it fails to recognise that pores near the edges of the zone can overlap. This problem is illustrated in Figure 4. The error is particularly significant for larger maximum pore sizes.