The computer code has been designed to be applicable to any mixture proportions of interest. The user needs to specify the aggregate particle size distribution and the best set of aspect ratios to use to characterize the shape of the aggregates. The ITZ thickness will generally be controlled by the median cement particle size , but will be further reduced in systems containing silica fume or other ultrafine particles. The code could be easily extended to model a 3-D concrete consisting of spherical air voids, ellipsoidal aggregates, and fibers, for any mixture proportion of interest. Each particle type could have its own ITZ characteristics so that lightweight aggregates with no discernible ITZ region could be mixed with conventional aggregates and air voids with a measurable ITZ thickness.
All of the studies presented in this paper have been conducted at a constant coarse aggregate to fine aggregate mass ratio of 1.5 to 1. Increasing this ratio, as is often the case when applying ACI mixture proportioning procedures for high strength concrete [45,46], has a tendency to shift the PSD towards the coarse coarse, coarse fine (cCcF) distribution, shown in Figure 2. One example of this would be the mixture proportions employed by Sanjayan and Stocks  for a high strength concrete which exhibited substantial spalling. They used a coarse aggregate to fine aggregate ratio of 2.12, as opposed to a ratio of 1.5 for their normal strength concrete (which did not exhibit spalling). This higher coarse to fine ratio would shift the PSD to the coarser region, where as indicated by Table I, the ITZ regions could easily be depercolated in a high performance concrete. Conversely, Shirley et al.  employed ratios varying between 1.0 and 1.6, and did not observe any spalling for either normal strength or high strength specimens. Ratios below 1.5 would tend to shift the PSD towards the fine coarse, fine fine (fCfF) distribution, where as indicated by the results in Table I, spalling would not be expected to be a problem. In this case, the ITZ regions would be expected to be percolated even for an HPC. Thus, the hypothesis developed in this paper lends support to the sporadicity of spalling observations in various research studies. Compressive strength alone is not the controlling variable, as it is the exact mixture proportions employed in each study that are of paramount importance. Likewise, the aggregate content alone is insufficient to make a spalling determination, as both aggregate volume fraction and particle size distribution are critical variables influencing the percolation of the ITZ regions.
For lightweight aggregate and ultra-high performance concretes, the ITZ regions can be effectively eliminated so that quite large concentrations of fibers (2 % to 5 %) may be needed to provide their own percolated pathway. In the case of lightweight aggregates, a promising compromise would be to use saturated lightweight fines along with normal weight coarse aggregates, with on the order of 0.5 % by volume of fibers to percolate the coarse aggregate network. This may be viable because, as observed in Figs. 4 and 5, it is the larger aggregate particles which comprise the major portion of the percolated network created by the addition of fibers. Additionally, the use of saturated lightweight fines will reduce self-desiccation and subsequent autogenous shrinkage, which is another Achilles heel of many HPCs [47,48,49,50]. As our basic understanding of concrete microstructure continues to develop, the potential for engineering solutions via "designer" concrete mixture proportions appears promising. The presented computational model provides a powerful tool for tailoring the exact concrete mixture proportions to the intended application.