Yahya Ghasemi Print III pdf

6. DISCUSSION AND CONCLUSIONS
6.1. Accuracy of particle packing models
Particle packing theory is commonly used as a tool for concrete mix design and thus it is 
necessary to study the accuracy of packing models. Suitability of the models was decided 
based on the mean difference from the laboratory data and it was concluded that all of the 
models can predict the packing density of the mixture with acceptable accuracy while some 
models are able to estimate packing density of specific mixtures better comparing to the 
others. The judgement of appropriateness in accuracy of the models comes from the fact that 
experimental packing density of a given sample after correction for container wall effect 
includes a deviation of 1 to 2% as a result of randomness in arrangement of the particles. 
Hence, errors less than 2% for the models are considered acceptable. Moreover, it was found 
that the deviation of the calculated data from laboratory measurements can be related to the 
mean diameter ratio between the two classes (mean diameter of fine and coarse fractions). 
Results of the studies imply that as the mean size ratio of fines over coarse material decreases 
the accuracy of CPM and Modified Toufar increase. Contrariwise, 4C is more suitable with 
higher mean size ratios.
While the descriptions on how the packing density is calculated are rather strictly 
demonstrated, the concept of optimum packing and the approach to define it remains unclear.
6.2. Estimation of specific surface area
Water and paste layer theories can be used as a tool in mix design where it is necessary to 
have an accurate measure of specific surface area (SSA) as an input in the models. However, 
there are no commonly accepted approaches to measuring the specific surface area of 
aggregates and in general the tests that can measure SSA are expensive and include highly 
device related complexities. 
An easier method for estimating the specific surface area is to calculate SSA derived from 
grading curve and based on the assumption of spherical shape for the particles. However, the 
mentioned method does not include the effect of square-cube law. In order to make the 
calculation of SSA more accurate, a group of scenarios were studied where the assumption of 
spherical shape was replaced by the assumption of platonic solid shape for the aggregates to 
count for the angularity and also to implement the square-cube law in the equations. It was 
found that the SSA can be much higher for certain aggregates if particles were assumed to be 

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Discussion and conclusions
cubic in shape instead of spherical. As an example, SSA of Quartz powder (see Table 5.1) 
becomes 50% larger if the assumption of spherical shape is replaced by cubical shape. This
shows the significance of shape of aggregates and the corresponding surface area/volume 
ratio growth (based on square-cube law) on computation of SSA and consequently the 
calculations related to water or paste layer theories. Thus, for more angular elongated flaky 
particles, the assumption of an angular platonic solid will lead to better estimation of SSA this 
is especially true for the materials with high fine content.