Development of a mass model in estimating weight-wise particle size distribution using digital image processing

Particle size distribution of coarse aggregates through mechanical sieving gives results in terms of cumulative mass percent. But digital image processing generated size distribution of particles, while being fast and accurate, is often expressed in terms of area function or number of particles. In this paper, a mass model is developed which converts the image obtained size distribution to mass-wise distribution, making it readily comparable to mechanical sieving data. The concept of weight/particle ratio is introduced for mass reconstruction from 2D images of particle aggregates. Using this mass model, the effects of several particle shape parameters (such as major axis, minor axis, and equivalent diameter) on sieve-size of the particles is studied. It is shown that the sieve-size of a particle strongly depend upon the shape parameters, 91% of its variation being explained by major axis, minor axis, bounding box length and equivalent diameter. Furthermore, minor axis gives an overall accurate estimate of particle sieve-size, error in mean size (D-50) being just 0.4%. However, sieve-size of smaller particles (<20 mm) strongly depends upon the length of the smaller arm of the bounding box enclosing them and sieve-sizes of larger particles (>20 mm) are highly correlated to their equivalent diameters. Multiple linear regression analysis has been used to generate overall mass-wise particle size distribution, considering the influences of all these shape parameters on particle sieve-size. Multiple linear regression generated overall mass-wise particle size distribution shows a strong correlation with sieve generated data. The adjusted R-square value of the regression analysis is found to be 99 percent (w.r.t cumulative frequency). The method proposed in this paper provides a time-efficient way of producing accurate (up to 99%) mass-wise PSD using digital image processing and it can be used effectively to replace the mechanical sieving.