Mix Proportioning of Aggregates for Concrete by Three Different Approaches

Mix proportions of $n$ aggregate groups to form a combined aggregate batch for each one of 28 target curves of gradations from very stony to very sandy, all within and parallel to the granulometric bound curves of the German Standard: DIN-1045, are computed by three different approaches. The sum of the ratios of $n$ aggregate groups must equal 1 by any method. For any one of $m$ standard sieves, the sum of percent passings of $n$ groups multiplied by their ratios must equal the percent passing of a target curve, which is a linear equation, and $m$ linear equations result for $m$ sieves. Therefore, along with the first equation, the first approach composes the rest ($n-1$) number of linear equations out of any ($n-1$) number of $m$ standard sieves. In the second approach, a quasi-least-squares algorithm is used to minimize the sum of squares of differences of percent passings of the combined aggregate batch from those of a target curve for all sieves. In the third approach, the artificial bee colony (ABC) algorithm is used to minimize the sum of the absolute differences of the percent passings of the combined aggregate batch from those of a target curve for all sieves. The three approaches give mostly close solutions for many cases.