An efficient way to determine the optimal packing offour aggregates with nonlinear modelling

Numerical methods leading to cement savings

One effective means of reducing cement consumption without losing on strength is by mixing aggregates in proper proportions. The minimum voidage obtained by mixing three aggregates is typically less than the minimum voidage obtained by mixing any two of those three. Similarly, the minimum voidage obtained by mixing four aggregates is typically less than the minimum voidage obtained by mixing any three of those four aggregates. It therefore makes sense to mix four aggregates in proportions which will result in minimum voidage. Still better, whenever there is a choice, one should select such four aggregates which will lead to a maximum advantage. It is not easy to accurately calculate the resulting voidage of a mix of three or more aggregates. The aggregates can have a narrow or a wide particle size distribution, and can have different shapes. Physical modelling in this situation is not very effective, neither is empirical modelling based on conventional, linear statistical techniques. Nonlinear modelling has been shown to be efficient in such situations. This article describes how nonlinear models from a modest series of experiments help determine the proportions of aggregates for minimum voidage or relative volume.

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