Nonlinear modelling of packing of aggregates of four sizes with fixed compaction effort


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Title: Nonlinear modelling of packing of aggregates of four sizes with fixed compaction effort

Author(s): Abhay Bulsari, Dr., Klaus Juvas

Publication: NCR

Volume: 42

Issue: 2

Appears on pages(s): 17-30

Keywords: Mix design, nonlinear modelling, aggregate packing

Date: 12/15/2010

Packing of particles of different sizes is of enhanced interest to concrete industries these days, particularly to be able to reduce cement consumption. It is not easy to mathematically describe the packing of particles of more than two different sizes, especially when the particle shape too might be difficult to describe. In the real world, each "size" or aggregate actually implies a particle size distribution which can be fairly wide, and overlapping with sizes of the other aggregates.In 2008, the authors presented a solution for packing of particles of three sizes, indicating how the minimum voidage can be calculated. Packing of particles of four sizes is more interesting from a scientific point of view, as well as from the industrial point of view. As this paper makes it clear, the optimal packing of particles of four sizes is at least as good as the optimal packing of three sizes, and usually better. This means that one can usually save more cement by optimally mixing particles of four sizes than by mixing only three sizes.It is difficult to develop physical models predicting the packing characteristics of particles of three or more sizes. Empirical modelling is a good approach if nonlinearities are taken into account. New techniques of nonlinear modelling, however, make this kind of model development feasible. From a limited amount of experimental data, one can develop nonlinear models of a good accuracy.This paper illustrates with an example how nonlinear models can describe sufficiently well the packing of aggregates of four sizes with a wide variation in their diameters.

Norwegian Concrete Association, International Partner Access.

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