Page 5 - February-2022

TECHNICAL PAPER

comprise a range of discrete particle size classes. As with the resulting powder material combination was incorporated as
CPM, the model considers geometric particle interaction by a constraint into an algorithm based on the MAAC (originally
‘wall’ and ‘loosening’ effects and the influence of compaction developed in ) to optimize the remaining fine and coarse
[8]
on the determination of packing density but, in addition, aggregate fractions. Integrating the CIPM and MAAC enabled
acknowledges the governing role of surface forces on powder consideration of surface force interaction for powder packing
material packing. It does so by using model constants (C a and but did not neglect the packing of fine and coarse aggregates,
C b ) to decrease and increase ‘wall’ and ‘loosening’ effects, while achieving acceptable computing times.
respectively, for particles with diameter < d c , a cut-off diameter

below which surface forces govern packing. In doing so, it 2.2 Preliminary experimental investigation
increases the accuracy of the prediction of power material Experimental packing density data was required initially to
packing density . The CIPM requires an input of the particle size calibrate the CIPM, and was obtained using the mixing energy
[3]
distribution (PSD) of the materials to be used and the packing test. Calibration procedures are detailed elsewhere .
[6]
density per size class of material. It is necessary to calibrate the
model for a particular experimental compaction process by 2.2.1 Powder packing density - mixing energy
assigning a compaction index (K), and for the extent of surface test
force interaction by the constants C a , C b , and d c . Governing
model relationships are described in detail in . The mixing energy test entailed the indirect measurement
[6]
of packing density by measuring the water demand of a
2.1.2 MAAC powder material [3,8] . The experiment entails measuring the
power consumption of a mixer while mixing a powder-paste
The MAAC was developed based on particle geometry (material <125 µm + water) as the water content is gradually
[7]
and dimensional analysis and is suited to modelling packing increased. The addition of water to a powder material leads to
of aggregate particles, primarily governed by shear and the formation of capillary bridges (pendular bonds) localized
gravitational forces. The MAAC considers a poly-disperse at particle contacts, causing the agglomeration of particles
system of particles to comprise a continuous distribution of (Figure 1). Capillary bridge bond strength increases with
particles. Broadly, the model proposes an ideal PSD for a liquid-vapour surface energy and depends on the inverse of
mixture of materials based on the PSD of each of the input the square of the particle diameter . While the mixture is still
[3]
materials, the absolute maximum and minimum particle sizes of undersaturated, the strength of the agglomerates increases
the mixture, and a distribution coefficient (q) equal to 0.37 . The with the addition of liquid and corresponds to increasing
[7]
ideal PSD is proposed as the mixture of materials that enables power consumption of the mixer. At the point of saturation,
the maximum packing density. there is an absence of internal liquid-vapour surfaces, causing a
sudden decrease in bond strength and a decrease in the power
2.1.3 Integration of the CIPM and MAAC consumption of the mixer with further addition of liquid.

The implementation of the CIPM in Microsoft Excel led to Figure 1 shows the progression of the saturation state of a
impractical computing times when extending it to consider all powder mixture as more water is added. Maximum power
particle size classes present in a concrete mix, from micrometres consumption occurs at the capillary state where the air is
(powders) to centimetres (coarse aggregates). This was therefore assumed to be completely displaced from the particle structure;
resolved by optimizing only powder packing density using the thereby, the water volume at this state is equated to the void
CIPM to specifically account for surface forces. Thereafter, the volume.

Air Particles Water

Pendular Funicular Capillary Droplet
Figure 1: Progression of the moisture state of a powder mixture with constant addition of water

8 THE INDIAN CONCRETE JOURNAL | FEBRUARY 2022