The Importance of Particle Packing

Particle packing is taught as part of basic materials processing courses at engineering schools but is poorly understood in the concrete industry. An understanding of the basics is important when making concrete and TecEco are working on software that will incorporate the science of particle packing as the lack of understanding is proving a problem for the implementation of our cements.

To understand particle packing start with a very basic packing of uniform sized round particles. Perfect spheres of the same size result in the least-dense packing, with approximately one-third of the volume being voids. Any deviation from perfect spheres or uniform size, and particles intrude into the nearby void space, reducing the void volume.

Particle Packing of Spheres

The size of spheres does not matter A roomful of basketballs or ping-pong balls still gives roughly one-third free volume. Particle packing for perfect spheres all of the same size is easily calculated.

Particle Packing and the Carbonation of Eco-Cements

Very few people seem to be able to understand the importance of particle packing for making a good Eco-Cement.

Too often the focus is on ease of use rather than end result, For example in the most used 1:1:6 or 1:2:9 (pc, lime, aggregate) type mortar mixes, the aggregates used are generally much too fine and well graded for the lime to serve as much other than a plasticiser. Given the increasing popularity of these mortars and the possibility of carbon credits for sequestration it is essential that the industry get its act together.

Using standard concrete spec sands in Eco-Cement Concretes will not result in good carbonation

Global warming is a major issue and the huge potential in the built environment for sequestering carbon cannot be ignored. There is therefore an urgent need to reconsider the merits of properly carbonating concretes (including mortars) in this context. Cementitious materials like Eco-Cements that go the full thermodynamic cycle gain strength by carbonation and have tremendous potential because the CO2 chemically released during manufacture can be recaptured resulting in significant overall sequestration. With capture during manufacture using the TecEco Tec-Kiln re-carbonation results in sequestration which given the size of the built environment is potentially on a massive scale.

Eco-Cements have the advantage over lime mortars of forming hydrated carbonates which go further as most of their volume is CO2 or water. Being fibrous or acicular they also add microstrucutral strength

Eco-Cements require a highly interconnected void space to allow air to pass through and are are thus best made with relatively mono-graded materials. When choosing aggregates for Eco-Cement Concretes it is therefore best to try to keep the particle sizes as close to the same as possible, so there is a maximum amount of free space available for air flow.

Porecocrete - An Example of a Mono Graded Eco-Cement Concrete

The relatively porous nature of Porecocrete is what allows water to pass through so it can act as a permeable or porous pavement. If water can pass through so can air allowing the Eco-Cements that is holding the stone together.to set by carbonation relatively rapidly.

The Rate of Carbonation is Proportional to Macro Porosity and Declines with Time.

Dense Packing in Tec-Cement Concretes

Most other concretes including Tec-Cement concrete require dense packing in order to minimise void space.

If the voids left by successively smaller particles are filled the density of packing can be substantially increased. Density can also be increased by using non round particles.

More Perfect Packing of Spheres (3 Sizes Case)

Sustainability and Particle Packing

The main goal of TecEco technology is to improve the sustainability of cementitious binders.

Three are several ways in which particle packing interacts with this goal. Eco-Cements only absorb CO2 if they are sufficiently porous and this requires an understanding of relatively mono-graded aggregates.On the other hand the denser Tec-Cements can be made the less binder required.

Optimising the particle packing of Tec-Cement concrete not only results in improved strength but also reduces the porosity, the segregation potential and increases durability. Another way of increasing the sustainability of concrete is to use waste as aggregates and the aim of TecEco is to incorporate as much waste as possible in concretes used in the built environment. Unfortunately few wastes are suitable for use either because of their chemical nature or because of their size distribution. The problem of internal reaction is solved by the chemistry of the new TecEco calcium-magnesium blends whilst more optimal particle packing will by modification allow wastes to be used as aggregates. By the addition of corrective aggregates the overall size distribution can be improved and thus performance. At TecEco we believe the improvement in sustainability that can be achieved with more optimal particle packing to be significant..

The Historical Record

The Romans had two distinct types of concrete mortar and they understood the particle packing requirements of both. One was made with simple lime and river sand, mixed at a ratio of three parts sand to one part lime. The other type used pozzolan instead of river sand and was mixed at a ratio of two parts pozzolan to one part lime. The former required coarse gritty aggregates described below whilst the latter was even tamped into position to increase density.

The oldest record we have come across addressing the issue of sands for carbonating cements is book II, chapter IV of the Ten Books of Architecture by Vitruvius Pollio (Vitruvius). According to Vitruvius “the best (sand for carbonating mortars) will be found to be that which crackles when rubbed in the hand, while that which has much dirt in it will not be sharp enough. Again: throw some sand upon a white garment and then shake it out; if the garment is not soiled and no dirt adheres to it, the sand is suitable” Vitruvious was talking about gritty sand with no fines.

There is no doubt that sand grading is one of the most important parameters for mortar and concrete. As a further example of older literature supporting our view that coarse sands lacking in fines are required for carbonating mortars are the comments by the 16th century architect Andrea Palladio, renowned for "The Four Books of Architecture" which were translated into English in the early 18th century and used as a principal reference for building for almost two centuries (Palladio, Isaac Ware translation, 1738). In the first book Palladio says, inter alia, "the best river sand is that which is found in rapid streams, and under water-falls, because it is most purged". In other words, it is coarse. Compare this with most sand for use in mortar today.

Further Information

The excellent text book by Francois de Larrard[1] provides a full mathematical analysis of particle packing. Experimental work backed up by the mathematical theory of Larrard (1999) indicates that the mean particle size of the magnesium oxide we use at around 8 micron is not far off the right size for ideal packing with Portland cement which in Australia has a mean particle size of around 20 um. (Thomas 2006 [2]). Assuming spheres Larrard calculates a ratio of 1:2.41 (Larrard, 1999).

Conference paper 25 by John Harrison our managing director.[3]


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[1] de Larrard, F. (1999). Concrete Mixture Proportioning: A Scientific Approach, E & FN Spon.

[2] Tony Thomas, chief concrete engineer for Boral Limited in Australia. Personal communication.

[3] Harrison, John (2005) Carbonating and Hydraulic Mortars - the difference is not only in the binder. Aggregates are also important. Proceedings Concrete 05, Concrete Institute of Australia, 17-19 October, 2005, Melbourne