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Compaction-interaction packing model: regarding the effect of fillers in concrete mixture design

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An Erratum to this article was published on 25 January 2013

Abstract

For the design of defined-performance concrete, predicting the material properties of concrete becomes more and more important. To be able to select the right type of fillers and control the water demand in such mixtures, an extension to the compressible packing model was developed to optimize the particle packing of aggregates as well as powders in concrete. Modelling mixtures with particles smaller than 125 μm requires advanced interaction equations, taking due account of surface forces like van der Waals forces, electrical double layer forces and steric forces. In this paper the equations for the newly developed compaction-interaction packing model are presented, including the additional effects of agglomerating particles on the wall and loosening effect. Calculated packing densities are related to the results of compressive strength experiments on 50 mortar mixtures. Higher packing densities leave less space for voids to be filled with water, which reduces the water demand and increases the strength of concrete mixtures. This is shown by the cement spacing concept. The relation between the cement spacing factor and strength can be used as a tool to predict concrete strength in defined-performance concrete mixtures.

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Abbreviations

α :

Packing density of a mixture (–)

α e :

Experimentally determined packing density of a mixture for a prescribed packing process and K value (–)

α i :

Packing density of size class i (–)

α t :

Calculated packing density of a mixture (–)

β :

Virtual packing density of a mixture (–)

β i :

Virtual packing density of size class i (–)

β ti :

Calculated virtual packing density of a mixture when size class i is dominant (–)

\( {\varphi_{cem}} \) :

Partial volume occupied by the cement in a stable particle structure (–)

\( \varphi_{cem}^* \) :

Maximum partial volume that the cement may occupy given the presence of other particles (–)

φ i :

Partial volume: the volume occupied by size class i in a unit volume (–)

\( \varphi_i^* \) :

Maximum partial volume that size class i may occupy given the presence of the other particles (–)

\( {\varphi_{mix}} \) :

Partial volume of all the particles of a mixture in a unit volume (–)

a ij :

Factor which describes the loosening effect caused by the particles in size class j on the packing density of the particles in size class i (–)

b ij :

Factor which describes the wall effect caused by the particles in class j on the packing of the particles in class i (–)

C :

Parameter in Féret’s equation (N/mm2)

C a :

Compaction-interaction constant within the loosening effect a ij,c (–)

C b :

Compaction-interaction constant within the wall effect b ij,c (–)

d c :

Transition diameter in the CIPM below which compaction-interaction is taken into account (m)

d i :

Diameter of size class i. In the CIPM i = 1 for the largest diameter (m)

f c :

Concrete compressive strength (N/mm2)

i :

Integer denoting the dominant size class in a mixture

j :

Integer denoting a size class in a mixture

K :

Compaction index (–)

K cem :

The sum of all K i values representing the size classes of the cement (–)

K i :

Partial compaction index of size class i within CIPM (–)

K t :

Compaction index of a mixture within CIPM (–)

n :

Number of size classes in a mixture

r cem :

Volume fraction of the cement in a mixture (–)

r i :

Volume fraction of size class i, by definition \( r_{i} = {{\varphi _{i} } \mathord{\left/ {\vphantom {{\varphi _{i} } {\sum\limits_{{i = 1}}^{n} {\varphi _{i} } }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{{i = 1}}^{n} {\varphi _{i} } }}{\text{ and }}\sum\limits_{{i = 1}}^{n} {r_{i} = 1} \) (–)

V :

Volume (m3)

V a :

Volume of the air in a mixture (m3)

V c :

Volume of the cement particles in a mixture (m3)

V ew :

Volume of excess water in a mixture (m3)

V p :

Volume of all the particles in a mixture (m3)

V vw :

Volume of void water in a mixture (m3)

V w :

Volume of the water in a mixture (m3)

w 0,a :

Function for maximum range of loosening effect (–)

w 0,b :

Function for maximum range of wall effect (–)

w a :

Constant denoting the maximum range of loosening effect (–)

w b :

Constant denoting the maximum range of wall effect (–)

CIPM:

Compaction-interaction packing model

CSF:

Cement spacing factor

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Acknowledgments

This research was supported by the Dutch Technology Foundation STW, applied science division of NWO and the Technology Program of the Ministry of Economic Affairs. The experiments were performed by the technicians of the Stevin Laboratory of Delft University of Technology, which is very much appreciated.

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  1. Delft University of Technology, Faculty of Civil Engineering and Geosciences, Stevinweg 1, 2628 CN, Delft, The Netherlands

    S. A. A. M. Fennis, J. C. Walraven & J. A. den Uijl

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  1. S. A. A. M. Fennis
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  2. J. C. Walraven
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  3. J. A. den Uijl
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Correspondence to S. A. A. M. Fennis.

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Fennis, S.A.A.M., Walraven, J.C. & den Uijl, J.A. Compaction-interaction packing model: regarding the effect of fillers in concrete mixture design. Mater Struct 46, 463–478 (2013). https://doi.org/10.1617/s11527-012-9910-6

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