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D.P. Bentz^{(1)}, J.T.G. Hwang^{(2)}, C. Hagwood^{(3)},
E.J. Garboczi^{(1)},
K.A. Snyder^{(1)}, N. Buenfeld^{(4)}, and K.L. Scrivener^{(4)}

^{(1)} Building and Fire Research Laboratory, Building 226, Room B-350,
National Institute of Standards and Technology, Gaithersburg, MD 20899 USA

^{(2)} Cornell University, Ithaca, NY 14853 USA

^{(3)} Information Technology Laboratory,
National Institute of Standards and Technology, Gaithersburg, MD 20899 USA

^{(4)} Imperial College of Science and Technology, London, SW7 2BP ENGLAND

** ABSTRACT**

Previously, a hard core/soft shell computer model was developed to simulate the overlap and percolation of the interfacial transition zones surrounding each aggregate in a mortar or concrete. The aggregate particles were modelled as spheres with a size distribution representative of a real mortar or concrete specimen. Here, the model has been extended to investigate the effects of aggregate shape on interfacial transition zone percolation, by modelling the aggregates as hard ellipsoids, which gives a dynamic range of shapes from plates to spheres, to fibers. For high performance concretes, the interfacial transition zone thickness will generally be reduced, which will also affect their percolation properties. This paper presents results from a study of the effects of interfacial transition zone thickness and aggregate shape on these percolation characteristics.

** INTRODUCTION**

In recent years, the importance of the cement paste-aggregate interfacial transition zone (ITZ) in influencing concrete properties has been recognized, as witnessed by this symposium's topic. It has been shown that, even when air voids are not considered, concrete must still be considered as a three-phase material (paste, aggregate, and ITZ) to properly investigate elastic properties [1,2], transport coefficients [3], and drying shrinkage [4]. Consideration of the ITZ is important because the microstructure of the ITZ in ordinary concrete is different than that of the bulk paste. It contains more and larger pores and less anhydrous cement and calcium silicate hydrate gel [5,6]. Therefore, its response to mechanical and thermal loadings and chemical ingress will also differ from that of bulk paste.

The magnitude of the influence of these microstructural differences on the composite's properties depends on two parameters: the relative difference in properties between ITZ and bulk paste, and the volume fraction and connectivity (percolation) of the ITZ regions [3]. This paper addresses only the latter of these topics, studying the influence of ITZ thickness and aggregate particle shape on the percolation of ITZ in a mortar or concrete. Experimental evidence of this phenomenon of interfacial transition zone percolation has been provided by mercury intrusion porosimetry studies [7,8,9] and by experimental comparisons of the transport properties of mortars with those of their constituent cement pastes [10].

** COMPUTER MODEL**

The computer model employed in this study is an extension of that employed
in the study described
in [8] in which particle shapes were limited to
spheres. Based on recent analytical work [11], a new computer
program was written to extend the model to triaxial ellipsoids,
with semi-axes of lengths a, b, and c and any arbitrary orientation.
Therefore, one may vary particle shapes from spheres (air voids) to cylindrical
ellipsoids (fibers) to triaxial ellipsoids (aggregates). Given any size
distribution of particles and scale factors a, b, and c, the program
places a requested number of particles in a three-dimensional cubic
volume, typically 10 mm on a side, such that no particles
overlap. The program proceeds from the
largest to the smallest particles. Interfacial transition zones are modelled
as ``soft shells'' of a constant thickness **t** surrounding each ``hard core''
aggregate particle [8]. The ITZ may overlap one another and also
may intersect the aggregate particles. After all particles have been
placed, the program uses a burning algorithm [12] to determine
the connectivity of the ITZ regions and volumetric point
sampling to determine the volumes occupied by aggregates, bulk cement paste,
percolated ITZ regions, and disconnected ITZ regions. By varying the
number of particles placed in the box, the percolation behavior can be
mapped out as a function of aggregate content.

The computer program was validated by determining the excluded volume of triaxial ellipsoids of different aspect ratios [13]. The excluded volume for an ellipsoid is the volume surrounding the ellipsoid where the center of an arbitrarily oriented second identical ellipsoid cannot be placed without some portion of the second ellipsoid overlapping a portion of the first one. For a variety of aspect ratios, the excluded volumes determined using the computer program, by sampling 500,000 random configurations, were within 0.5% of the exact analytical result [14].

In this study, three interfacial transition zone thicknesses (10, 22.5,
and 50 µm) and five combinations of aspect ratios (1:1:1, 1.25:1:0.8,
1.5:1:0.667, 2:1:0.5, 1.59:0.794:0.794) were studied. The aspect
ratios were chosen to maintain a constant particle volume (abc=1)
while varying the aggregate surface area. Surface areas were calculated
using formulas presented in [15], which can also be found more recently
in [16]. In a given execution of the
simulation, the aspect ratio was held constant, but it could be easily
varied to follow some distribution of particle shapes. The aggregate particle
size distribution (PSD) for the mortars corresponded to that
of a typical sand used in concrete, as measured
experimentally in [17]. The particle diameters ranged between
75 and 4750 µm. For the 1000 mm^{3} cubic volumes used
in this study, between seven and twenty thousand aggregate particles were
required to represent an actual mortar. Fig. 1 shows
two-dimensional slices from three-dimensional microstructures for
systems with 16,000 particles (aggregate volume fraction=43%), an ITZ thickness
of 50 µm, and the two aspect ratios indicated.

**Figure 1:** Two-dimensional slices from three-dimensional microstructures
for aspect ratios of 1:1:1 (left) and 1.25:1:0.8 (right) (white: aggregate,
grey: bulk cement paste, black: ITZ cement paste).

** RESULTS AND DISCUSSION**

The ITZ thickness, **t**, of 22.5 µm, was chosen as an
estimate of a typical thickness to be encountered in a mortar or concrete
[8]. Fig. 2 shows a plot of the fraction of
``ITZ paste'' percolated vs. the aggregate content for the five aggregate
particle aspect ratios investigated in this study. One clearly notices that
as the aggregates become more elongated (higher aspect ratios), significantly
lower aggregate contents are needed to form a percolated ITZ path
across the microstructure. This result is in agreement with
percolation studies
of totally overlapping particles [13,18]. Interestingly, when
one plots these results against

**Figure 2:** Percolated interfacial transition zone fraction vs. aggregate
content. Three data sets are shown for the 1:1:1 aspect ratio system to
provide some indication of variability.

**Figure 3:** Percolated interfacial transition zone fraction vs. interfacial transition zone volume fraction.

ITZ Thickness (µm) | Agg. Vol. Frac. Range (%)^{a} |
ITZ Vol. Frac. (%)^{a} |

10 | 44-50 | 6 |

22.5 | 30-37 | 10 |

50 | 16-24 | 16 |

**Table 1:** Volume Fractions at Percolation vs. Interfacial Transition Zone Thickness

**Figure 4a:** Percolated interfacial transition zone fraction vs. aggregate surface
area for **t**=50, 22.5, and 10 (dotted lines) µm from left to right, without scaling surface area

**Figure 4b:** Percolated interfacial transition zone fraction vs. aggregate surface
area for **t**=50, 22.5, and 10 (dotted lines) µm from left to right, with scaling of surface area.

A third scenario which can be addressed using this simulation model is the
effect of aggregate PSD on ITZ percolation. Using spherical particles and a **t**
value of 22.5 µm, Fig. 5 shows the effects of removing
the smallest particles (**<** 150 µm in diameter) from the original
aggregate PSD. Physically, this would be equivalent to sieving the aggregate
and discarding the portion which passed through a sieve with an opening size
of 150 µm. In coarsening the aggregate PSD, one finds that a greater
volume of aggregate, but a smaller volume of ITZ paste (indicated by the solid points
in Fig. 5) is needed to percolate the
system. In this case, one can imagine maintaining percolation by replacing an
already percolated cluster of small aggregate particles by a single larger
aggregate particle, which would indeed increase aggregate volume while
somewhat decreasing ITZ volume.

**Figure 5:** Percolated interfacial transition zone fraction vs. ITZ volume (solid points)
and aggregate volume fraction (open points) for **t**=22.5 µm
showing the effect of removing the finest aggregate particles. The squares are
the original aggregate distribution, while the circles are distributions with
the finest particles removed.

** CONCLUSIONS**

A computer experiment has been performed to study the effects of interfacial transition zone thickness and aggregate shape on the percolation of ITZ in mortars. Both parameters can have significant effects on the percolation characteristics of these systems. For a given aggregate particle size distribution and ITZ thickness, the curve of ITZ fraction connected vs. ITZ volume fraction was found to be relatively independent of particle shape, while elongated aggregate shapes resulted in lower aggregate contents being required for ITZ percolation than spherical ones. Future experimental studies will concentrate on a systematic assessment of the effects of ITZ connectivity on transport coefficients, such as ionic diffusivity, permeability, and sorptivity, both for mortars made with typical sands and with spherical aggregates.

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