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Introduction

The D.C. electrical conductivity of mortar and concrete is important both as a means of probing the structure of these materials and as a measure of ionic diffusivity [1], via the Nernst-Einstein relation [2]. Diffusivity is of interest in connection with a range of issues related to durability, such as sulfate attack and chloride ion-induced corrosion of steel reinforcing bars [3].

Concrete conducts electricity because of its porous cement paste matrix, which is a conductor when saturated with the electrolytic pore fluid [4,5,6]. Much recent work has been done on understanding how the microstructure of cement paste determines its electrical conductivity [4,5,7,8,9]. However, relatively little work has been done on how the conductivity of concrete depends on quantities like the number and arrangement of aggregate particles, and on the cement paste-aggregate interfacial zone [6,10]. This is at least partly due to the complicated random structure of concretes and mortars. Experimentally, some synthetic aggregate:cement paste geometries have been investigated [11,12] that did not, however, take into account the random geometry and topology of the real material phases.

Concrete is a random composite material at many length scales [13], from the nanometer length scale of the C-S-H structure in the cement paste matrix, to the micrometer length scale of the unhydrated cement grains and larger capillary pores, and finally up to the millimeter and centimeter length scale of the aggregate particles used in a typical concrete. Accordingly, it is not practical to try to predict the electrical properties from the material structure while simultaneously considering all these length scales. Instead, one must focus on a given length scale and describe the microstructure and properties in mathematical language appropriate to this length scale. In this paper, we are concerned with the approximately 10-1000 micrometer length scale that adequately describes a typical mortar [14,15]. Within this framework mortar (and concrete) can be approximately viewed as a three-phase composite [16,17,18]: bulk cement paste, aggregate, and interfacial zone cement paste [see Figure 1], where all three phases can be thought of as uniform continuum materials. In a mortar, the aggregate particles typically range in size from 100 micrometers to a few millimeters. Interfacial zones are significantly smaller, on the order of 10-50 micrometers in thickness [19,20]. Typical volume fractions occupied by the aggregate particles in mortars are about 50%, with the remaining volume comprised of bulk and interfacial zone cement paste. Aggregate volume fractions are usually somewhat higher in concrete, on the order of 60% [14].

Figure 1: The structure of mortar, as represented by the random aggregate model described in Sec. 2. There are four sizes of sand grains, with diameters (in micrometers) of 1500 (red), 750 (green), 500 (light blue), and 250 (dark blue). The thickness of the interfacial zone region (yellow) is 20 micrometers. The bulk matrix cement paste is shown in gray. The total volume fraction of sand is 54%, with the sand size distribution as given in Table 1.

In a three-phase composite model, the volume fraction assigned to the interfacial zone phase depends on what thickness is taken to define the boundary between the interfacial zone and the bulk cement paste. Figure 2 shows, using a recently developed model for the structure of mortar [15], how the volume fraction of cement paste belonging to the interfacial zone phase varies as a function of this assumed thickness. Curves are given for different values of the sand volume fraction. In this model, sand grains are taken to be spherical, with a realistic size distribution [15]. The interfacial zones are viewed as uniform thickness shells placed concentrically around each aggregate or sand grain. Since the average particle size of the cement is much smaller than the average particle size of the sand, the thickness of the interfacial zone is determined by the cement particle size and may then be assigned the same value for each sand grain [21]. Figure 2 clearly shows that, for values of the interfacial zone thickness around 20 micrometers, for the highest amount of sand, the interfacial zone cement paste occupies 20-30% of the total cement paste volume, and therefore 10-15% of the total mortar volume. Since the interfacial zone cement paste occupies a significant volume fraction, the physical properties of this phase will certainly have an influence on the overall behavior of the mortar/concrete composite [22,23]. This would be true even if this phase were discontinuous. However, recent modelling and mercury injection experimental work showed that, even if the interfacial zone thickness is taken to be as small as 10 micrometers, the interfacial zone cement paste phase can still form a continuous percolating channel, which implies an even larger effect on the transport properties of the composite [15,24].

Figure 2: For size distribution of sand grains determined experimentally [15], the fraction of the total cement paste volume occupied by the interfacial zone cement paste is shown as a function of the interfacial zone thickness. [Here the grains are assumed to be spherical.]

In Section 2 we discuss the physical properties of the three phases in our model. The structural characteristics of the models and a brief discussion of our computational techniques are the subject of Section 3. Section 4 presents our results for electrical conductivity, and in Section 5 we consider the implications of our results for other experimental measurements. Section 6 outlines future work, and Section 7 summarizes the main results of this paper.