Next: Periodic Models
Up: Three phase (hard
Previous: Three phase (hard
We emphasize at the outset that concrete is a random composite material at many length scales [8], from the nanometer scale of the calcium silicate gel to the micrometer scale of the porous cement paste to the millimeter and centimeter scale of the aggregate particles. Thus, it is not practical to describe the electrical properties from the material structure by simultaneously considering all these length scales. In this paper, we are concerned with the 10 -1000 µm length scale that describes a typical mortar [9,10]. Within this framework, mortar can be viewed as a three-phase composite [11,12]: matrix cement paste, aggregate sand grains, and interfacial zone cement paste [see Fig. 1], where all three phases can be thought of as uniform continuum materials, characterized by a single conductivity per phase. The thickness of the interfacial zone can vary between 10 and 50 µm [13]. The volume fraction occupied by the aggregate particles in a mortar is typically 50--60% with the remaining volume comprised of bulk and interfacial zone cement paste.
Since the interfacial zone can occupy a significant volume fraction, the physical properties of this phase will certainly have an influence on the overall behavior of the composite. 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 no more than 10 µm, this phase can still form continuous percolating channels [10].
For the purposes of electrical conduction, it is assumed that the sand grains in the mortar are simply inert obstacles to the flow of current. The basic model is then defined by three input units: (1) the structure of the interfacial layer, (2) the electrical contrast between this layer and the bulk cement paste and (3) the concentration and size distribution of the sand grains. Following previous models we will assume that the sand grains are all spherical and that the interfacial zones are always spherical shells of constant thickness. While the thickness of the interfacial zone, h, may be as large as 50 µm, mercury intrusion measurements and modelling results [10] suggest that h = 20 µm is a more typical value. Within this zone, both the pore size and the porosity of the cement paste are larger than in the bulk [13]. Accordingly the conductivity and fluid permeability are higher. We assume that the conductivity within the interfacial shell takes a constant value, σs, and that the conductivity of the cement paste, σp, is also constant. Assuming that the conductivity inside the interfacial shell is constant is an aproximation, since actually there is a gradient of porosity and thus conductivity in this region. Since there is no experimentally established value for σs / σp, we allow this parameter to vary freely in our calculations. Thus, for a given sand concentration, we study the dependence of the composite conductivity on the value of σs / σp. We also look at the conductivity as a function of sand concentration for several fixed values of σs / σp .