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# Basic Concepts

Typical kinds of transport processes important in concrete are: 1) the transport of water, either due to a hydrostatic pressure head or wetting forces (capillary suction) and 2) the migration of ions, either due to diffusion under a concentration gradient, or to transport by moving water. For both of these processes, how (and if) the relevant pores are connected to each other matters very much. Phrased more rigorously, the percolation properties of the random microstructure and particularly of the pore space are the critical geometrical and topological factors upon which the microstructure:transport property relationships are based.

The ideas of percolation theory are helpful in understanding the important features of random structures. The main concept of percolation theory is the idea of connectivity. Picture some sort of structure being built up inside a box by the random attachment of small pieces to each other. Percolation theory attempts to answer the question: at what point does the structure span the box? An alternate form of this question, for a random structure that already spans the box, is: if pieces of the structure are removed at random, when will it fall apart? The percolation threshold is defined by the value of some parameter, say volume fraction of the structure in the box, right at the point where the structure either achieves or loses continuity across the box.

An example of percolation phenomena is displayed by the model of randomly placing freely overlapping objects in a matrix (this actually roughly simulates the growth of solids due to reactions like those seen in concrete). The objects gradually form larger and larger clusters, because they can connect via overlap, until a percolated structure is formed. This model has been studied extensively in 2-D and 3-D (see Refs. [7] and [8] and many references therein). Consider the following simple 3-D example. The objects used are overlapping spheres, placed at random positions in a 3-D matrix. The volume fraction covered by the collection of spheres is monitored until they form a continuous structure. It is found numerically that they will become continuous when they occupy approximately 29% of the total volume [8]. This is an example of the percolation of a structure that is being randomly built up. If the spherical objects become ellipsoids, then this critical volume fraction decreases as the ellipsoid aspect ratio either increases or decreases away from unity [8]. For the sphere case again, if we now think of the matrix as a uniform conducting material, and the overlapping spheres as insulators, then the composite material will lose its ability to carry an electrical current when the matrix loses connectivity at a matrix volume fraction of about 3% [9]. This is an example of the percolation of a structure that is being randomly torn down. Concrete exhibits both kinds of percolation processes, at more than one length scale.

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