Concrete is a composite material made up of the primary phases of cement paste, pores, and aggregates of various sizes. However, it is not a simple composite material. It can be classified as a porous, multi-scale [1,2,3,4], interactive  composite material. It is a porous material because the cement paste matrix is a porous material, where the pores are produced mainly by the chemical reactions between cement and water and the original size and spatial distribution of the particles. It is a multi-scale material, because there are morphologically different microstructures of importance at length scales ranging from nanometers to millimeters . The distribution of pores in the pore space is modified by the presence of aggregates, which is why we call concrete an interactive composite. As more aggregates are added, the additional, highly porous interfacial transition zone regions force the bulk matrix to be denser in order to conserve the overall water:cement ratio .
This paper focuses on the cement paste matrix of concrete, which controls the transport properties of concrete. In this paper, "transport properties" mean diffusion of ions and flow of water through the pore space of the cement paste. Any porous material allows transport through its pores if the following conditions are fulfilled: (1) the pores themselves allow transport within them, and (2) these pores are continuous or percolated  through the material. An illustration of the first condition is whether or not a pore is saturated with water in a cement paste. If the pore is dry, obviously no ions will diffuse through the pore space, but gases can diffuse through the empty pore. If the pore is full of water, then ions can diffuse through it, but now gases cannot (unless they first become dissolved in the liquid water). Only fully saturated cement paste will be considered in this paper. To understand the second condition, just imagine that the entrained air voids were the only pores in a concrete. Since these are in general isolated from each other, there will be no diffusive or fluid transport through these pores, since they do not form a connected network.
The fact that the pores that allow transport are percolated does not completely determine the rate of transport. The tortuosity of the pore network and the size of the pores also influence this rate . Different transport processes depend differently on these pore space parameters, however. For example, fluid permeability depends directly on the square of a pore size, while ionic diffusivity depends much less sensitively on pore size [6,7].
Like concrete, cement paste is also a random composite material. The original cement grains are themselves made up of many chemically distinct phases, and the chemical reactions with the mixing water produce many other chemically distinct phases. In any random material, one may ask the following question about any one of the phases: is it percolated or isolated? If it is the pore phase that is being considered, one can also ask what is the ionic diffusivity or fluid permeability through these pores, if they are connected?
The current version of the model considered in this present work has been thoroughly described in a recent review article . The model consists of a 3-D digital image, with cubic pixels, where each pixel is identified by a phase label that tells which phase inhabits that pixel. Images of cement particles are superimposed on the lattice using various methods , and hydration is simulated by dissolving the cement pixels and allowing the dissolved species to diffuse in the pore space and form new products according to cellular automaton rules that mimic the known chemistry of the original cement particles. At any given point in time, the algorithm can be interrupted, and various properties measured, like degree of hydration, phase percolation, diffusivity, elastic moduli, heat signature, or chemical shrinkage. Ref.  describes how full portland cement chemistry is now handled by the model, in contrast to earlier models that were for C3S only .
Any model of a random particulate material has sources of error inherent in its representation. For example, the hydration model only represents a piece of cement paste, of sub-millimeter dimensions. There can be errors that occur because the small size of the model, relative to usual cement paste sample dimensions, cannot completely capture the statistics of how real cement particles are spatially arranged. Since the cement particles are randomly mixed, two different arrangements of the particles in the unit cell of the model can in principle give different results. A third source of error comes about because the model uses a digital image to capture the real shapes of hydrated and unhydrated phases. Inadequate resolution, which is the real spatial length per pixel, can cause errors in the outputs of the model.
The focus of this paper is to evaluate the effect of the above three potential sources of error on the predictions of the model for percolation and transport properties. In doing this, we will also consider the effect of changes in chemistry, computer power, and new understanding of the parameters of the model. The coupling of model statistics and real microstructure will be considered and discussed. This paper can be considered to be an update of several earlier works [9,10], as well as a critical analysis of the "nuts and bolts" of the hydration model.