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Introduction

As cement hydrates in water to form cement paste, its microstructure undergoes a marked transformation. Macroscopically, the system is converted from a viscous suspension of cement particles in water, into a rigid, albeit porous, solid. The properties of the final solid, including strength and durability, are inherently controlled by the microscopic structure of the cement paste. This microstructure consists of solid and porous phases, and it is the spatial and topological arrangement of these phases that is ultimately responsible for the strength and transport properties of the paste. One key topological attribute is the connectivity or percolation of phases within the microstructure. A percolating phase forms a three dimensional spanning cluster, while a phase that has not percolated consists of isolated clusters.

Phase percolation influences many of the critical properties of cement-based materials. The set time of a paste, mortar, or concrete is determined by the point at which the total solid phase within the microstructure becomes connected, forming a rigid backbone that has a non-zero elastic stiffness. As hydration continues, the solid phases (hydration products, unhydrated cement, and mineral admixtures) become highly connected. This connectivity is responsible for the load-bearing capacity of cement-based materials. The durability or service life of cement- based materials is also directly influenced by phase percolation. The transport properties of such materials are determined to a large degree by the amount and connectivity of the capillary porosity within the microstructure. For diffusion of degradative species, such as chloride or sulfate ions, both the connectivity of the pore space and of the porous hydration products are critical. As the capillary porosity becomes disconnected at long hydration times, diffusion rates become controlled by transport through the gel porosity of the highly-connected calcium silicate hydrate phase.

From the above examples, it is clear that percolation is a critical element in the ultimate performance of cement-based materials. Unfortunately, phase percolation is not easily measured experimentally. Mercury intrusion porosimetry and permeability measurements do provide some insight into the percolation of the capillary porosity as does compressive strength testing for the percolation of total solids, but these techniques are indirect assessments of the percolation phenomena. To quantitatively characterize phase percolation, a complete representation of microstructure is required. Experimentally, this is difficult because the two-dimensional representations of microstructure, that scanning electron micrographs provide, are inadequate to assess three-dimensional percolation properties. For example, the capillary porosity of a hydrating cement becomes disconnected in two dimensions long before it does in three dimensions. Thus, three-dimensional characterization techniques such as serial sectioning [1] and three-dimensional reconstruction must be utilized. These techniques are time- consuming and impractical except in special cases. Future advancements in tomographic techniques may permit the rapid and inexpensive representation of three-dimensional structures [2].

Alternatively, three-dimensional representations of cement microstructure can be obtained as the output of a microstructure model. If the model adequately captures the relevant aspects of the real material, this three-dimensional representation can be analyzed to determine percolation characteristics and other material properties such as transport coefficients. Recently, a microstructure model of cement, specifically tricalcium silicate, hydration, executable in either two or three dimensions, has been developed that generates realistic cement paste microstructures [3]. Using the model, the discontinuity of the pore space [3], characterization of the cement-aggregate interfacial zone [4], and calculated diffusivities [5] have been determined and found to be in reasonable agreement with experimental data. The microstructural model has been utilized to study phase percolation under a variety of hydration conditions. The effects of water-to-cement (w/c) ratio, degree of hydration, α, and the presence of mineral admixtures on percolation properties are given in this paper. The model is also used for interpreting previously observed experimental results on cement pastes.