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Immediately after mixing cement powder and water together, the solid phases are discontinuous, or connected only via van der Waals-type forces [14], and so the freshly mixed cement paste is a viscous liquid. The solid phase is then built up through random growth of reaction products, and at some point becomes continuous across the sample, mainly due to the formation of the C-S-H surface products [15]. Experimentally, this setting process can be detected using a needle penetration test [16], ultrasonic shear wave propagation [17], or by measuring the shear strength of the paste [14,18]. The set point can be defined rigorously, using percolation concepts, as the point where percolation of the total solid phase occurs. This point can be computed, using a three-dimensional computer model based on a simplified cement composed only of monophase C3S particles. This chemical simplification of the particles is justified by the experimental observation that the C-S-H surface product causes set [15] and by the fact that this simple model generates almost the same quantity of surface products as those produced in real cements [19]. Also, most real portland cements are usually composed of at least 60% C3S.
Using this model, in conjunction with a burning algorithm [19] to compute connectivity, one can determine the degree of hydration necessary to first have a continuous network of cement particles linked by C-S-H gel product. This seems to be a reasonable definition of set, especially since the combined phase of cement and C-S-H will percolate before any individual solid phase. In addition, the original configuration of the cement particles can be simulated as being flocculated or dispersed. Figure 4 shows a quantitative comparison between model and experimental results.
Figure 4: Showing the capillary porosity remaining at the set point, for several
experimental and
model cement pastes involving different initial cement particle configurations, as a function of the
w/c ratio of the cement paste.
The data from Jiang et al. [18] were calculated as the capillary porosity at the point where the cement paste exhibited a shear resistance of 0.08 MPa. The data points of Chen and Odler [15] correspond to the measured porosities at the beginning and end of set according to the ASTM standard needle penetration method [16]. Model results, corresponding to the point when a spanning cluster of C3S particles connected together by the C-S-H gel first exists, are presented for flocculated, random, and dispersed systems based on a discretized version of a real measured particle size distribution [20,21]. In general, the comparison among these three data sets is reasonably good, particularly so for the experimental data of Jiang et al. [18] and the model results for the random/flocculated systems. As the w/c ratio decreases, less hydration is needed to achieve set, since the initial interparticle spacing is less. Based on the model results for random systems, degrees of hydration of 1.8, 2.7, and 4.6% are required to achieve solids percolation for w/c ratios of 0.3, 0.4, and 0.5. The capillary porosities at set obtained by Jiang et al. [18] are consistently higher than those of Chen and Odler [15], suggesting that the ASTM needle penetration test method measures set time based on a resistance somewhat greater than that corresponding to a shear strength of 0.08 MPa. As might be expected, in general, the model flocculated systems require less hydration to achieve set than their dispersed counterparts, in agreement with experimental studies [22,23]. It should be noted that the experimental measurements were generally made on portland cements while the model results are for C3S pastes. However, the similarity in volumes of surface and pore products formed for these two pastes [19] allows valid comparisons to be made between model and experimental results.
Because it is the connection of cement grains by C-S-H gel product that regulates set, a finer particle size cement will actually require a greater degree of hydration to achieve set than a coarser one. Thus, even though a finer cement typically hydrates at a faster rate, it may lead to a longer setting time than a coarser, slower hydrating cement, where fewer particle-to-particle contacts are necessary to achieve set, as has been verified experimentally [14]. This analysis assumes that the volume of C-S-H product needed to connect two cement particles is roughly invariant, so that as the particle size increases at at fixed total volume of cement, the number of particles and therefore the number of connections needed will decrease [24].
