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The original size, spatial distribution, and composition of portland cement particles have a large influence on hydration, microstructure development, and ultimate properties of cement-based materials. In this paper, the effects of cement particle size distribution on a variety of performance properties are explored via computer simulation and a few experimental studies. Properties examined include setting time, heat release, capillary porosity percolation, diffusivity, chemical shrinkage, autogenous shrinkage and internal relative humidity evolution, and interfacial transition zone microstructure. The effects of flocculation and dispersion of the cement particles in the starting microstructures on resultant properties are also briefly evaluated. The computer simulations are conducted using two cement particle size distributions that bound those commonly in use today and three different water-to-cement (w/c) ratios: 0.5, 0.3, and 0.246. For lower w/c ratio systems, the use of coarser cements may offer equivalent or superior performance, as well as reducing production costs for the manufacturer.
Keywords: Cement paste (D); Hydration (A); Modeling (E); Particle size distribution (B); Transport properties (C)
Many studies have been conducted examining the relationships between portland cement particle size distribution (PSD) and hydration and hardened paste strength properties [1-6]. For a given water-to-cement (w/c) ratio, a reduction in median particle size generally results in an increased hydration rate and, therefore, improved early properties such as high early strengths. For this reason, portland cement finenesses have generally increased over the years. However, Mehta  has pointed out that for durability considerations, finer cements may not always be preferable to coarser ones. Furthermore, it has recently been argued that in high-performance concretes with relatively low w/c ratios, coarser cements may offer equivalent long term performance to finer cements , resulting in energy savings due to a reduction in grinding time. This conclusion was based on simulation studies of the degree of hydration vs. time behavior of a set of cements ground to different finenesses. The purpose of this paper is to extend that study to investigate a wide range of properties for two cement finenesses (640 m2/kg and 210 m2/kg) significantly different from the cement fineness of about 350-400 m2/kg typically produced by the cement industry today.
Experimental and Modelling Approach
All simulations presented were conducted using the NIST microstructural model which has been described in detail elsewhere [9,10]. Based on a set of cellular automaton rules, the model operates on a three-dimensional digitized microstructure consisting of a volume of pixel elements to simulate the reactions between cement and water. For the present study, the following modifications were made to the base model described in reference . First, the reaction of hemihydrate to produce gypsum was included so that various forms of sulfate could be studied. Second, the dissolution algorithm was changed so that the twelve next nearest neighbor pixels (in 3-D), in addition to the six immediate neighbors, are considered as possible dissolution sites. This modification increases the long-term hydration of the larger (> 10 µm) cement particles in the model cements. Finally, the induction period was incorporated into the NIST model for the first time in a simple manner by making the dissolution probabilities of the cement phases proportional to the formation of one of the reaction phases, the C-S-H. While several induction period mechanisms have been developed and advanced , the hypothesis gaining support most recently is that the induction period is controlled by the nucleation and growth of the C-S-H phase . This simple dissolution rule will produce an autoacceleratory reaction, which will decay at longer times due only to spatial effects, as further hydration becomes impeded by the previously produced hydration products.
The microstructural model has been developed to operate under a variety of curing conditions (water saturated, sealed, etc.). For this study, to simulate well-cured systems, all hydration simulations were executed under saturated conditions until the capillary porosity depercolated, at which point all subsequent hydration was executed under sealed (no further water ingress) curing conditions . Once the model switches to sealed conditions, the necessary empty porosity, corresponding to the chemical shrinkage caused by hydration, will automatically be created .
The model was applied to simulate the experimentally observed hydration behavior of two cements of vastly different finenesses made from the same clinker . Laser diffraction techniques were used to determine the PSD of each of the cements, and quantitative X-ray diffraction was applied to determine the fraction of tricalcium silicate (C3S ) that had reacted at ages of (1, 2, 3, 4, 7, 14, 28, and 56) days for a w/c=0.5 cement paste. The cumulative PSDs for the two cements are shown in Fig. 1. The cement PSDs will be referred to as <5 µm> and <30 µm> proceeding from left to right in Fig. 1, corresponding approximately to the average size obtained in fitting the PSDs to a Rosin-Rammler distribution . Ordinary ASTM Type I portland cements commonly used today would fall somewhere in between these two curves, but would in general lie closer to the curve on the left. The composition of the cement, determ ined by quantitative microscopy, is 59 % C3 S, 25.9 % C2 S, 0.6 % C3 A, and 14.2 % C4 AF, with hemihydrate added at a mass percentage of 4.6 %.
Figure 1: Measured particle size distributions for the two portland cements.
The measured PSDs and clinker compositions were used in constructing the model initial microstructures for cement pastes with w/c ratios of 0.246, 0.3, and 0.5. The calculations for the w/c=0.5 model runs were used as a baseline, because experimental measurements of the degree of hydration of the C 3S were performed at this w/c ratio. These initial systems were hydrated using the NIST microstructural model to study the effects of PSD on hydration kinetics and the following properties: setting time, heat release, capillary porosity percolation, diffusivity, and chemical shrinkage. All hydrations were executed for 5000 cycles of the model, corresponding to 25 000 hours (about 3 years) of real time at 20 ºC. Generally, the cement particles were flocculated before hydration commenced. However, for the w/c=0.5 systems, two additional microstructures consisting of dispersed cement particles (each particle separated from all neighbors by at least one pixel or 1 µm) were investigated. In a further set of simulations, a single flat plate aggregate, two pixels thick, was added to the central portion of the 100 pixel x 100 pixel x 100 pixel microstructure prior to cement particle placement to quantitatively evaluate the effects of w/c ratio and cement PSD on interfacial transition zone microstructural development. This latter study was conducted for the w/c=0.3 and 0.5 systems, for each of the two cement PSDs.
Percolation properties of total solids (set) and the capillary porosity phase were monitored periodically throughout the hydration process. Additionally, microstructures were output after (0, 100, 200, 300, 500, 1000, 2000, and 5000) cycles of hydration for evaluation of diffusivities using a finite difference code developed by Garboczi . For the diffusivity calculation, the empty and water-filled porosity were assigned a relative diffusivity of 1 and the C-S-H gel was assigned a value of 1/400 , with all remaining cement phases being assigned a diffusivity of 0. The empty porosity was assigned a diffusivity of 1 based on the assumption that, over time, these pores will become saturated with water . This assumption represents a worst case scenario, so that the computed relative diffusivities will be upper bounds.
Results and Discussion
To calibrate the model to real time, one parameter that relates model cycles
to time in an equation of the form
time(h) = B * cycles 2 needs to be specified . Based on the experimental measurements for w/c=0.5 at 20 ºC for the
<5 µm> cement, B was set at a value of 0.001 (h/(cycle2 )) (compared with previously used values of 0.0017  and 0.0011 , both at 25 ºC). Using this factor, Fig. 2 provides a plot of the conversion of tricalcium silicate as a function of time for both the model and real systems. The agreement between model predictions and experimental observations is excellent, falling well within the relative standard uncertainty of 13 % for the experimental measurements. This suggests that the model adequately describes the effects of PSD on hydration kinetics. It is clear from Fig. 2 that for a w/c=0.5, finer grinding results in enhanced hydration (and therefore enhanced strength) at all ages investigated in this study.
Figure 2: Experimental (data points) and model (lines) results for degree of hydration of C3S for w/c=0.5 at 20 ºC. Error bars for <30 µm> data points indicate a 13 % relative standard uncertainty in all experimental measurements.
The setting of cement is controlled by the formation of a network of partially hydrated cement particles connected by hydration products , which can resist a shear force. In the model, set is determined as the time or degree of hydration required to first form a percolated pathway through the 3-D microstructure consisting of cement particles connected to one another either by C-S-H gel or ettringite. Table I reports the results obtained for the three different w/c ratios and the two cement PSDs. Both hydration time and degree of hydration are reported to separate the effects of hydration kinetics from microstructural considerations. Thus, even though the finer cement requires less time to achieve set due to its increased hydration rate, it actually requires more hydration, as more particle-to-particle bridges need to be built to form a percolated pathway. This simulation result is consistent with a set of rheological measurements  which indicated that for a C3 S cement with the smallest particles removed, less hydration was needed to achieve set than with the original C3 S cement. For the w/c=0.5 systems, as shown in Table I, executing the simulation for dispersed cement particles resulted in small increases in both the time and degree of hydration needed to achieve set, as more hydration is needed to link the particles when they are initially dispersed further apart. This microstructural observation may partially explain the retardation generally observed when using water-reducing agents or superplasticizers, in addition to any chemical effects these admixtures may produce. As the w/c ratio is increased, the difference in setting times between the <5 µm> and <30 µm> cements becomes more significant (several hours for w/c=0.5 vs. about 30 min for the two lower w/c ratios).
||Time of set (h)
||Degree of hydration
Naturally, the finer cement hydrates more rapidly, resulting in a higher initial rate of heat release as shown in Fig. 3. For w/c=0.3 cement pastes, however, after 5000 cycles of model hydration, the cumulative degrees of hydration (Table II) and heat released are nearly equivalent. For many applications, the avoidance of a rapid initial heat release is beneficial in limiting the development of thermal stresses and minimizing early-age cracking problems. Thus, this is one area where the use of a coarser cement may offer a performance benefit relative to a finer one. For the w/c=0.5 cement pastes, even after 5000 cycles of model hydration, the degree of hydration of the coarser cement still lags far behind that of the finer cement, 0.83 vs. 0.95. This suggests that in conventional concretes, the finer cements definitely offer a performance benefit in terms of an enhanced degree of hydration.
Figure 3: Cumulative heat release for hydration under isothermal conditions for w/c=0.3 cement pastes.
Capillary Porosity Percolation
The percolation properties of the phases in cement paste have been examined previously using a computer model . In that initial study, based on a simple model of C3S hydration only, a percolation threshold of about 18 % was identified for the capillary porosity phase. Using the most recent version of the NIST microstructural model, Fig. 4 presents results for the two different cement PSDs at the three different w/c ratios examined in this study. One can clearly see that the cement PSD has a significant effect on the capillary porosity at which depercolation occurs. This topic is being explored further in current research and will be the topic of an upcoming paper . With a coarser cement, the average interparticle spacing is larger, so that more hydration is needed to close off the capillary porosity. Compared to the effects of PSD, those of w/c ratio are minor. For the w/c=0.5, PSD= <30 µm> system, the model is unable to hydrate the cement sufficiently to achieve depercolation of the capillary porosity. But, even in this case, the percolation curve is asymptotically approaching those of the two lower w/c ratios. In general, the percolation threshold for the <30 µm> systems is about 18 % while that for the <5 µm> systems is about 22 %. For the w/c=0.5 systems, the effects of flocculation/dispersion on the capillary porosity percolation were negligible, as the data sets for the dispersed systems (not shown) basically overlapped those shown for the flocculated ones in Fig. 4.
Previously, this depercolation has been discussed in terms of the "curability" of the concrete . In a cement paste, once the capillary porosity depercolates, the imbibition of water to replace that lost due to chemical shrinkage during hydration slows significantly , as transport shifts from being dominated by the capillary pores to being controlled by the much smaller gel pores in the C-S-H . Thus, the longer it takes for the capillary porosity to disconnect, the longer one has to continue to add water to the interior of the concrete. For example, for the w/c=0.3 cement pastes, depercolation occurs after 32 hours and 250 hours of hydration for the <5 µm> and <30µm> systems, respectively, implying an increased "curability" for the coarser cement systems. This change in percolation threshold could also have major effects on diffusivity and chemical shrinkage in these systems, as will be investigated in the following two paragraphs.
Figure 4: Model results for capillary porosity percolation for cement pastes.
When evaluating the diffusivity properties of cement pastes of widely varying cement PSDs, one must be careful to separate out hydration kinetics effects from microstructural effects. For example, Fig. 5 shows a plot of relative diffusivity coefficients (the diffusivion coefficient of an ion in the concrete relative to its value in free water ) vs. hydration time. Because the finer cement hydrates much more rapidly, for each w/c ratio, its relative diffusivities are much lower at early times (< 300 hours). Eventually, for the lower w/c ratios, the coarser cement's hydration will catch up with that of the finer one, and the two relative diffusivities will be nearly identical.
Figure 5: Modelled relative diffusivity vs. hydration time for the six cement
To separate out the microstructural effects, the relative diffusivities are plotted against a microstructural parameter, total capillary porosity, in Fig. 6. Here, one can examine the effects of cement PSD on diffusivity from a microstructural viewpoint. For capillary porosities above the percolation threshold, one observes that the relative diffusivities of the coarser cement are about twice those of the finer cement at the same porosity. This is most likely due to the larger pores present in the coarser cement systems. Although diffusivity is not directly dependent on pore size, it is inversely proportional to pore tortuousity which will be decreased and directly proportional to pore connectivity which will be increased in the systems with larger pores. This can be verified in Fig. 4 where the connected fraction of the porosity for the coarser cements always lies above that of the corresponding w/c ratio finer cement. After the capillary porosity depercolates, the relative diffusivities of the different systems are much more similar, with all approaching a limiting value of about 0.0004 at very low porosities.
Figure 6: Modelled relative diffusivity vs. total capillary porosity for the
six cement paste systems. Solid line is the fitted function and dashed lines
represent a factor of two above and below the fitted function.
The general shape of the curve fitted to the data in Fig. 6 is similar to that developed previously by Garboczi and Bentz . Specifically, the relationship between relative diffusivity (D / D0 ) and capillary porosity () is given by:
Chemical Shrinkage, Internal RH Evolution, and Autogenous Shrinkage
As cement hydrates, the volume occupied by the hydration products is less than that of the reactants [6,20]. Thus, unless water is supplied from an external source, this chemical shrinkage will result in the formation of empty pores within the cement paste microstructure. This empty porosity not only influences the hydration kinetics , but also results in a reduction in internal relative humidity (RH) and a measurable autogenous shrinkage of the material . Because this shrinkage generally occurs during the early life of the concrete, it often results in cracking and a loss of performance.
Because chemical shrinkage is directly proportional to degree of hydration [9,20], cement fineness will influence the time evolution of this property via its influence on hydration kinetics. In a totally sealed curing environment, the chemical shrinkage will result in the creation of empty porosity from time zero (or once set is achieved). At a fixed time, this chemical shrinkage will be much greater in the finer cement PSD system, due to its enhanced hydration rate at early times. However, from a microstructural viewpoint, at equal degrees of hydration, the chemical shrinkage of the two systems will be identical.
Additionally, in the scenario of curing under saturated conditions, cement fineness will influence chemical shrinkage through its influence on the depercolation of the capillary pore space, the point at which empty porosity will start to be formed within the material. Table II summarizes the empty porosity present in the systems examined in this study after 5000 cycles of hydration. Because the finer cement depercolates and changes to "sealed" curing at a higher porosity (less hydration), its ultimate values of empty porosity are greater than those of the coarser cement, even when their degrees of hydration are similar.
For comparison, Table II also includes an entry for the w/c=0.3, PSD=<30 µm> system for hydration under totally sealed conditions. In this case, not only is the final empty porosity fraction much greater, but the effects of curing under sealed conditions on the ultimate degree of hydration are also apparent . Since hydration can no longer take place in the empty porosity, a substantial reduction in the ultimate degree of hydration is observed relative to that obtained for "saturated" curing.
Another effect of the chemical shrinkage is a reduction of the internal RH. As chemical shrinkage progresses, smaller and smaller pores become empty. Neglecting the effects of dissolved salts on RH, the size of the largest remaining water-filled pore will determine the local internal RH, according to the Kelvin-Laplace equation :
Figure 7: Internal RH evolution vs. time for cements ground to two different
finenesses, w/c=0.30, 20 % silica fume, T=30ºC.
The chemical shrinkage occuring within the cement paste microstructure results in a measurable physical autogenous shrinkage of a much lower magnitude. Similar to the case of drying shrinkage , the magnitude of the autogenous shrinkage is proportional to the amount of water in tension within the microstructure and the capillary stress developed in the water . Of course, the constant of proportionality will change with time due to hydration of the cement and creep of the C-S-H gel. The capillary stress is given by :
Thus, there are two conflicting effects of cement fineness on autogenous shrinkage. On the one hand, a finer cement results in a greater RH reduction, resulting in higher values of the capillary stress. On the other hand, as illustrated in Table II, the amount of water-filled porosity may be less in the finer cement paste due to its higher amount of chemical shrinkage and empty porosity when cured under the "saturated" conditions employed in this study. Because of the strong sensitivity of capillary stress to RH reduction, one would expect that in most cases of practical importance, the former effect will be dominant and a greater amount of autogenous shrinkage will be observed in the finer cement systems. Figure 8 shows the equivalent autogenous shrinkage measurements for the two systems whose RH evolutions were provided in Fig. 7 . Indeed, in this case, the autogenous shrinkage observed for the finer cement is substantially greater than that exhibited by the coarser cement. Taken together, these results suggest that under adequate curing conditions, the performance of coarser cements should be superior to finer cements with respect to the development of autogenous shrinkage and the early cracking that it often causes.
Figure 8: Autogenous shrinkage evolution vs. time for cements ground to two
different finenesses, w/c=0.30, 20 % silica fume, T=30ºC.
Interfacial Transition Zone Microstructure
The final property examined as a function of cement PSD is the microstructure of the interfacial transition zone (ITZ). Initial 2-D microstructural images for the 3-D model are shown in Fig. 9 for the four systems investigated in this study. One can clearly observe differences in the packing efficiency near the aggregate surface for the different w/c ratios and cement PSDs. Since the thickness of this zone generally scales as the median cement particle diameter , one would expect to observe major differences between the two cement PSDs examined in this study. Indeed, this is the case for the w/c=0.5 systems, as shown in Fig. 10 which plots the initial and final (after 5000 cycles of model hydration or about 25 000 hours) porosity distributions for the two different cements. For the coarser cement, one can clearly observe an increased porosity in the ITZ region. This increased porosity would generally have detrimental effects on both the mechanical properties and transport coefficients of the concrete. For diffusivity, this effect is fairly small, but for permeability, it could be significant .
Figure 9: Original microstructure images for upper left: w/c=0.3 PSD=<5µm>, upper right: w/c=0.3 PSD=<30 µm>, lower left: w/c=0.5 PSD=<5 µm>, and lower right: w/c=0.5 PSD=<30 µm>. Colors corresponding to phases are as follows: red−C3S , aqua−C2S, green− C3A, yellow− C4AF, pale green− hemihydrate, and porosity. Central magenta bar extending across the microstructure is the flat plate aggregate.
Figure 10: Porosity fraction vs. distance from aggregate surface for w/c=0.5 cement pastes.
However, as illustrated in Fig. 11, for the w/c=0.3 systems, the differences in the porosity distributions of the two systems are relatively similar after the 5000 cycles of hydration. One interesting feature of this graph is the appearance of a small local maximum in the porosity distribution for each hydrated system at a distance of about 5 pixels from the aggregate interface. The cause of this feature is the chemical shrinkage and self-desiccation occurring during hydration (after the capillary porosity depercolates), as verified by examining 2-D images of the microstructure after hydration. In the model, the largest pores are the first to empty during self-desiccation. In a system with an aggregate particle, the largest pores are generally those closest to the aggregate surface so that a large fraction of the empty porosity forms in the ITZ region. This is particularly true in the case of the coarser cement. This observation is consistent with direct microstructural measurements performed using scanning electron microscopy , where relatively large pores are observed in the ITZ regions. In the past, these pores have been attributed to hollow-shell hydration (Hadley) grains  or to the dissolution of calcium hydroxide crystals in systems containing silica fume , but they could also be the result of self-desiccation in lower w/c ratio mortars and concretes.
Figure 11: Porosity fraction vs. distance from aggregate surface for w/c=0.3 cement pastes.
Based on modelling and a few experimental studies, the following preliminary conclusions can be drawn with respect to the effects of cement PSD on performance properties:
For the w/c=0.5 systems, a study of cement particle flocculation/dispersion indicated that only the setting characteristics were significantly influenced by this parameter. For the dispersed systems, more time and more hydration were needed to achieve set. In this study, capillary porosity percolation, chemical shrinkage, and relative diffusivity were found to be relatively unaffected by the flocculation state of the initial microstructures.
In all of the simulations, "ideal" curing conditions were utilized. Coarser cements will require more attention to be paid to curing in the field, to achieve their full potential. If adequate curing can not be guaranteed, the finer cements are preferable due to both their increased early hydration rate and their earlier depercolation of the capillary porosity (which minimizes water loss). While no one cement particle size distribution is ideal for all applications, the cement PSD can be optimized for each particular application.
The purpose of this study has been to point out the advantages of carefully considering cement fineness when designing a concrete for a specific task. The power of using a combined experimental/microstructural modelling approach to this problem has been demonstrated and will be developed further in future cooperative research.
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