Critical Grain Size of Fine Aggregates in the View of the Rheology of Mortar
© The Author(s) 2017
Received: 28 August 2016
Accepted: 6 September 2017
Published: 7 December 2017
The aim of this research was to investigate the validity of the Krieger–Dougherty model as a quantitative model to predict the viscosity of mortar depending on various aggregate sizes. The Krieger–Dougherty model reportedly predicted the viscosity of a suspension, which includes cement-based materials. Concrete or mortar incorporates natural resources, such as sand and gravel, referred to as aggregates, which can make up as much as 80% of the mixture by volume. Cement paste is a suspending medium at fresh state and then becomes a binder to link the aggregate after its hydration. Both the viscosity of the suspending medium and the characteristics of the aggregates, therefore, control the viscosity of the cement-based materials. In this research, various sizes and gradations of fine aggregate samples were prepared. Workability and rheological properties were measured using fresh-state mortar samples and incorporating the various-sized fine aggregates. Yield stress and viscosity measurements were obtained by using a rheometer. Based on the packing density of each fine aggregate sample, the viscosity of the mortar was predicted with the Krieger–Dougherty model. In addition, further adjustments were made to determine the water absorption of fine aggregates and was transferred from successful experiment to simulation for more accurate prediction. It was also determined that both yield stress and viscosity increase when the fine aggregate mean size decreases throughout the mix. However, when the mean size of the fine aggregates is bigger than 0.7 mm, the yield stress is not affected by the size of the fine aggregate. Additionally, if aggregate grains get smaller up to 0.3 mm, their water absorption is critical to the rheological behavior.
Viscosity is defined as resistance to flow of fluid under shear stress and taken as the ratio between the shear stress and shear rate (George and Qureshi 2013). Viscosity helps prevent segregation during handling processes such as delivering, and placing for cementitious materials such as mortar or concrete (Khayat 1995). In a concrete mixture, the segregation of coarse aggregate is dominated by the viscosity of mortar. To achieve a high performance on its strength and durability, securing the viscosity for a stable mix becomes more important. On the other hand, an unstable supply of river sand and gravel due to the depletion of natural resources results in the use of various types of coarse and fine aggregates, which include crushed, manufactured, recycled, or marine aggregates. Their physical properties including shape, size, texture, and grading including micro-fines can vary significantly from the reference state of aggregates that originated in a river. Even though they marginally satisfy the standard of aggregates, its poor quality causes difficulty in mix proportioning (Bairagi et al. 1990; Goltermann and Johansen 1997). Also the physical properties of the aggregate affect the performance of concrete and especially dominate workability in its fresh state (Erdoğan and Fowler 2005; Westerholm et al. 2008; Nanthagopalan and Santhanam 2011; Wallevik and Wallevik 2011; Quiroga and Fowler 2004; Mahmoodzadeh and Chidiac 2013). Therefore, evaluating the aggregate effect on the viscosity of freshly mixed cementitious materials allows us to control and guide the selection of the proper type of aggregates.
Based on the idea of coarse aggregates suspended in mortar, the viscosity of mortar dominates the segregation resistance and rheological behavior of the concrete mixture. Predicting viscosity of mortar, composed of fine aggregate and cement paste goes back to the principles behind aggregate particles suspended in cement paste (Erdem et al. 2010; Hidalgo et al. 2009; Toutou and Roussel 2006). This study analyzes the size effect of fine aggregates on the viscosity of the mortar. For this portion of the study we tested mono-sized sands with 10 different diameters, which were mixed with a constant proportioning ratio. Blending the mono-sized sands required gap grading and controlled packing density of fine aggregates (Goltermann and Johansen 1997; Park et al. 2004). The second research objective focuses on the effect of packing density and the associated rheological properties of the mortar samples. The third objective is to determine the effect of aggregates size on their water absorption and the subsequent viscosity of mortar mixtures.
2 Materials and Sample Preparation
2.1 Mortar Samples
The result of sieve analysis of 1000 g sand sample.
Sieve size (mm)
Percent passing (%)
Fundamental properties of the fine aggregate samples.
Mean size (mm)
Error bound (mm)
Absorption ratio (%)
Fill the fine aggregate sample in a 1-L steel cylinder and measure its weight. The fine aggregate sample should then be fully packed using a rubber hammer and the surface leveled.
Calculate the volume of the fine aggregate sample by dividing the weight measured from the previous step by the density of the fine aggregates. The volume occupied by the fine aggregates, per unit volume, would be the packing density. Consequently, the maximum fillable volume ratio of fine aggregates can be obtained for each sample. The measured packing density value of each sample is summarized in Table 2.
The densest packing of uniform spheres is given by closed-packing microstructures. Face centered cubic (FCC) or hexagonal close packing (HCP) generates the highest packing density, π/3√2 = 0.74. In contrast, Song et al. (2008) analytically determined that random close packing (irregular or jammed packing) does not exceed the value of 0.634. The experiment in this study corresponds to the case, and the margin of the spherical diameter in Table 2 addresses the excess of jammed packing. With a margin larger than ±0.2 mm, G 1.77, G 1.43, G 0.89 and G 0.64 exceeded the maximum jammed packing. Thus, the mixed samples and the river sand certainly increased the packing beyond the limit.
The sieve test required oven-dried sand samples; however, when the sand sample is mixed with cement paste as a mortar, the oven-dried sand sample absorbs the mixing water. Hence, it was necessary to determine the absorption rate to calculate the saturated but surface dry (SSD) condition of each sample. Furthermore, since smaller sizes of fine aggregates have higher specific surface areas, fine aggregate samples with the smaller mean size absorbed more water than the larger fine aggregates. This relates to the solid concentration of mortar and its need for a water-to-cement ratio. When this ratio is properly applied, it gives the mortar a higher yield stress and viscosity. The absorption ratio of each fine aggregate sample was evaluated based on ASTM C128 (ASTM International 2015). Table 2 lists the fine aggregate samples’ absorption rates. The absorption ratio increased as the mean size of the fine aggregate sample decreased, as expected. Notably, for G 0.34, about 7.26% of the highest absorption was observed.
Chemical composition of ordinary Portland cement.
3 Tests Results
3.1 Workability of the Mortar Samples
To evaluate the workability of fresh state mortar depending on the sand size, mini-slump flow test and channel flow test were conducted. Basically, the mini-slump flow test was executed with the same method of ASTM C1611 (ASTM International 2010), but a smaller cone mold was used for the mortar consistency test. The dimension of the mini-slump cone is 70 mm-diameter at the top and 100 mm-diameter at the bottom with a height of 50 mm. The channel flow test measure the one-sided flow of a cube sample having 100 mm on each side (Kim et al. 2014, 2015, 2017). For both tests, the measured data was (1) flowing distance and (2) the time duration until flowing stopped.
Workability tests results.
3.2 Rheology of the Mortar Samples
Under these conditions, the yield stress and the plastic viscosity cannot be calculated unless the measured data points are fitted using a nonlinear optimization method.
Comparing predicted viscosity value and measured viscosity value.
Predicted viscosity (Pa·s)
Measured viscosity (Pa·s)
Relative error for the prediction (%)
The difference is within 10% excluding samples G 0.64 and G 0.34. Still it is needed to discuss the high error of G 0.64. It should be noted that its measured viscosity is out of trend, which strongly points to measurement error. Sample G 0.34 showed extremely high viscosity, which caused the estimation to lose its accuracy. Water absorption of fines reportedly maximizes with smaller particles, which will be discussed in the next paragraph. The other samples can be explained by the Krieger–Dougherty equation, which is also valid for the mixed sample case. Measurement of wet packing, contrary to the dry packing adopted in this study, is expected to decrease the difference because the hydrodynamic properties of grains are not consistent when they are floating in a suspended medium (Kwan et al. 2012). Additionally, as a possible factor, the chemical admixtures used in this research are affected by changing packing density under wet conditions, which induces errors between predicted viscosity and dry packing density. For better prediction, although the wet packing conditions of suspension should be evaluated with the influence of chemical admixtures, as per Bentz et al. (2012), it is difficult to evaluate the influence of superplasticizers on packing conditions of suspensions. Furthermore, according to Wallevik and Wallevik (2011), superplasticizer is considered to only affect yield stress of cement paste; furthermore, VMA changes the medium of the suspension rather than the particles. Although this theoretical background as per Quiroga and Fowler (2004) and Bentz et al. (2012) may not follow a prescribed methodology in a practical aspect, this research agrees with their findings that the addition of chemical admixtures to the samples can be considered a factor causing prediction error.
The viscosity estimation error for G 0.34 was approximately 63% in Table 5, and the sample gave the highest water absorption—more than double that of the other samples—as reported in Table 2. The following experiment was designed to verify that the water absorption generates error of the viscosity estimation. Two samples, G 0.45 and G 0.34, were compared. The difference in their water absorption was 3.50%, but their packing densities were very similar, 0.633 and 0.626, respectively. Simply adding 3.50% absorbed water to the S60 sample allows it to maintain same solid volume fraction as G 0.45. After the absorption rate was corrected for G 0.34, the value in parentheses, the rheology parameters and difference to the predicted values were added in Table 5. The prediction of rheological properties was possible at 0.34 mm of the fine aggregate sample size, while the workability difference was observed as smaller than 0.89 mm of the fine aggregate sample size. Therefore, it can be concluded that workability decreases with decreasing particle mean size and is only influenced by water absorption in a range from 0.34 to 0.89 mm. Considering the water absorption effect keeps the Krieger–Dougherty model valid, the hydrodynamic state of the mortar samples is consistent in the range of aggregate size.
Mini-slump and channel flow of mortar showed decreased flowing distance and reaching time with smaller fine aggregate grains. The workability change according to the dimension of aggregates can be related to the relationship between viscosity and the mean size of the fine aggregate sample.
The relation of torque-rotational speed can be analyzed with the Reiner–Rivlin model for quantitative expression of yield stress and viscosity of fresh-state mortar. From the analysis, as the mean size of the fine aggregate decreased, yield stress and viscosity of the fresh state mortar increased. However, the size of the fine aggregate did not influence the yield stress when the aggregate size exceeded 0.70 mm.
The Krieger–Dougherty model allows prediction of the viscosity of mortar, and the viscosity of mortar can be decreased with low packing density of fine aggregate. The packing density was increased from single-sized gradation to multi-sized gradation because of filling effect of various size particles.
Smaller grains of fine aggregates showed higher adsorption per unit mass. For air-dried conditions, since the mortar including the fine aggregate with higher absorption rate decreases water-to-cement ratio, yield stress and viscosity of the mortar can be increased. From the absorption rate measurement, when the mean size of the fine aggregate sample is higher than 0.34 mm (S60), the absorption rate of the fine aggregate is remarkably increased as the mean size of the fine aggregate is increased. In this case, compensating the absorption ratio provided a more accurate prediction of viscosity with the Krieger–Dougherty model.
Therefore, by using the method suggested in this research, the viscosity of a given mortar can be predicted by measuring the viscosity of cement paste and packing density of fine aggregate. This indicates that accurate prediction of the rheological behavior of mortar is possible by conducting a packing density test of various fine aggregate types.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2015R1A1A1A05001382).
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