The relative plastic viscosity was calculated for all mixtures by dividing the plastic viscosity of the mixture containing the coarse aggregates or particles with the plastic viscosity of the matrix (mortar or cement paste). Care was taken to ensure that the matrix that was measured alone was identical to the matrix in the mixture.
All the relative plastic viscosities measured are plotted in Fig. 2. It can be seen that all data are approximately on the same curve. It should be pointed out that the geometry of the various rheometers were not the same and also that the absolute values of the plastic viscosity are not even expressed in the same units in some cases (i.e., IBB). This is explained by Eqs. (1) and (2) and the related discussion. The relative plastic viscosity eliminates the correction factor as seen in Eq. (2). At this point, we do not know the uncertainty of the data shown in Fig. 2 because there was only one trial at each of the data points presented. This is an area that will be further investigated.
Obviously, it is expected that varying the shapes of aggregate would generate a family of curves (relative viscosity versus aggregate concentration) similar to the one shown in Fig. 2. This statement should be confirmed by acquiring more data with different mixture designs, aggregate shape and size distributions, and other rheometers. Assuming that this finding is true, the following scenarios could be imagined for quantitatively comparing rheometers:
First, if a mortar is measured using a rheometer that could be calibrated, using a standard oil for example, all plastic viscosity values could be corrected using a factor (CF) that is the ratio between the mortar plastic viscosity measured with the calibrated rheometer ( ηm1) and with the concrete rheometer ( ηm2). The correction factor will be:
| CF = ηm1/ ηm2 | (3) |
This correction factor does not depend on the condition that all relative viscosities fall on one curve. On the other hand, in order to compare concrete viscosities, it is necessary to examine the relative plastic viscosity, because the CF factor cannot be obtained for concrete, as there are no calibrated concrete rheometers. From Eq. (2) we can state that the relative plastic viscosity is independent of the rheometer or units used for the measurement. Figure 2 shows that the relative plastic viscosity of concrete does not depend strongly on the rheometer used but rather mainly on the concentration of coarse aggregates. Therefore, the following equation could be written:
where ηm is the as-measured plastic viscosity of the matrix or mortar ηc is the as-measured plastic viscosity of the concrete ηTm is the true or absolute plastic viscosity of the matrix or mortar
ηTc is the true or absolute plastic viscosity of the concrete
From Eqs. (3) and (4), we can calculate ηTc:
Therefore, the true value of the plastic viscosity of a concrete can be calculated from Eq. (5). Note that Eq.(5) is definitely dependent on the validity of Eq. (4), while Eq. (3) is not at all dependent on Eq. (4)
Second, if a calibrated rheometer is not available and the goal is to simply compare the as-measured viscosities from two or more rheometers, one of the rheometers could be used as a "reference", and one could then proceed with the same calculation as presented above.
Finally, it is obvious that it might not always be necessary to calculate the absolute value of the concrete plastic viscosity. Different concrete mixtures could simply be compared using the relative plastic viscosity alone. This will allow the comparison of measurements obtained from various rheometers even if the plastic viscosity results were not in the same units.
The procedure based on Eq. (4) depends on the observation that all relative plastic viscosities versus aggregate concentration are on the same curve. It is possible that factors that were not considered here might intervene, such as the coupling of the walls with the coarse aggregates. The significance of the variation needs to be established by conducting more measurements. Further data need to be collected to definitively establish the existence of a master curve relating relative plastic viscosity with coarse aggregate concentration, shape, or other factors.
In conclusion, it has been shown for the rheometers used that the relative plastic viscosity does not seem to depend on the rheometer but only on the amount of coarse aggregate (or particle) that were added to the matrix (mortar or cement paste). Therefore, the relative plastic viscosity can be used to compare data from various instruments even when a calibration with a standard material is not available and the results from the rheometers are given in different units. Some tests mortar will be included in phase II of the ACI sponsored round-robin tests of four commercially available concrete rheometers to be held in 2003, in order to further test the validity of this method. Another implication of this conclusion is that modeling of the flow concrete can be reduced to the flow of particles in matrix. The only variable to be modified is the shape and concentration of the particles or aggregates. If relative plastic viscosity is given and the mortar plastic viscosity is measured, the plastic viscosity of the concrete can be calculated. This procedure is being developed at NIST by creating a database searchable by shape and the gradation of the coarse aggregates. data will be presented as a curve of relative plastic viscosity versus the concentration of the coarse aggregates [14]. This method of presenting the data related to plastic viscosity will allow a leap forward in the interpretation of the data provided by various concrete rheometers, which will eventually allow optimization of concrete workability in terms of the materials used and the desired performance.