Estimation of the fundamental rheological parameters on the basis of the modified slump test

Models to evaluate yield stress

Based on finite element analysis of the slump test and on measurements of the yield stress using the rheometer and of the slump, Hu proposed a general formula relating the slump s to the yield stress ₀ (De Larrard et al. 1994 [4]) in the following form:

₀ =  / 270 (300 - s)           (2)

where (density) is expressed in kg/m³ ₀ in Pa, and s in mm. A correlation with experimental data was shown to give a reasonable prediction of the Bingham yield stress. However, despite the fact that the plastic viscosity is not taken into account in the Equation 2, it does play a role. Hu found that the correlation is poor if the concrete's plastic viscosity is greater than 300 Pa·s.

In the present case, the predictions for the yield stress provided by this model are quite reasonable. There is an average error of 195 Pa for the yield stress in the range [100 - 2000 Pa], Figure 6). However, one finds a systematic underestimate of the yield stress in the low range, that is for self-leveling concretes. The accuracy of Hu's model can be improved empirically by adding a constant term and modifying the slope term. The following equation:

₀ (300 - s) / 347 + 212          (3)

results in a 162 Pa average deviation with respect to the measurements (see Figure 7). The improvement is particularly notable for the very fluid mixtures.

Figure 6. Comparison between the experimental yield stress measured using the rheometer and predictions from Hu's model ((Equation 2) (De Larrard 1994 [4] (SP = HRWRA)

Figure 7. Comparison between experimental yield stresss measured using the rheometer and predictions from equation 3. (SP=HRWRA)

A semiempirical model to evaluate plastic viscosity

To evaluate the plastic viscosity from the results of the modified slump test, the following assumption was invoked: for the same final slump and the same density concrete; a difference in slump time can be attributed to a difference in plastic viscosity. From a dimensional analysis, it is to be expected that the factor µ/g T (where µ is the plastic viscosity calculated from the measurements done with the rheometer and T the slump time) are functions of the final slump. The density is expressed by and g represent the gravitational acceleration. The relationship between µ/ gT and the final slump is shown on the plot on Figure 8, excluding the self-levelling concretes (right area of the diagram, slump higher than 260 mm). For these mixtures, the scatter is larger because of the very short slump times and the higher probability of segregation.

Figure 8. Relationship between the ratio /T and the final slump

If we consider only concretes having a slump lower than 260 mm, the best fit to the data is given by the following equation:

	µ = T·1.08·10 -3 (S - 175)	for 200 < S < 260 mm
	µ = 25·10-3 T	for S < 200 mm	(4)

From these equations, the plastic viscosity can be estimated from the unit mass, the final slump (in mm) and the partial slump time in seconds. The average error for this model for all the concretes with a slump between 120 and 260 mm is 66 Pa· s (Figure 9). Two mixtures that deviated significantly from the correlation (Ferraris et al. 1997[6] ), can be considered outliers because their compositions included an excess of gravel (which is rare in practice especially for concretes containing HWRA), and because there was a lack of cohesion during the slump tests (Ferraris et al. 1997 [6] ). Excluding the two outliers, a linear correlation having a slope of 1.09 + 0.03 (Figure 9) is found between the theoretical and measured viscosity. This slope indicates a very good correlation between the two entities. To avoid calculations using equation 4, nomographs are given on Figure 10 to rapidly calculate the yield stress (in Pa) and the viscosity (Pa·s) from the measurements of the final slump and the slumping time with the modified slump test for a concrete with a unit mass of 2400 kg/m³.

Figure 9. Comparison between experimental measured using the rheometer and predictions of the plastic viscosity model ( Equation 4) for concretes with a slump between 120 and 260 mm. The slope of the best fit straight line, shown, passing through the origin is 1.09 + 0.03.

Figure 10. Nomographs for estimating the yield stress and plastic viscosity of concrete from the results of the modified slump test (for a concrete with a density of 2.400 kg/m³).

In conclusion, the model presented gives an evaluation of the plastic viscosity of concrete from the measurements with the modified slump cone with a lower precision than the rheometer. Nevertheless, the new test should be useful for quality control in the field, while the rheometer is to be prefered as an instrument for determining the optimum mixture design for a specific application.

Estimation of the fundamental rheological parameters on the basis of the modified slump test

Models to evaluate yield stress

Based on finite element analysis of the slump test and on measurements of the yield stress using the rheometer and of the slump, Hu proposed a general formula relating the slump s to the yield stress ₀ (De Larrard et al. 1994 [4]) in the following form:

₀ =  / 270 (300 - s)           (2)

where (density) is expressed in kg/m³ ₀ in Pa, and s in mm. A correlation with experimental data was shown to give a reasonable prediction of the Bingham yield stress. However, despite the fact that the plastic viscosity is not taken into account in the Equation 2, it does play a role. Hu found that the correlation is poor if the concrete's plastic viscosity is greater than 300 Pa·s.

In the present case, the predictions for the yield stress provided by this model are quite reasonable. There is an average error of 195 Pa for the yield stress in the range [100 - 2000 Pa], Figure 6). However, one finds a systematic underestimate of the yield stress in the low range, that is for self-leveling concretes. The accuracy of Hu's model can be improved empirically by adding a constant term and modifying the slope term. The following equation:

₀ (300 - s) / 347 + 212          (3)

results in a 162 Pa average deviation with respect to the measurements (see Figure 7). The improvement is particularly notable for the very fluid mixtures.

Figure 6. Comparison between the experimental yield stress measured using the rheometer and predictions from Hu's model ((Equation 2) (De Larrard 1994 [4] (SP = HRWRA)

Figure 7. Comparison between experimental yield stresss measured using the rheometer and predictions from equation 3. (SP=HRWRA)

A semiempirical model to evaluate plastic viscosity

To evaluate the plastic viscosity from the results of the modified slump test, the following assumption was invoked: for the same final slump and the same density concrete; a difference in slump time can be attributed to a difference in plastic viscosity. From a dimensional analysis, it is to be expected that the factor µ/g T (where µ is the plastic viscosity calculated from the measurements done with the rheometer and T the slump time) are functions of the final slump. The density is expressed by and g represent the gravitational acceleration. The relationship between µ/ gT and the final slump is shown on the plot on Figure 8, excluding the self-levelling concretes (right area of the diagram, slump higher than 260 mm). For these mixtures, the scatter is larger because of the very short slump times and the higher probability of segregation.

Figure 8. Relationship between the ratio /T and the final slump

If we consider only concretes having a slump lower than 260 mm, the best fit to the data is given by the following equation:

	µ = T·1.08·10 -3 (S - 175)	for 200 < S < 260 mm
	µ = 25·10-3 T	for S < 200 mm	(4)

From these equations, the plastic viscosity can be estimated from the unit mass, the final slump (in mm) and the partial slump time in seconds. The average error for this model for all the concretes with a slump between 120 and 260 mm is 66 Pa· s (Figure 9). Two mixtures that deviated significantly from the correlation (Ferraris et al. 1997[6] ), can be considered outliers because their compositions included an excess of gravel (which is rare in practice especially for concretes containing HWRA), and because there was a lack of cohesion during the slump tests (Ferraris et al. 1997 [6] ). Excluding the two outliers, a linear correlation having a slope of 1.09 + 0.03 (Figure 9) is found between the theoretical and measured viscosity. This slope indicates a very good correlation between the two entities. To avoid calculations using equation 4, nomographs are given on Figure 10 to rapidly calculate the yield stress (in Pa) and the viscosity (Pa·s) from the measurements of the final slump and the slumping time with the modified slump test for a concrete with a unit mass of 2400 kg/m³.

Figure 9. Comparison between experimental measured using the rheometer and predictions of the plastic viscosity model ( Equation 4) for concretes with a slump between 120 and 260 mm. The slope of the best fit straight line, shown, passing through the origin is 1.09 + 0.03.

Figure 10. Nomographs for estimating the yield stress and plastic viscosity of concrete from the results of the modified slump test (for a concrete with a density of 2.400 kg/m³).

In conclusion, the model presented gives an evaluation of the plastic viscosity of concrete from the measurements with the modified slump cone with a lower precision than the rheometer. Nevertheless, the new test should be useful for quality control in the field, while the rheometer is to be prefered as an instrument for determining the optimum mixture design for a specific application.