While laboratory rheometers provide comprehensive data, present field methods are severely limited because most of time they give only a value related to either yield stress or plastic viscosity. Laboratory rheometers are sophisticated and expensive, while most field test are easy to use and inexpensive. Due to the variability of the composition of the components and the difficulties in determining the proper water dosage, concrete mixtures are typically not optimized for performance. On the contrary, concrete should be subject to rigorous quality control with the possibility of correcting in real time, if necessary, to improve the uniformity of the material's most important properties, including the rheological properties. The measurement of rheological properties of concrete is straightforward in the laboratory using a rheometer of the type described in this report but it must be used by trained personnel and it is expensive. Therefore, there is a need for a simpler, inexpensive device for making rapid and reliable measurements in the field.

Even if the rheological behavior of the concrete is reduced to two parameters (yield stress and plastic viscosity), the array of current rheological tests for field use does not permit them to be evaluated, except very roughly. While the slump test, the grandfather, and most widely used, of all tests, provides an indication that is reasonably well correlated to the yield stress [7], the other tests — DIN flow table, VEBE apparatus, etc. [42] — provide results that are not very useful in terms of characterizing the rheological parameters. In most of these tests, the concrete flows under the effect of a dynamic loading. Thus, the behavior of the concrete under vibration is brought into play, although nothing indicates that this is related directly to the behavior of the unvibrated concrete (as illustrated by the Bingham parameters).

A survey of the state of the art showed that none of the current "field" tests (in distinction to rheometers) makes it possible to assess the plastic viscosity of the concrete [42]. However, this parameter is assuming increasing importance in modern concretes. For high-performance concretes, it frequently constitutes the critical parameter that controls pumpability [7], and ease of finishing. This chapter describes a modification of the slump apparatus that, on the basis of the measurement of a partial slump time, makes it possible to evaluate the yield stress and the plastic viscosity in the field.

5.1.1. Previous work of Tanigawa et al. [9, 10]

Professor Tanigawa's team in Japan has played a large role in development of the applications of the rheology of fresh concrete. In particular, these researchers have performed finite-element analyses of the current rheological tests to establish equivalencies between the results of these tests and the fundamental rheological properties [9]. However, for lack of a concrete rheometer, it was not possible to validate most of their calculations by test results, which limits their application and is a possible reason why Japan, although very active in research on the properties of fresh concrete, has not yet routinely utilized the concepts of rheology in industrial practice (to the authors' knowledge).

Concerning the standard slump cone test, Tanigawa et al. [9, 10] performed measurements of the slump as a function of time (Figure 21). They found that the slump-time curve could be simulated by finite element analysis of the fresh concrete assumeng it to be a Bingham material. The slump-time curve depends on both the yield stress and the plastic viscosity. Since the final slump is related directly to the yield stress, it is reasonable to assume that the time-dependance of slump is likely to be controlled by the plastic viscosity. Considering that the slump test is currently the only field test in the world for most practitioners, the apparatus was modified slightly in this study in an attempt to measure both the yield stress and the plastic viscosity of fresh concrete. This chapter describes the modification made to the standard slump test apparatus, test procedure and calculation to determine both the yield stress and the plastic viscosity.

Figure 21. Experimental setup of Tanigawa et al. [9, 10] for recording the slump as a function of time.

Since the goal was to develop a test that was above all simple, robust and inexpensive, it was not practical to record the slump as a function of time. To do a complete recording, it would have been necessary to provide for electronic data acquisition. The interpretation of the resulting curve would also have been too complex. Therefore, it was decided to try to characterize the plastic viscosity based on an average rate of slumping in the slump test. Thus, measurement of the time necessary to reach an intermediate height between the initial and final values appeared a priori to be a good means of discriminating among the concretes according to their plastic viscosity.

The choice of this "partial slump" took into consideration two potential problems: (1) a height that was too small would lead to very small slump times and thus poor relative precision of measurement; (2) a partial slump that was too large would rule out all of the concretes with a smaller final slump. Since the range of concretes that can be characterized by the rheometer is, as already stated, approximately that for which the slump is greater than 100 mm, this value was chosen for the partial slump.

The Tanigawa setup for measuring slump as a function of time would be too fragile for a work-site environment [9]. Therefore, we adopted the use of a plate, allowed to slide on a centrally-located rod as the means for monitoring the time to reach the 100-mm slump. The rod coincides with the axis of symmetry of the conic frustum. Since the axis of symmetry was in principle preserved during the flow of the concrete, the rod would not be expected to greatly disturb the slump. This point was later verified.

In order to measure the partial slump time, it was adequate to use a stopwatch controlled by the operator on the basis of a visual criterion (such as in the VEBE test). The stopwatch is started at the begining of raising of the cone, and is stopped when the sliding plate placed on the fresh concrete reaches the stop on the rod (Figure 22). The dimensions of the apparatus and the test setup are shown in Figure 23 and Figure 24.

Figure 23. Rod and top plate in the modified slump apparatus.

Figure 24. The modified slump test apparatus: A) View from above the mold showing the top plate; B) View of the mold, the rod attached to the base and the top plate at the final position.

The following components are needed to conduct the modified slump test:

• A horizontal base to which the rod is attached;
• A standard mold for the slump test (ASTM C143 [17]);
• A sliding disk (the upper plate);
• A rubber o-ring seal, the purpose of which is to prevent fine materials from interfering with the fall of the disk;
• A rod to consolidate the concrete;
• A small trowel to finish the upper surface of the concrete;
• A ruler to measure the slump;
• A stopwatch with a resolution of 0.01 s.

The concrete was placed in the same manner as in the standard slump test (ASTM C143-90 [17]). The various stages are as follows:

1. Carefully clean the rod and coat it with grease or petroleum jelly (down to the stop);
2. Using a wet sponge, moisten the base and the inside wall of the mold;
3. Place the mold on the base, assuring that the rod is centered with respect to the upper opening;
4. While keeping the mold in place on the base (either with attachments provided for this purpose or by standing on the foot pieces welded to the outside of the mold), fill it in three layers of equal volume, rod each layer 25 times;
5. Strike off the surface of the concrete, assuring that it is level as possible with the top of the mold;
6. Using a rag, clean the part of the rod that projects above the concrete specimen;
7. Slide the disk along the rod until contact is made with the surface of the concrete;
8. Raise the mold vertically while starting the stopwatch;
9. While the concrete is slumping, continually observe the disk (through the top of the mold) and stop the stopwatch as soon as the disk stops moving;
10. Once the slump has stabilized, or no later than one minute after the start of the test, remove the disk and measure the slump with the ruler.

The modified slump test as described was performed on all of the mixtures and the partial slump times (which will hereafter be called the slump times) are given in the tables in Appendix IV-VI. When the mortars and concretes for which the final slump was less than 100 mm are excluded, the measured slump times range from 0.63 to 15.97 seconds.

One question was whether the minimum time was controlled by the slump of the concrete, with the disk remaining in contact with the concrete during the fall. The theoretical time for an initially stationary body subject to gravity to free fall a distance h of 100 mm is , or 0.14 seconds. Two measurements of the fall time of the disk on the rod (without concrete) gave values of 0.16 and 0.15 seconds. Hence, it was concluded that any separation from the concrete was unlikely (at least with the concretes tested). In addition, the precision of measurement is on the order of 1/10 of a second due to the reaction times of the operator. Also, the variability will be larger because the cone lifting is not precisely controlled [43].

The consistency of the measurements was examined by considering the variation in slump time within each mixture group. With rare exceptions, the times are on a single curve when plotted against the volume of mixing water: they decrease regularly as the water dosage increases. On the other hand, comparison of the average values of series of measurements is equally instructive and encouraging. The average slump times of all mixtures without HRWRA is 1.51 seconds (range of + 0.54 seconds), while the values for mixtures with HRWRA are generally greater and more widely spread (average of 4.80 seconds, range of + 4.66 seconds). Therefore, this test will be more useful in determining the plastic viscosities of concretes with HRWRAs.

A check was done to determine whether the modification to the standard slump test affected the final slump measurement. This was necessary to have complete compatibility with the unmodified test.

The mass of the disk (212 g) increases the vertical stress on the sample by a maximum value equal to its weight divided by the upper area of the frustum, i.e., 0.27 kPa. When the disk reaches the stop, the height h of the concrete is 200 mm. Hence, the vertical compression stress at the base of the sample equals gh (where   =  2400 kg/m³ is the approximate density of the fresh concrete and g is the acceleration due to gravity), i.e., about 4.8 kPa. It is thus seen that the vertical stress due to the disk is at most on the order of 6% of the stress due to the concrete. The friction of the concrete along the rod would tend to reduce the final slump. To verify that the effects of the disk and the rod are negligible, a comparative study was done with six compositions chosen to be representative of the range of slumps obtained. The two tests (the standard slump test and the modified test) were conducted in parallel. Figure 25 shows the comparison between the two tests. The best fit line with an intercept of 0 has a slope of 1.01 with a standard error of 0.03. The residual of the line is a standard deviation of 17 mm. Therefore, the slumps measured with the two tests are identical.

Figure 25. Comparison of the slump values between the standard slump test and the modified test.

5.3.1. 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 [8] in the following form:

0 =    (300-s) /  270

(18)

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 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. Figure 26 compares the experimental yield stress obtained from the Herschel-Bulkley model with a estimated yield stress based on equation (18).

Figure 26. Comparison between the experimental yield stresss from fitting the Herschel-Bulkley model and predictions from Hu's model (equation 18) [7]. The line represent the perfect correlation (45 º line).

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 of 100 to 2000 Pa. (Figure 26). However, there is a systematic underestimate of the yield stress in the low range, typical of 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

(19)

results in a 162 Pa average error with respect to the measurements (see Figure 27). The improvement is particularly notable for the very fluid mixtures.

Figure 27. Comparison between experimental yield stress from fitting the Herschel-Bulkley model and predictions using equation 19. The line represent the perfect correlation (45 º line).

To evaluate the plastic viscosity from the results of the modified slump test, the following assumption was invoked: for concretes with 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 can be expected that the factor µ / gT (where µ is the plastic viscosity and T the slump time) is a function of the final slump. Figure 28 shows the value of the factor µ / T plotted as a function of slump for the mixtures with slump less than 260 mm. For the mixtures with higher slumps (self-leveling concretes), the scatter is larger because of the very short slump times and the higher probability of segregation.

Figure 28. Relationship between the ratio µ/T and the final slump

µ =  1.08 · 10-3 (S - 175)  T	for 200 < S < 260 mm
µ =  25 · 10-3  T	for S < 200 mm	(20)

where  = density in kg/m³ (in our case = 2400 kg/m³), T = slumping time in seconds, S = final slump in mm, µ =  Viscosity in Pa·s.

From these equations, the plastic viscosity can be estimated from the density, the final slump (in mm) and the 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 29). Two mixtures (BHP4C and BHP4B), that deviate significantly from the correlation, can be considered outliers because their composition included an excess of gravel (which is rare in practice especially for superplasticized concretes), and because there was a lack of cohesion during the slump tests. Excluding the two outliers, a linear correlation a slope of 1.09 + 0.03 (Figure 29) is found between the theoretical and measured plastic viscosity. This slope indicates a very good correlation between the two entities.

To avoid calculations using equations 19 and 20, nomographs are given in Figure 30 to rapidly estimate the yield stress (in Pa) and the plastic viscosity (Pa·s) from measurements of the final slump and the slumping time with the modified slump test for a concrete with a density of 2400 kg/m³.

In using these models and empirical equations to determine the yield stress and the plastic viscosity, we assumed that the concrete followed the modified Bingham model described in section 3.1.4.

In conclusion, the modified slump tests and model presented allows an evaluation of the plastic viscosity of concretes but with a lower accuracy than from the rheometer. Therefore, the modified slump test is most likely to be used as a quality control procedure in the field, and the rheometer as a development instrument for determining the optimum mix design for a specific application.

Figure 29. Comparison between measured plastic viscosity using the BTRHEOM and predictions from the plastic viscosity model (equation 20) for concretes with slumps between 120 and 260 mm. The slope of the best fit straight line, shown, passing by the origin is 1.09 with a standard error of 0.03.