Development of an adaptive coaxial concrete rheometer and rheological characterisation of fresh concrete

5.1.1 Standard measuring procedure – aluminium profiles

In the first investigation series, the SCC was measured in three measurement series, with one measurement series consisting of five individual measurements without changing the specimen. The results of all 15 individual measurements are shown in Figure 6. The mean temperature of the first measurement series was T m = 22.17 ± 0.27 ° C , for the second measurement series T m = 22.20 ± 0.11 ° C , and for the third measurement series T m = 19.77 ± 0.12 ° C , whereby the temperatures as expected increased slightly with the increase in the individual measurements for each measurement series. Regarding the reproducibility, the measured values, with the exception of the individual measurements 3 and 5 of the third measurement series, agree quite well. A deviation in the third measurement series can be explained by the lower temperature as an indication of a comparatively reduced reaction of the concrete and hence a less pronounced structural build-up, causing a lower shear stress compared to measurement series 1 and 2 .

Figure 6

Representative values of SCC, measured in the standard process with modified aluminium profiles.

It can be seen that the shear stress increases significantly with the increase in the individual measurement number. This can be attributed to the reaction of the concrete and the structural build-up over time. This behaviour is particularly important in the context of the reproducibility of future measurements, as it highlights the relevance of adhering to a strict schedule when measuring concrete.

Furthermore, the flow behaviour of the concrete can be characterised in more detail. For low shear rates of approx. γ ̇ rep = 5 s − 1 , the curves indicate a shear thinning behaviour, which changes to Newtonian flow behaviour in the medium shear rate range of approx. γ ̇ rep = 5 – 35 s − 1 . If the shear rate increases above γ ̇ rep = 35 s − 1 , dilatant behaviour seems to arise. These characteristics could be explained by the properties of highly concentrated suspensions. As the shear rate increases, the particles form sliding planes, which lead to a reduced resistance, i.e. shear thinning behaviour, and then converges to a steady state with Newtonian behaviour. If the relative velocities of the particles become too high at high shear rates, the impact probability of the particles and thus the energy dissipation increases, which could explain the dilatant flow behaviour. But the alleged dilatant behaviour at high shear rates may also be the result of too less pre-shearing and an already existing structural build-up at the beginning.

Furthermore, the shear thinning behaviour at low shear rates must be considered in more detail. During some measurements, a completely unsheared area was formed, probably due to a drop below the yield stress, resulting in a reduction in the measuring gap starting from the outer cylinder, Figure 7. In such a state, the shear rate is effectively higher than assumed and the influence of coarse-grained particles in the reduced gap is bigger, so that the measured shear stresses lose validity. However, this phenomenon occurred primarily in the later individual measurements, so that at least the first individual measurements are valid for classical rheological investigation. A correction of this block building phenomenon is almost impossible due to the large number of influencing parameters. Not only the yield stress of the fresh concrete, which depends on the time and the load history, is relevant, but also the parameters already mentioned, such as the particle-to-gap ratio, the particle shape, the orientation of the particles during shear, and the particle migration. It is also unclear to what extent the local concrete composition changes with this reduction in the measuring gap, since, at least apparently, an increased water content could be observed in the reduced gap. Furthermore, the occurrence of the gap reduction can only be detected by observing the measuring gap and not from the measurement values themselves.

Figure 7

Schematic representation of the angular velocity and yield stress dependent gap reduction from R o , 0 to R o ( ω , τ y ) in the presence of τ y > τ o from the sectional view with shear stress profile (left) and the plan view (right).

A possible solution to this problem would be the increase in the geometry parameter β , since this minimises the difference between τ o and τ i , and the yield stress on the outer cylinder would only be undercut at very low shear rates, if at all. Although β can be increased in the ACCR by using thicker-walled measurement profiles, the particle-to-gap ratio would decrease and make further measurements doubtful in this regard. A scale up of the whole system would come with other problems like general manufacturing, measurement operability, or positioning accuracy.

In the following, the applicability of the common flow models (Bingham (B), Herschel-Bulkley (HB), modified Bingham model (MB)) for concrete, see Section 2.3, will be used for further characterisation. Since the values in the high shear rate range ( γ ̇ rep > 35 s − 1 ) are considered problematic due to a lack of knowledge regarding sufficient pre-shearing, only measured values up to γ ̇ rep ≈ 35 s − 1 are examined. The measured values in the low shear rate range ( γ ̇ rep < 5 s − 1 ) are also discussed carefully due to the abovementioned gap reduction, which occurred only in the later individual measurements 4 and 5 . Therefore, only the first three individual measurements are considered in the following evaluation. In addition, since the third measurement series only matched the other measurement series to a limited extent due to the deviating temperature and strong deviation of the individual measurements 3 and 5 , only the mean values of the first two measurement series are included in the evaluation. Figure 8 shows the mean values of the considered individual measurements and the corresponding fitting parameters can be found in Table 2. The classical concrete models describe the flow behaviour of the SCC well, but there are some deviations in the low shear rate region ( γ ̇ rep < 5 s − 1 ). No significant difference can be seen between the Bingham and the modified Bingham model, only the Herschel–Bulkley model seems to be able to somehow reproduce the shear thinning region for γ ̇ rep < 5 s − 1 .

Figure 8

Mean values of the individual measurements of SCC from the first two measurement series fitted with the Bingham model, the Herschel–Bulkley model, and the modified Bingham model.

Taking a closer look at Table 2, it can be seen that the yield stress increases significantly for all models with the increase in the individual measurement and is about twice as high for the third individual measurement. A reason for this might be the structural build-up. However, the yield stresses are of the same order of magnitude for all models with very low deviations.

The parameters describing the viscosity ( η pl and k ) are also of the same order of magnitude for all models in the first individual measurement, but deviate more strongly from one another for the further individual measurements. It is striking that for the Bingham and the modified Bingham model, the plastic viscosity η pl changes only slightly with the increase in the individual measurement, but the consistency k of the Herschel–Bulkley model increases strongly. While both the Bingham models thus indicate a flow behaviour in which only the yield stress increases with time, but the plastic viscosity remains almost constant, the Herschel–Bulkley model indicates a basic change in the flow behaviour. This is shown not only by the increase in consistency, but also by the flow index n , which by a steady decrease indicates an increasingly pronounced shear thinning behaviour with the increase in the individual measurement.

To this extent, it is not possible to clearly identify which of the models is best suited to describe the flow behaviour of the SCC based on the model parameters listed in Table 2 and Figure 8. If, due to the gap reduction, only the first individual measurement is considered, the Herschel–Bulkley model seems to be the best in terms of both error sum of squares and visual matching with the measured values. However, since the differences are minute and this evaluation is based on only two measurements, further investigation is necessary, see Section 5.2.

The reaction of the aluminium was assumed to be negligible in this investigation because the contact area of the aluminium to the concrete had been very small compared to the total sample material. Nevertheless, during this investigation series, it was found that the gas bubbles had risen. For this reason, all subsequent investigations have been carried out with stainless steel profiles.

5.1.2 Hysteresis measurements

In the context of this work, the flow behaviour of SCC is generally characterised by conducting an NSR starting at high shear rates and then decreasing the shear rate step by step. Nevertheless, investigation via hysteresis measurements can provide a deeper insight into the rheology of SCC. Therefore, a PSR starting at low shear rates and then increasing the shear rate was added to the standard measurement procedure, which is performed directly after the negative ramp. Figure 9 presents the results of the hysteresis measurements where two measurement series were performed with two individual measurements each. Due to the longer investigation period, only two measurement cycles were possible before stronger hardening became relevant. The mean temperature for the first measurement series was T m = 23.80 ± 0.15 ° C and for the second measurement series T m = 22.20 ± 0.3 ° C . As before, the temperatures increased slightly for each individual measurement. Again, maintaining the same temperature for all measurements is very difficult and the deviations in the results can be ascribed to the insufficient temperature control. Nevertheless, a qualitative analyzation is possible. First of all, it can be noted that the curve of the PSR shows a clearly different characteristic than the NSR. While the NSR at the beginning, i.e. at shear rates in the range of γ ̇ rep = 35 – 40 s − 1 , indicates a dilatant behaviour, this cannot be recognised for the PSR at any time. This supports the assumption of insufficient pre-shearing already made in Section 5.1.1. Furthermore, in the range of low shear rates ( γ ̇ rep < 10 s − 1 ), the PSR shows a slightly more pronounced shear thinning behaviour than the NSR. However, it is unclear whether this behaviour could also be due to the phenomenon of gap reduction and/or structure build-up, since the values of the PSR for the low shear rate range show much larger fluctuations than those of the NSR. An interesting effect becomes obvious analysing the NSR curves recorded immediately after the PSR curve, i.e. measurements 1.1 PSR → 1.2 NSR and 2.1 PSR → 2.2 NSR, as they lie below the values of the PSR curve and intersect them in both cases at a shear rate of about γ ̇ rep = 10 s − 1 . This behaviour suggests that more structures were present in the earlier timed PSR measurements. This leads to two conclusions. There is a structure formation even if low shear is present and the structure destruction may be strongly dependent on the shear rate and the time.

Figure 9

Representative values of the hysteresis measurements of SCC for performing two measurement series with two individual measurements each.

Therefore, the dilatant behaviour at the beginning of the NSR might occur due to insufficient pre-shearing since this behaviour could not be observed in the PSR. These results clearly emphasize how important a sufficient pre-shearing and the use of NSR is.

5.2.1 Reproducibility

All 15 measurement series conducted can be seen in Figure 10 (first individual measurements) and Figure 11 (second individual measurements). When comparing the two diagrams, it is obvious that the fluctuations during one measurement are more pronounced in the first individual measurements. Even if the pre-shearing has already been greatly increased, this, again, could be an indication that various accumulations of structures were still present. However, a clear cause for these curves could not be determined. Especially for the second individual measurements, it is noticeable that some individual measurements strongly deviate from the majority and were excluded from further investigation. These are 1.2, 9.2, 12.2, 14.2, and 15.2. These deviations coincide with the macroscopic concrete behaviour observed during the measurements, since either an increased temperature was detected (1) or the formation of shear bands (unsheared, circular ring-shaped areas moving with the direction of rotation) occurred (9, 12, 14, 15). Even though in a good agreement with the other individual measurements, measurements 2 and 6 were also excluded from consideration because of the same reasons. Figure 12(a) and (b) shows the remaining measurements and the good reproducibility. As an objective indication for the reproducibility, the coefficient of variation v , the quotient of standard deviation and the arithmetic mean, was calculated and plotted against the shear rate in Figure 13. As expected, the values of v are smaller for the second individual measurements. It is also noticeable that the coefficients in both cases decrease with the increase in the shear rate, which can be explained by the concrete behaviour at low shear rates already described.

Figure 10

Representative values of the adjusted concrete mix for the first individual measurements of the 15 measurement series.

Figure 11

Representative values of the adjusted concrete mix for the second individual measurements of the 15 measurement series.

Figure 12

Selected representative values of the adjusted concrete mix of the first individual measurements (a) and the second individual measurements (b).

Figure 13

Values of the coefficient of variation v vs the shear rate for the first individual measurements ( v 1 ) and the second individual measurements ( v 2 ) with mean values of v 1 = 0.033 ± 0.011 and v 2 = 0.026 ± 0.007 .

In principle, the evaluation of the coefficient of variation depends on the considered area, but in general, coefficients below 0.1 can be described as good [54], which shows the high reproducibility of the ACCR with v max < 0.05 .

5.2.2 Rheological characterisation of fresh concrete

Since the previous obtained values showed a very good reproducibility, they were averaged for the individual measurements 1 and 2 to obtain only one curve for each individual measurement, Figure 14(a). The mean temperatures are T m , 1 = 21.99 ± 0.27 ° C and T m , 2 = 21.95 ± 0.21 ° C . The standard deviation is smaller than the line thickness and the thickness of the measuring points so that it is not presented in the diagrams. Additionally, some values are excluded (see marked values) and the curves are fitted with the common concrete models in Figure 14(a), which will be discussed later.

Figure 14

(a) Representative mean values of the first and second individual measurements of the selected measurement series with excluded shear rates and fitted models. (b) Representative measured values of an additional measurement with increased shear rate.

While the course of the first individual measurements is almost linear for shear rates γ ̇ rep > 10 s − 1 and for the previously critically considered high shear rates ( γ ̇ rep > 35 s − 1 ), the course of the second individual measurements shows stronger curvatures both for γ ̇ rep > 10 s − 1 and for γ ̇ rep > 35 s − 1 . Thus, the first individual measurements indicate a Newtonian flow behaviour from γ ̇ rep > 10 s − 1 , while the second individual measurements indicate a slightly shear thinning behaviour for 10 s − 1 < γ ̇ rep < 30 s − 1 , which appears to reverse the dilatant behaviour from γ ̇ rep > 30 s − 1 . For shear rates, γ ̇ rep < 10 s − 1 , the curves are similar, at least with respect to curvature, and suggest shear thinning behaviour. The shear stresses are in the range of τ rep ≈ 150 – 650 Pa throughout the measurement range for the first individual measurements, while for the second individual measurements, it is τ rep ≈ 200 – 700 Pa , which again can be explained by time hardening.

Since the course of the first individual measurements is now also almost linear for γ ̇ rep > 35 s − 1 , the previously interpreted dilatant behaviour (c.f. Section 5.1) can be attributed to insufficient pre-shear (time and/or intensity). However, this is different for the second individual measurements with a more aged concrete mix. To get a better insight in the high shear region, further investigations were performed with an increased maximum shear rate from γ ̇ i > 45 to 47 s − 1 , Figure 14(b).

Comparing Figure 14(a) and (b), it can be clearly seen that the onset of the apparent shear thickening shifts to higher shear rates, which again is an indication for insufficient pre-shearing, especially for the second individual measurements. The hysteresis measurements, see Section 5.1.2, also showed no increase in this shear rate range for the PSR, while showed an increase for the NSR. Therefore, the described effect can clearly be attributed to insufficient pre-shearing and not to dilatant flow behaviour. This also becomes obvious when looking at the course of the torque, see supplementary material S3, since the torque for the first measurement value has not yet reached a pure steady state value in the second individual measurement, but has already done so in the first individual measurement. Therefore, the measured value at the highest shear rate of the second individual measurements is not included in the further evaluation. Again, the effect of gap reduction occurred at low shear rates, as discussed in detail in Section 5.1.1. The start of the gap reduction can only be determined to a limited extent via the measured values, which makes it a critical problem for the measurement. It is only possible to identify a kind of “step course” in both the individual measurements from a shear rate of approx. γ ̇ rep < 5 s − 1 , which >somehow coincides with the optical observation of the gap reduction starting from a shear rate of γ ̇ rep ≈ 5 s − 1 for the first individual measurements and from γ ̇ rep ≈ 8 s − 1 for the second individual measurements. Therefore, this low shear region was also excluded in the following characterisation, c.f. Figure 14(a).

Looking at the first individual measurements, the values show a linear and thus Newtonian behaviour. Although the first point ( γ ̇ rep = 38.13 s − 1 ) suggests a slightly increasing tendency, this cannot be assessed with certainty at this point and can be interpreted as a fluctuation in the measured values. The Newtonian behaviour is also obvious in the very good model fits (Bingham, Herschel–Bulkley, modified Bingham model), see Table 3, although the Herschel–Bulkley model ( n = 1.08 ) and the modified Bingham model ( c = 0.029 ) indicate a very slight dilatancy. However, these parameters are close to one and zero, respectively, and thus have little to no influence, see equations (8) and (9). Furthermore, when comparing the rheological parameters, it is noticeable that both the yield stresses and the characteristic values describing the viscosities are in a similar range ( τ y ≈ 200 Pa , k and η pl ≈ 10 Pa s ( n ) ). Thus, to this extent, all models resemble the concrete behaviour in a very good manner in a medium shear rate range.

The situation is different for the second individual measurements. As already described in the consideration of the entire shear rate range, a slight tendency to shear thinning up to γ ̇ rep ≈ 25 s − 1 is evident here, which then changes to Newtonian behaviour. Thus, the yield stress for the Bingham model is clearly above the value of the first individual measurement and also marks the maximum value when compared with the values of the other models. The plastic viscosity, on the other hand, deviates only slightly from the value of the first individual measurement, so that the Bingham model, roughly speaking, would only mark an increase in the yield stress from the first to the second individual measurement. The situation is similar for the modified Bingham model. There is an increase in yield stress, but less pronounced and also a slight rise in plastic viscosity can be seen. The negative coefficient c = − 0.062 Pa s 2 indicates an overall slightly shear thinning behaviour, but, as in the first individual measurements, it is very close to zero. The parameters of the Herschel–Bulkley model have developed in a purely different way. There is a strong increase in consistency, which is about four times that of the first individual measurements. The flow exponent has also changed from an approximately Newtonian behaviour ( n = 1.08 ) to a clearly pronounced shear thinning behaviour ( n = 0.71 ). However, the yield stress remains almost identical. This is a very interesting aspect, since it basically argues against the application of the Herschel–Bulkley model. In all previously performed series of measurements, there has been an increased shear stress with the increase in the individual measurement, which has been justified by the increasing structure formation over time.

Usually, the yield stress is related to exactly such phenomena, which means that an increased structure formation must also result in an increase in the yield stress. Due to the NSR, it could be argued that an increasing destruction of the structures takes place over the measurement period and that both the individual measurements have the same initial state and thus the same yield stress at the end of the measurement ( γ ̇ rep = 0 ). However, this would require that even low shear rates can prevent structure formation, which can be excluded due to the general trend of higher values of the second individual measurement. Therefore, it is to conclude that the Herschel–Bulkley model tends to underestimate the yield stress and the other models are better suited to describe the rheological behaviour of fresh concrete in the investigated shear rate range.

In future investigations, the characterisation of fresh concrete should be extended to shear rates γ ̇ rep < 1 , which would allow the applicability of the flow models and the flow behaviour of the concrete to be analysed even more. However, due to the onset of gap reduction, this was not possible in this work and would only be feasible by constructing a much larger rheometer with a radius ratio of β ≈ 1 .

5.2.3 Investigation of sedimentation tendency

In order to assess the sedimentation and segregation tendency, additional measurements were carried out during the adjustment of the concrete mix and during the second test series. These consisted of a so-called cylinder sedimentation test [55] and representative sample taking after individual measurements.

The execution of the cylinder sedimentation test is shown schematically in Figure 15. For this purpose, three stacked cylinders ( d i = 150 mm , h cylinder = 150 mm , h total = 450 mm ), which have a total volume of approx. V total = 8 l , are filled with concrete directly after the mixing process. Following a rest period of t = 30 min , the cylinders are individually analysed and the grains are separated via washing and sieving. The mesh sizes used for sieving were 2.0 and 2.3 mm . After the grains have been dried, the mass is determined and the maximum degree of sedimentation ∆ m is defined according to equation (13) [55]. In the case of standard concretes with largest grains ≥ 8 mm , sufficient sedimentation resistance is said to exist if ∆ m does not exceed 20 % [55].

Figure 15

Schematic representation of the cylinder sedimentation test according to ref. [55].

For the concrete investigated in this work with largest aggregates ≤ 4 mm , the results for both the mesh sizes are given in Table 4. It can be seen that the degrees of sedimentation of ∆ m = 3.25 % (mesh size 2.3 mm ) and ∆ m = 4.16 % (mesh size 2.0 mm ) are achieved, marking the system as sedimentation stable. The weight distribution is random and no trend for higher grain content at the bottom could be seen. However, the cylinder sedimentation test is only suitable for characterizing concretes that have not been stressed yet and therefore has a limited significance for sedimentation or segregation in a rheometer.

Therefore, a lance was constructed to take samples directly from the rheometer gap at different heights. The lance has four sealable cups (A1 (top) to A4 (bottom)) with a volume of 11.65 c m 3 each, which are evenly distributed over the measuring gap length of L = 300 mm , see Figure 16. For sampling, the closed lance was inserted into the gap after a complete series of measurements. As soon as it was in position, the cups were opened and the lance was moved slightly back and forth so that the concrete could flow into the cups. The cups were then closed and the lance pulled out of the gap.

Figure 16

CAD construction of sample lance; left = bottom and right = top.

After the individual samples were washed over a sieve with a mesh size of 700 µ m , the particle size distributions have been determined optically via microscope (Carl Zeiss International AG (Axiocam 506 colour)) using the software “ZEN core V3.1,” Figure 17. The particle diameter d E corresponds to the diameter of a sphere equal to the projection area and based on this diameter, the number distributions q 0 ( d E ) were calculated in size classes of 100 µ m . The number distributions clearly show that there are no segregation and sedimentation effects, since no trend can be detected as to whether a certain particle size is predominantly located at a certain height of the measuring gap. Thus, the concrete is not only sedimentation-stable before it is sheared, but also shows no segregation during shear.

Figure 17

Particle size distributions of the sample cups (A1–A4) for a representative measurement.