The accessibility to rheological parameters for concrete is becoming more and more relevant. This is mainly related to the constantly emerging challenges, such as not only the development of high-strength concretes is progressing very fast but also the simulation of the flow behaviour is of high importance. The main problem, however, is that the rheological characterisation of fresh concrete is not possible via commercial rheometers. The so-called concrete rheometers provide valuable relative values for comparing different concretes, but they cannot measure absolute values. Therefore, we developed an adaptive coaxial concrete rheometer (ACCR) that allows the measurement of fresh concrete with particles up to . The comparison of the ACCR with a commercial rheometer showed very good agreement for selected test materials (Newtonian fluid, shear thinning fluid, suspension, and yield stress fluid), so that self-compacting concrete was subsequently measured. Since these measurements showed a very high reproducibility, the rheological properties of the fresh concrete could be determined with high accuracy. The common flow models (Bingham (B), Herschel–Bulkley, modified Bingham (MB) models) were also tested for their applicability, with the Bingham and the modified Bingham model proving to be the best suitable ones.
In the last decades, the development of new concretes gained more and more importance, which is mainly related to emerging challenges such as high-performance concretes, 3D printable concretes, or predictive flow simulations. To achieve this and superior concrete performance, the profound understanding of the rheology of fresh concrete is an essential requirement and therefore of high significance [1,2,3,4].
However, determining the exact rheological properties of fresh concrete is still very difficult today. This is mainly due to the fact that the measuring gap of commercial rheometers is too small for big aggregates. Therefore, the so-called “concrete rheometers” were developed, which are mostly similar to a coaxial system [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20], but there are also some that work on the principle of a parallel-plate system [21,22,23,24] or characterise the concrete via spreading tests . In many cases, these rheometers are research projects and thus not commercially available. However, there are some commercial “concrete rheometers” offered by Schleibinger with the Viskomat XL, Viskomat NT, and eBT-V models. For determining the pumpability of concrete, Schleibinger also offers a very practice-oriented measuring device called SLIPER, which, however, cannot be compared with a rheometer purely in terms of principle.
All these devices are usually referred to as “concrete rheometers,” which, with a few exceptions, is due to the fact that the characteristic measured values are rotational speed and torque (analogous to common rheometers). In most cases, the Reiner–Riwlin equation , which is based on the Bingham model, is used to determine the flow properties, regardless of the actual flow behaviour. Therefore, even if the designation “rheometer” implies that absolute rheological parameters can be determined, this is only possible with difficulty or not at all possible with almost all “concrete rheometers” developed in the past . This is due to the measuring geometries, which do not provide a mandatory analytical describable shear field (e.g. vane-like geometries, paddles, or spheres). This inevitably also means that different concrete rheometers are not comparable.
To counteract this problem at least for selected concrete rheometers, round-robin tests were carried out in 2,000 at LCPC in France and in 2003 at Master Builders Solutions in the USA [14,27]. The aim was to develop correlations between the rheometers by measuring identical concrete mixes, so that in future it would be possible to compare different concrete mixes measured in different concrete rheometers. The rheometers used were the BTRheom [21,22], the IBB , the Two-point rheometer , the ConTec BML [8,9], and the CEMAGREF-IMG . Although different rheological properties, such as yield stress and plastic viscosity, were analysed, it was not possible to find a general solution for correlating these devices. Therefore, different suggestions for future investigations were raised, e.g. the establishment of standardised measurement methods for concrete and the use of suitable reference materials [14,27]. One of the goals pursued with these suggestions was the development of better rheometers, with which absolute values of concrete can be determined and used in simulations . Since such rheometers have not been developed in the recent years, we developed an innovative concrete rheometer, the adaptive coaxial concrete rheometer (ACCR), to tackle the aforementioned challenges, which were met with great success.
2.1 Rheometry of concentric coaxial cylinder systems
The measuring gap of concentric coaxial cylinder systems is formed by two cylinders with the same symmetry axis, the inner cylinder (bob, radius , length ) and the outer cylinder (cup, radius ). Although standardised systems have a rather small ratio , typically with values of , the increasing cylindrical plane in the measuring gap cannot be neglected, leading to a dependency of the shear stress on the radius , as shown in equation (1).
For Newtonian fluids, the shear rate can directly be expressed by equation (2), where and are the angular velocity at the inner and outer cylinder, respectively, and . Since most commercial rheometers and also the ACCR are searle type cylinder systems, meaning only the inner cylinder is rotating, and thus , the viscosity can be calculated by equation (3) [28,29].
2.2 Correction of unknown flow behaviour
A rather simple method is the Schümmer correction, which uses the representative shear rate and the representative shear stress . This method is based on the work of Schümmer , who was able to define a representative radius in the measuring gap at which the shear rate and the shear stress are equal to those of a Newtonian fluid. Giesekus and Langer  extended Schümmer’s approach and developed equations for further calculation of and , equations (4) and (5).
However, this correction method is mainly accurate for fluids with certain flow behaviour, so that a more general and accurate correction method developed by Krieger and Elrod should be applied, if possible [28,31].
The Krieger–Elrod correction is based on the general formulation of the shear rate, which was developed in a power series, equation (6). The parameter represents the slope of the curve obtained by pointwise differentiation in the – -diagram.
The accuracy of this correction depends on the factor . For , it is sufficient to only consider the first two terms, since the resulting error is below . If , the remaining terms of the series must also be included in the correction. As the derivation for the development of the series assumes that , this correction is not suitable for materials with yield stress [28,32].
2.3 Flow behaviour of fresh concrete
The most established model for describing the flow behaviour of cement-based suspensions is the Bingham model [14,27,33,34,35]. Bingham fluids are characterised by a yield stress with subsequent Newtonian flow behaviour and can be described mathematically by equation (7) .
The slope of the straight line in the -diagram is referred to as the plastic viscosity in order to distinguish it from the common Newtonian viscosity.
However, nonlinear flow behaviour of especially self-compacting concretes has been observed in numerous investigations [36,37,38,39,40] and the application of the Bingham model led to physically impossible negative yield stress values [36,37,41]. Therefore, the so-called Herschel–Bulkley model was increasingly used to describe the rheological properties, equation (8).
This model replaces the original linear Newtonian relationship between and with the approach for power law fluids developed by Ostwald and de Waele. The Parameter is the consistency of a fluid and describes the flow exponent, which is for shear thickening and for shear thinning fluids.
Even though the Herschel–Bulkley model initially appears to be suitable for characterizing nonlinear behaviour, some further investigations have concluded that the yield stress values determined are strongly dependent on the flow exponent. The comparison of this model with other models has consistently shown a yield stress that is too low for shear-thinning materials  and too high for shear-thickening materials [43,44]. To overcome this problem, the Bingham model was extended by the quadratic term , from which the so-called modified Bingham model was derived, equation (9) . The parameter is an empirical coefficient for the quadratic term and a more precise definition of this value is missing in the literature.
When applying the modified Bingham model, it has been observed that the yield stress determined via this model always lies between the yield stress determined via Herschel–Bulkley and Bingham and therefore, seems to be a more accurate estimation . In addition, according to Feys et al., the yield stress is determined independent of the degree of shear thickening, which can further support the accuracy of this model .
3 Development and construction of the ACCR
In principle, rheometry offers a wide range of rheometer types, but the choice of a suitable measuring system for determining absolute flow properties as accurately as possible is limited. The most common rheometers are parallel-plate systems, coaxial systems, and capillary rheometers. However, for a highly concentrated, coarse-grained suspension such as concrete, which, depending on its composition, tends to sediment, parallel-plate rheometers and capillary rheometers are not suitable. For a parallel-plate system, even a slight sedimentation would cause the upper plate to apparently slip and the sheer dimension of the measuring gap, due to the particle size, would most probably lead to a flow-out of the concrete during or even before the measurement itself. In a capillary rheometer, there would be no possibility to prevent wall slip or to perform time dependent or yield stress measurements. Thus, only a coaxial rheometer is suitable. Figure 1 shows the schematic structure of the ACCR.
3.1 Basic dimensions
When dimensioning a coaxial system for suspensions, the maximum particle size is the first thing to be determined. The maximum measurable particle size is limited by the size of the measuring gap of the rheometer.
Second, according to ISO 3219, the radius ratio should be chosen as follows :
To maintain this ratio is mandatory to achieve an uniform shear rate and stress distribution among the gap [29,46]. For manufacturing and handling reasons, a maximum measurable particle size of was chosen and accordingly, the radii of the ACCR are and , resulting in a gap width of .
With regard to the rheometer dimensions, the ISO 3219 further specifies that the following relationship must apply to the ratio of the inner cylinder length and the inner radius to neglect edge effects .
However, since there is no rheological justification to exact this ratio in ISO 3219 and a corresponding length of has not been possible for manufacturing reasons, the cylinder length of the ACCR is , which corresponds to a ratio of . Considering all the components of the rheometer, this results in a measuring volume of .
3.2 Rotating bottom plate
In all coaxial systems, front face influences occur on the upper and lower front faces of the inner cylinder, which, without correction or other measures, lead to erroneous results. The upper front face influence can be eliminated by filling the measuring gap to the upper edge of the inner cylinder only. Since the upper face and other components of the rheometer above it are only in contact with air, the influence is in general negligibly small.
The situation is different on the lower front face of the inner cylinder. An additional parallel-plate system with a theoretical measuring gap would form between the lower front face of the inner cylinder and the bottom of the outer cylinder, which can have a considerable influence on the measuring results. For this reason, the ISO 3219 also specifies the value for the gap with , with the aim of keeping the influence of the lower front face negligibly small, since the shear stress decreases linearly with the distance for a parallel-plate system.
In the case of the ACCR, a design with this specification is not expedient because of handling issues and a significantly higher, impractical sample volume. Instead, the effect was inhibited with a rotating bottom plate below the inner cylinder moving at the same speed, Figure 2. Thus, the material between the rotating bottom plate and the inner cylinder is not sheared at all and therefore the torque is not increased. In order to ensure that the rotational speed of the inner cylinder and the bottom plate match as closely as possible, both components are driven by identical motors and gears.
Furthermore, the whole bottom part of the rheometer is, unlike commercial rheometers, detachable to empty and clean the rheometer after measurement, Figure 2.
3.3 Adaptive measuring profiles with integrated cooling
When measuring suspensions, apparent wall slip is a common problem, so that wall adhesion can no longer be guaranteed and the use of roughened or profiled measuring surfaces is usually practiced [47,48,49,50,51]. To allow a slip inhibition for the ACCR, an adaptive approach with several, exchangeable measuring profiles was implemented. The measuring surface of the coaxial system therefore consists of six individual measuring profiles at the inner and outer cylinders, which, when lined up together, form a circular ring. The standard measuring profiles for materials prone to wall slip are made of stainless steel with a length of and have square like longitudinal grooves with a dimension of , which corresponds to the maximum measurable particle size, Figure 3. For non-reactive, wall-adhering fluids, sandblasted profiles made of aluminium are also available, which were mainly used for reference measurements.
In addition, the standard profiles (stainless steel) for the outer cylinder cool the measured fluid in the gap. A copper coil is integrated in each profile to be fed with a temperature-controlled cooling fluid, Figure 3. The cooling fluid is fed in parallel through the profiles, ensuring a homogeneous temperature. Alternatively, a cooling coil wrapped around the outer cylinder can be used for cooling, which is sufficient for non-exothermally reactive materials and was used in the context of comparative measurements together with the smooth aluminium profiles, see Section 4, and partly during the first series of tests, see Section 5.1. It is important to mention that a cooling device is always required because of the self-heating caused by the shearing. In commercial rheometers, cooling can be realized with little effort, since the sample volume is very small. However, in the ACCR with a much larger sample volume, heat is generated not only by the shear process, but also by the reaction of the fresh concrete itself. Therefore, the cooling of the concrete is generally a very difficult challenge, but one that has been mastered very well with the cooling profiles when the temperature values achieved are considered, see Section 5.
3.4 Overall design and key parameters
Figure 4 shows the setup of the whole rheometer. The inner cylinder and the bottom plate are each driven by an AC asynchronous motor from Lenze (type MXXMA), which has a nominal rotational speed of (controlled via an incremental encoder) and a nominal torque of . In order to be able to guarantee low rotational speeds with a high degree of running smoothness, a Bonfiglioli gearbox (type 32 2 P 52.4 HS V5) with a ratio of is installed between the motor and the corresponding drive shaft. This combination allows shear rates in the range of The torque is measured between the gear unit and the drive shaft of the inner cylinder via a sensor from burster (type 8661). The sensor has a measuring range of with a relative linearity deviation of in relation to the end value of the measuring range. An encoder disk with increments for speed and angle of rotation measurement is also integrated in the sensor. Alternatively, a smaller torque sensor from Lorenz can be installed for fluids with significantly lower viscosity. It has a measuring range of with a relative linearity deviation of in relation to the measuring range end value. However, the large sensor is used as a standard, the small sensor was used only for the initial comparative measurements of the rheometer, see Section 4. The rheometer is controlled via a self-written LabVIEW program.
3.5 Error analysis
To assess the validity of the results presented in this study, it is necessary to estimate the measurement accuracy of the ACCR. Therefore, all possible sources of error were identified and evaluated. The relevant errors for the rheological parameters shear rate and shear stress were characterised in more detail in a Gaussian error propagation, which lead to relative inaccuracies of and . Further information on the calculation is given in the supplementary material S1.
4 Comparative measurements
For evaluation purposes, the ACCR was tested first with simple, controllable fluids and compared to a commercial Anton Paar MCR 501 using a CC27 standard system ( , , and ). A highly concentrated sugar solution (Newtonian flow behaviour), a cream bath (shear thinning properties), a suspension (shear thinning properties and low yield stress), and mayonnaise (shear thinning properties and high yield stress) were chosen as test fluids to comprise a great range of rheological behaviour.
For the sugar solution and the cream bath, a positive shear rate ramp (PSR) starting with and raising it to was applied. For the suspension and the mayonnaise, a negative shear rate ramp (NSR) lowering from to . This is recommended for yield stress fluids with time-dependent structural build-up like the later investigated fresh concrete suspensions . Thus, the (reversible) structure formation is inhibited till the end of the measurement, enhancing the reproducibility. This would not have been necessary for the fluids investigated at this point but was done to facilitate a comparison to the concrete measurements. In addition, a pre-shearing step ( for ) was performed on the suspension and mayonnaise after the materials were filled into the gap to homogenise the fluids, and a direct pre-shearing step ( for ) was performed before each individual measurement to inhibit structural build-up over time. Each measurement point was held for and averaged over the last s, since the torque curves appeared to be constant in this time range. There were different measuring series which always comprised three individual measurements without changing the specimen (Table 1). Before every series, the friction of the system was measured and considered during evaluation. Following the above protocols, the mean standard deviation between measurements was below (sugar solution, cream bath, and suspension) and (mayonnaise) and therefore, too small to be shown in Figure 5. To calculate the deviation between the commercial system and the ACCR, the results were fitted using an adequate fit and a mean deviation over the measurement range was calculated. For all measurements the ACCR was equipped with the smooth aluminium surface and the appropriate torque sensor, see Section 3.4.
|Fluid||MS||Temperature (°C)||Correction||Fit||Deviation (%)|
The fit-numbers represent the used polynomial degree, except for the mayonnaise, where the Herschel-Bulkley-model was used.
4.1 Newtonian fluid–sugar solution
The aqueous sugar solution contained a sugar mass fraction of and a citric acid mass fraction of to inhibit crystallisation. It can be clearly seen from Figure 5(a) that the results of both the rheometers agree well and clearly show a Newtonian behaviour at a viscosity of and . The values of the ACCR tend to be slightly higher than those of the MCR 501.
4.2 Shear thinning fluid–cream bath
For the cream bath measurements, an additional pre-shearing step for at with a subsequent pause of was added to the schedule to homogenise the fluid in the measuring gap. Since the flow clearly shows a shear thinning behaviour, Figure 5(b), a correction according to Krieger–Elrod was applied. Again, the results agree quite well and the values of the ACCR tend to be slightly higher than those of the MCR 501 in the medium shear rate range ( ), although this behaviour seems to reverse in the higher shear rate range ( ).
4.3 Shear thinning suspension–cream bath with polyamide particles
To evaluate the ACCR regarding suspensions, it had to be first decided whether the exact same suspension or a similar suspension with the same particle diameter to gap ratio should be used, while both the variants promise different advantages. Since preliminary measurements showed that there is nearly no tendency for wall slip (plate-plate and coaxial systems), it was decided to use the exact same suspension (particle volume fraction , , cream bath as matrix fluid) as it was easier to prepare, knowing that it might behave different in both the rheometers because of the particle to gap ratio, even though the recommended particle to gap ratio smaller than was met, equation (10). The mean particle diameter was chosen according to the commercial system. With a value of , the polyamide particles have a density close to that of the cream bath with and thus flotation effects can be neglected, at least during the time of measurement. Since a suspension also behaves non-Newtonian, the Krieger–Elrod correction was applied, Figure 5(c). Although materials with yield stress should not be corrected via the Krieger–Elrod method, this influence was considered negligible, since the uncorrected values indicated that a yield stress, if present at all, is close to zero. The measured values of both the rheometers also agree very well and the shear thinning behaviour of the suspension becomes evident. An extrapolation of the polynomials leads to yield stresses of (ACCR) and (MCR), although these values depend on the fit and have to be considered with care. The slight tendency of the ACCR values lying above the values of the MCR is also obvious here. However, since the preliminary investigation has shown a minute tendency to wall slip in the MCR, this deviation might be even smaller due to the less pronounced wall slip in the ACCR (smaller particle to gap ratio and sandblasted aluminium surface).
4.4 Yield stress fluid–mayonnaise
For mayonnaise, a decrease in the measured values was observed with the increase in the individual measurements for both the rheometers, so that the individual measurements (X.1–X.3) are presented instead of a single mean curve. The reason for this behaviour might be rising air bubbles during the measurements that had been entrapped in the filling process, structural changes in the mayonnaise due to drying processes, or even an influence of the different loading processes. The effect is stronger for the ACCR, which corresponds with the mentioned assumptions. Wall slip can be excluded as a reason since preliminary investigations showed no tendency. Due to the high yield stress, a correction via Krieger–Elrod is not possible, so that the Schümmer-correction was applied. However, the Herschel–Bulkley model could be fitted to the values for calculating the deviations and analysing the yield stresses, Figure 5(d). The results show that the values of the ACCR are below the values of the MCR. There are deviations in the range between (X.1) and (X.3). But again, a good agreement was achieved. For the yield stresses derived from the Herschel–Bulkley model, deviations between (X.1) and were measured.
The first three comparisons clearly show that the ACCR delivers consistent absolute rheological values within a close error margin to commercial measuring systems. On a closer look, a constant offset of about is present. The fourth measurement of the more complex mayonnaise shows slightly stronger deviations in the other directions. This can be accredited to the more complex loading process and the bigger volume of the ACCR compared to the MCR, which seems to enforce certain errors. Because of the general good agreement, no further calibration was carried out and the ACCR was used for the investigation of real concrete.
5 Rheological characterisation of fresh concrete
One of the most important reasons why a generally valid rheological classification of fresh concrete is much more difficult than for other materials is the fact that the term “concrete” does not refer to a clearly defined substance, but rather to an entire class of materials. Concrete consists of four components (cement, water, aggregates, and various additives) in different ratios. Even the mixing time and the time to the measurement are relevant, since it is a reactive material. Therefore, it is necessary to define a mixture as well as an accurate mixing and measuring procedure to allow for comparable measurements. The exact composition and handling are described in the supplementary material S2. All measurement results are approximated by representative values according to Schümmer. From this point, the following wordings are used to distinguish between different sets of measurements:
Measurement series (consisting of multiple individual measurements)
Investigation series (consisting of multiple measurement series)
Series of tests (consisting of multiple investigation series)
5.1 First series of tests
During the first series of tests, the self compacting concrete (SCC) was investigated in two investigation series, which are presented and discussed below. The first investigation series consisted of measuring the SCC using originally smooth aluminium profiles, which were fitted with brass flat bars ( thick and wide) to prevent wall slip. The reaction occurring between aluminium and concrete with the formation of hydrogen  was considered negligible, since no visible wear could be detected when the profiles were cleaned. The second investigation series comprised hysteresis measurements using stainless steel profiles. During these first series of tests, the concrete was still measured with the alternative tempering system (cooling hose on the outside) and was filled into the rheometer via suitable funnels.
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 individual measurements are shown in Figure 6. The mean temperature of the first measurement series was , for the second measurement series and for the third measurement series , 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 and 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 and .
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. , the curves indicate a shear thinning behaviour, which changes to Newtonian flow behaviour in the medium shear rate range of approx. . If the shear rate increases above , 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.
A possible solution to this problem would be the increase in the geometry parameter , since this minimises the difference between and , and the yield stress on the outer cylinder would only be undercut at very low shear rates, if at all. Although 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 ( ) are considered problematic due to a lack of knowledge regarding sufficient pre-shearing, only measured values up to are examined. The measured values in the low shear rate range ( ) are also discussed carefully due to the abovementioned gap reduction, which occurred only in the later individual measurements and . 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 and , 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 ( ). 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 .
|1st individual measurement||2nd individual measurement||3rd individual measurement|
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 ( and ) 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 changes only slightly with the increase in the individual measurement, but the consistency 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 , 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 and for the second measurement series . 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 , 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 ( ), 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 . 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.
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 Second series of tests
The first series of tests have provided valuable results, especially with regard to the rheological properties of fresh concrete and the test procedure. However, many sources of error were also identified, which must be considered for a more reliable rheological characterisation of fresh concrete.
As the temperature was a major problem in both the measurement series of the previous tests with a deviation of or degrees, the directly cooled profiles, see Section 3.3, were used in the following second series of tests. Additionally, the pre-shearing step was intensified due to the observations made in Sections 5.1.1 and 5.1.2, Table S2.3 (supplementary material S2). Since the reaction with aluminium could not be excluded and even little gas bubbles emerged during earlier measurements, stainless steel profiles were used for further investigation, as already done for the hysteresis measurements. To reduce the influence of the filling process, a filling aid was introduced. The filling aid essentially consists of a large hopper in which the concrete is force-fed through an auger and filled into the rheometer gap via a hose. This makes it possible to fill the rheometer more reproducible than using the funnels, and additionally, shear can be applied in the measuring gap during the filling process, which not only serves to homogenise and destroy structures, but also contributes to deaeration. A preliminary investigation with the new setup showed that, despite being stored in vacuum, the cement mix appeared to have changed a little and no coherent measurements were possible. Therefore, it was necessary to adjust the concrete composition. To change the mixture as less as possible, a rheological thickener was added (Sika® Stabiliser-165, by weight of cement), which successfully reduced the spread flow to a value originally achieved i.e. approx. , resulting in a similar behaviour as before. The mixing process was adapted to add the thickener. During the initial mixing of all components, the thickener was distributed over a large area while the mixing was paused for . This process was added to the mixing procedure, see supplementary material S2, Table S2.2, in the time . However, the corresponding stage was not extended by , so that all other time steps remained identical. Further measurements were performed using this adjustment.
The results presented below are divided into three sections: reproducibility, rheological characterisation, and additional measurements. The additional measurements focus on sedimentation. Since the concrete already showed a high degree of consolidation in the individual measurements 4 and 5 in the previous series of tests, only the first two individual measurements were investigated from here on.
All 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 , 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 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.
In principle, the evaluation of the coefficient of variation depends on the considered area, but in general, coefficients below can be described as good , which shows the high reproducibility of the ACCR with .
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 and . 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.
While the course of the first individual measurements is almost linear for shear rates and for the previously critically considered high shear rates ( ), the course of the second individual measurements shows stronger curvatures both for and for . Thus, the first individual measurements indicate a Newtonian flow behaviour from , while the second individual measurements indicate a slightly shear thinning behaviour for , which appears to reverse the dilatant behaviour from . For shear rates, , the curves are similar, at least with respect to curvature, and suggest shear thinning behaviour. The shear stresses are in the range of throughout the measurement range for the first individual measurements, while for the second individual measurements, it is , which again can be explained by time hardening.
Since the course of the first individual measurements is now also almost linear for , 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 to , 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. , which >somehow coincides with the optical observation of the gap reduction starting from a shear rate of for the first individual measurements and from 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 ( ) 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 ( ) and the modified Bingham model ( ) 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 ( , and ). Thus, to this extent, all models resemble the concrete behaviour in a very good manner in a medium shear rate range.
|First individual measurement||Second individual measurement|
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 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 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 ( ) to a clearly pronounced shear thinning behaviour ( ). 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 ( ). 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 , 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 .
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  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 ( , , ), which have a total volume of approx. , are filled with concrete directly after the mixing process. Following a rest period of , the cylinders are individually analysed and the grains are separated via washing and sieving. The mesh sizes used for sieving were and . After the grains have been dried, the mass is determined and the maximum degree of sedimentation is defined according to equation (13) . In the case of standard concretes with largest grains , sufficient sedimentation resistance is said to exist if does not exceed .
For the concrete investigated in this work with largest aggregates , the results for both the mesh sizes are given in Table 4. It can be seen that the degrees of sedimentation of (mesh size ) and (mesh size ) 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.
|Cylinder||Mass of aggregates||Deviation to mean value|
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 each, which are evenly distributed over the measuring gap length of , 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.
After the individual samples were washed over a sieve with a mesh size of , 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 corresponds to the diameter of a sphere equal to the projection area and based on this diameter, the number distributions were calculated in size classes of . 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.
The ACCR presented in this study was developed for the purpose of determining the rheological properties of suspensions, primarily fresh concrete, with a maximum particle size of . Comparative measurements with a commercial rheometer (Anton Paar MCR 501) have shown that the ACCR is able to generate precise measurement results within a common accuracy. It was possible to create a SCC concrete mixture with nearly no tendency of segregation and sedimentation, that was used for investigation.
After the difficulties of concrete measurements encountered in the preliminary tests had been solved, the fresh concrete could be rheologically characterised with extremely high reproducibility. The applicability of the common flow models for concrete (Bingham, Herschel–Bulkley, and modified Bingham model) could be satisfactorily analysed. It was shown that especially the Bingham and modified Bingham model are suitable for the description of the concrete used in this work, while the Herschel–Bulkley model seems to underestimate the yield stress and represents shear-thinning behaviour. Furthermore, only the values of the first individual measurements are valid for further evaluation of rheological properties, since the influence of structural build-up in the second individual measurements is too high to be neglected and can lead to a false interpretation of the rheological behaviour.
However, a limited shear rate range has resulted due to the yield stress and the structural build-up of the concrete, which in particular have led to a reduced measurement gap. This mainly affected the low shear rate range. Within the scope of this work, this phenomenon could not be avoided and can also only be reliably fixed in the future by redesigning the rheometer with a closer to . The investigation of the low shear rate range would be of great interest in the future, as it would not only allow the applicability of the current rheological models to be better investigated, but also the yield stress and therefore the real flow behaviour to be determined much more accurately.
Funding information: We would like to thank the German Research Foundation (DFG) for supporting the research within the priority program SPP 2005 “Opus Fluidum Futurum.”
Author contributions: Conceptualisation: S.J. and S.J.; data curation: S.J.; formal analysis: S.J. and S.J.; funding acquisition: H.-J.S. and S.J.; investigation: S.J.; methodology: S.J. and S.J.; project administration: S.J. and H.-J.S.; supervision: H.-J.S.; validation: S.J. and S.J.; visualisation: S.J.; writing – original draft: S.J.; writing – review and editing: S.J. and H.-J.S.
Conflict of interest: The authors declare no conflict of interest.
Ethical approval: The conducted research is not related to either human or animal use.
Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
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