Avoiding inaccurate interpretations of rheological measurements for cement-based materials

CEMCON-04960; No of Pages 10 Cement and Concrete Research xxx (2015) xxx–xxx

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Cement and Concrete Research journal homepage: http://ees.elsevier.com/CEMCON/default.asp

Avoiding inaccurate interpretations of rheological measurements for cement-based materials Olafur H. Wallevik a,b, Dimitri Feys c, Jon E. Wallevik a,⁎, Kamal H. Khayat c a b c

ICI Rheocenter, Innovation Center Iceland, Arleynir 2-8, 112 Reykjavik, Iceland Reykjavik University, Menntavegur 1, 101 Reykjavik, Iceland Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO, United States

a r t i c l e

i n f o

Article history: Received 13 April 2015 Received in revised form 4 May 2015 Accepted 5 May 2015 Available online xxxx Keywords: Rheology (A) Experimental error Modeling (E) Kinetics (A) Dispersion (A)

a b s t r a c t Rheology is a high quality tool to evaluate the effect of variations in constituent materials and mixture proportions on fresh properties of cement-based materials. However, interpreting rheological measurements is relatively complicated, and some pitfalls can lead to wrong conclusions. This paper offers a review of measuring devices and transformation equations used to express rheological parameters in fundamental units. The paper also discusses some of the major issues that can lead to errors during the interpretation of rheological measurements. Although the Bingham model is mostly used for cement-based materials, some non-linearity has been observed, necessitating the selection of an alternative rheological model, which could influence the rheological parameters. Other measurement errors related to thixotropic and structural breakdown, plug flow and particle migration are also demonstrated. The paper also discusses the challenges of using numerical simulations to derive rheological parameters for complicated rheometers or industrial devices, such as a concrete truck. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction Research on cement-based materials has expanded rapidly over the last decades, focusing on multiple aspects and materials that influence the behavior in fresh, hardening and hardened state. In the last decade, many initiatives have been made to render concrete a more sustainable material and increase the service life of concrete structures. Advances in concrete science have led to new greater use of alternative materials, including supplementary cementitious materials (SCMs) [1–4] and SCMs from alternative sources [5,6]. Several efforts dealing with the development of novel construction materials have necessitated better understanding of aggregate packing [7–10] and the implementation of a variety of chemical and mineral admixtures to enhance concrete performance [11–13]. In addition, large efforts have been made by the cement industry to create more sustainable products and reduce energy needed in cement production. In parallel, many advances have been made in the last few years regarding the use of rheology to optimize the behavior of novel construction materials, such as self-consolidating concrete (SCC) and evaluate material science aspects of the suspension, including binder–admixture interaction and hydration kinetics. Understanding the rheological properties is key in automation and special material processing, such as 3-D printing with cement-based materials.

⁎ Corresponding author. Tel.: +354 522 9000; fax: +354 522 9111. E-mail address: [email protected] (J.E. Wallevik).

The consequences of the developments in research and implementation of new cement-based construction materials are being studied in the fresh, the hardening and the hardened state of the material. New advances are also made in the characterizing equipment, adding specifications on concrete properties, beyond the 28-day required compressive strength. Similarly, to characterize fresh properties, rheology is introduced as an alternative to the nearly 100-year old slump test [14–16]. The advantage of rheology is the scientific description of the flow properties of cement-based materials and the more complete information gathered. In general, the resulting rheological properties are highly dependent on how the measurements are executed and on data interpretation [15,17]. Rheological measurements enable the determination of yield stress, plastic viscosity as well as thixotropic build-up at rest, thixotropic- and structural breakdown, and their variations with time. Slump testing offers an indication of yield stress of cement-based materials [18,19]. Further workability-oriented tests are necessary to evaluate other important rheological parameters, such as plastic viscosity and structural build-up at rest. The more complete characterization of fresh cement-based materials by means of rheology is a helpful tool in the development of specific chemical admixtures that alter the fresh properties [11,20,21] (see Fig. 1). Furthermore, even the cement properties, which show some variation slightly alter due to the complexity of the production process, can in some cases significantly affect the fresh properties of cement-based materials [22–27]. Examples are known of variations in yield stress and plastic viscosity, and their evolution in time, with

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Please cite this article as: O.H. Wallevik, et al., Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.05.003

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Fig. 3. Deformation of a fluid element.




Fig. 1. Effect of mix design parameters (w/cm, AEA and plasticizer) on the rheological properties of mortar [20].

cement date are illustrated in Fig. 2 [26]. Rheology allows a more precise characterization of cement-based materials, based on principles also applied in other scientific domains. Rheology extends our capacity in finding analytical or numerical solutions for specific flow problems. Rheology is a complex tool, especially for a complex composite material as concrete. Many errors or inaccuracies in measurements and data interpretation can occur leading to erroneous conclusions. The paper presented here offers a general review of rheological principles and measurements and reviews some of the major pitfalls of rheology measurements to enhance the reliability of rheological measurements. The paper presents transformation equations that can be used with different rheological models. It also discusses data interpretation problems that can result from high thixotropy, plug flow and particle migration during rheological testing. 2. Definitions In the science of rheology, the relationship between shear stress (τ, in Pa) and shear rate (γ , in s−1) describes the behavior of a liquid. Shear stress and shear rate are fundamental quantities, which are independent of the measuring system. These two quantities are calculated pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi by τ ¼ σ : σ =2 and γ ¼ 2 ε:ε , in which σ is the extra stress tensor,














and ε is the rate-of-deformation tensor [28,29]. As demonstrated in

[30], the definition of shear rate γ actually coexists with the definition of shear stress τ, as it should be, since when a shear stress τ is applied on a fluid element, a certain rate of shear will result as shown in Fig. 3. The simplest relationship between shear stress and shear rate can be expressed with a linear model that goes through the origin of the shear stress–shear rate graph. This corresponds to Newtonian liquids, such as water and oil in which the only parameter describing the rheological properties of the liquid is the viscosity (η, Pa s) [17]. The power-law model adds some complexity, by imposing a power “n” to the shear rate, making the model non-linear [17]. Some materials exhibit a yield stress (τ0, Pa), which corresponds to a stress that needs to be overcome to initiate flow. The simplest type of such fluid is the Bingham fluid. The Bingham fluid is named after E.C. Bingham, who first described paint in this way in 1919 [31]. Paint, slurries, pastes, and food substances like margarine, mayonnaise and ketchup are good examples of Bingham fluids [31]. However, more complicated yield stress fluid also exists, like the modified Bingham fluid [32,33] or the Herschel–Bulkley fluid [34]. Regardless of type, these materials are generally referred to as viscoplastic fluids [35]. For viscoplastic fluids, at stresses below the yield stress, the shear rate is null, causing the rheological model to intersect the stress axis above the origin. If the shear stress–shear rate relationship is linear once the yield stress is exceeded, the model constitutes the abovementioned Bingham type and defines along with the yield stress the plastic viscosity, which is the slope of the line. Plastic viscosity is typically denoted with μp and has Pa s as unit. Plastic viscosity should not be confused with apparent viscosity, which is the slope of a line connecting a point in the graph to the origin [36]. For Bingham materials, the plastic viscosity is constant, while the apparent viscosity decreases with increasing shear rate. Other rheological models are also available in literature, of which some will be discussed further in this paper. When a viscoplastic fluid (fluid with a yield stress) flows, a situation may occur that in some parts of the flow domain, the applied shear stress is lower than the fluid's yield stress. As a consequence, in that part, the shear rate is zero, and the material flows at uniform (linear

Fig. 2. Example of variation in slump flow and yield stress of concrete and mortar with changes in cement production date [26].

Please cite this article as: O.H. Wallevik, et al., Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.05.003

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or angular) velocity, or remains stationary. This situation is referred to as plug flow and has been observed in pipe flow (pumping), and in coaxial cylinders rheometer. The reader is referred to Section 5.2 for a more detailed discussion. Thixotropy is a time-dependent phenomenon, best characterized as fluidification of the material under (high) shear and stiffening at rest (or at low shear rates) [37,38]. Per definition, thixotropic behavior is fully reversible. One of the consequences of thixotropy is that the rheological properties (yield stress, plastic viscosity, etc.) are dependent on the shear rate applied. Applying higher shear rates will result in lower rheological properties. In contrast to thixotropy, which is mainly the consequence of coagulation and dispersion of small cement(-itious) particles [39], the workability loss mainly results from the hydration reaction of cement in the dormant period. Breakdown of initial connections between cement particles due to hydration can also contribute to structural breakdown: the decrease in shear stress at constant shear rate [15,40], which is often confused with thixotropic behavior [41]. For workability loss, the rheological parameters will increase with elapsed time [42], as cement-based materials transform from a liquid into a solid material. Cement physical and chemical properties, as well as chemical admixtures can significantly alter the rheological properties, including thixotropy, structural breakdown and workability loss.

3. Rheometers and transformation equations 3.1. Rheometer geometries Rheometers are used to determine the rheological properties of different materials, thus to identify the relationship between shear stress and shear rate. However, none of the rheometers measure directly shear stress and shear rate. Instead, torque or force, linear or rotational velocity measurements are registered and transformed into shear stress and shear rate values. The simplest geometry for rheological device would be two parallel plates, sliding over each other. The stress is the applied force divided by the contact area, while the shear rate corresponds to the velocity difference between the two plates divided by the separation distance of the plates (Fig. 4) [17]. However, this type of rheometer is neither practical nor feasible. The only two rheometer types that offer analytical transformation equations that are suitable for cement-based materials (with suspended particles) are the concentric (or coaxial) cylinder and the parallel rotating plate geometries. If the geometry of a rheometer is not similar to one of these two types, the determination of the real rheological properties is more challenging, as no analytical transformation exists. Outside these geometries, potential solutions to deduce rheological parameters may be achieved by comparative measurements between different devices [43], conducting numerical simulations to understand governing shear stress–shear rate values [44] or simply by using the raw data for a given rheometer without the need for transformation equations.

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3.2. Importance of transformation equations When a concentric cylinder rheometer is employed, shear stress can be calculated as [45]: τðr Þ ¼

T 2πr 2 h

ð1Þ

where τ = shear stress (Pa), T = torque (Nm), r = radial parameter (m) and corresponds to the spread between inner radius Ri and outer radius Ro and h = height of the cylinder (m). The shear rate is, however, not straightforward to calculate. As the shear stress already evolves with 1/r2, the shear rate is also a complex function of r, dependent on the (unknown) rheological model. In the rheology literature, two solutions are proposed: • The gap is considered small (Ri/Ro ≥ 0.99), then the shear rate can be approximated as constant in the gap. In this case [17,46]:




γ ðRi Þ ¼

2ωo R2o

ð2Þ

R2o −R2i

where ωo = angular velocity at the outer cylinder (rad/s). Note that the equation is similar if the inner cylinder rotates. • If the gap is not small, the shear rate calculation becomes more complex [17]: 2ωi γi ¼   2 =n  n 1− RRoi


ð3Þ

Supposing the inner cylinder rotates in this case, and with n¼

d ln ðT Þ d ln ðωi Þ

In fact, n is the slope of the T–ω line in a log–log scale. It corresponds thus to the power “n” in the power-law model. The use of the small-gap equation Eq. (2) can be acceptable if the fluid is close to Newtonian (i.e. ratio of yield stress to plastic viscosity τ0/μp is low). But such condition rarely applies for cementitious materials, especially when investigating rheological behavior as a function of time from water addition. This equation is also applicable if the ratio Ri/Ro is very close to 1 (say 0.99). But such a configuration cannot be used for mortar or concrete, as the aggregate particles will be too large for the device. Furthermore, even the large-gap equation (Eq. (3)) is not straightforward to use in case of a yield stress materials, as “n” depends on the rotational velocity. Similar problems are experienced in parallel rotating plate rheometers, in which the determination of the shear stress becomes challenging. However, there is an alternative solution which does not require the calculation of the shear rate in the gap of the rheometer. This transformation procedure is called the Reiner–Riwlin equation (not to be confused with Reiner–Rivlin equation, which is a constitutive equation [45]). Its derivation is for example available in [45,33,47], and it transforms a relationship between torque and rotational (or angular) velocity into a relationship between shear stress and shear rate. It does not provide a point-topoint transformation, but it expresses the obtained relationship in fundamental units (Pa and Pa s):   1

  −1 R2  o  G τ0 ¼ 4πh ln Ro R R2i

Fig. 4. The parallel sliding plates rheometer has simple transformation equations, but is practically very difficult to use.

ð4Þ

i

Please cite this article as: O.H. Wallevik, et al., Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.05.003

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  1 μp ¼

R2i

−

  1

8π2 h

R2o

ð5Þ

H

where G and H are determined from the torque–rotational velocity relationship (T = G + H N). In order to illustrate the utility of the Reiner–Riwlin equation and the importance of using adequate set ups in rheological testing, a series of experiments was carried out using a commercially available rheometer to evaluate viscosity of a vegetable oil that exhibits a Newtonian behavior. The data obtained using coaxial cylinders rheometer of different geometries are reported in Table 1. Data obtained with the two narrow gap systems with Ri/Ro of 0.922 are similar despite the fact that one inner coaxial cylinder had a smooth surface compared to a sandblasted one for the other system. The widegap system had a Ri/Ro ratio of 0.576 and smooth inner surface. A linear decrease in shear rate from 100 to 1 s−1 during 60 s was used, registering data every 0.5 s. Data between 10 and 90 s− 1 were retained for analysis. Four procedures were used to determine viscosity, as follows: • Average of all apparent viscosities, based on the viscosity output of the rheometer. • Average of all apparent viscosities, based on narrow gap equation to calculate shear rate. • Average of all apparent viscosities, based on large-gap equation to calculate shear rate (n = 1, as the material is Newtonian). • Calculation of the (differential) viscosity, based on the T–N relationship and applying the Reiner–Riwlin equation for various geometries. Since the material is Newtonian, the apparent viscosity and the differential viscosity, which is the slope of the line at each shear rate, are equal. Technically, all measurements should deliver the same viscosity value, or at least a viscosity value independent of the geometry. However, Fig. 5 shows the opposite, clearly indicating significant problems interpreting the data when narrow gap equations are used, and when the rheometer is used as a black box system. The Reiner–Riwlin procedure appears to deliver the smallest variation in viscosity assessment. It should be noted that these observations were made with a “standard rheometer” from the polymer industry, and that a Newtonian material was used. As is shown further, complexity increases when using non-Newtonian materials, such as cement-based materials, and more complex rheometers. The above example is carried out for coaxial cylinders rheometer, not applicable for mortar or concrete. For concrete/mortar rheometers (i.e. of much larger dimension), the implementation of the wrong shear rate formulas (as shown above) can lead to more dramatic errors. For example, for typical rheological parameters for concrete (e.g., μp = 25 Pa s and τ0 = 385 Pa), the variation of torque (T) as a function rotational velocity (N) can be illustrated in Fig. 6a. The slight non-linearity in the curve is due to plug propagation. As already mentioned, it is easy to convert the torque values T into shear stress, τ. Because of the difficulties in generating correct shear rate values, γ , software programmers are tempted to use equations like proposed by HAAKE, i.e. Eq. (2) [46]. Fig. 6b shows the error in using this approach, with the line marked as “wrong”. For comparison, the line marked as “right” is calculated using Eq. (9) (see further). By curve fitting (in the least-squares sense) the “wrong” line, the obtained plastic viscosity is μp = 29.3 Pa s and yield stress τ0 = 502 Pa (plastic viscosity is overestimated by 4.3 Pa s and

Fig. 5. Evaluation of viscosity of a Newtonian vegetable oil with the three different geometries from Table 1 and the four analyzing procedures discussed.

the yield stress by 117 Pa). Doing the same for the “right” line (by Eq. (9)), the correct values are obtained, namely μp = 25 Pa∙s and τ0 = 385 Pa. The problem of using Eq. (9) in generating the “right” curve in Fig. 6b, is that it relies on information that the rheometer is trying to obtain (i.e. an unknown quantity). Also, it assumes that the plug radius (Rs) is known at each rotational velocity beforehand (if plug is present). Thus, the direct utilization of Eq. (9) to obtain correct τ = τ (γ ) (and thus correct τ0 and μp) is quite difficult.





Table 1 Different coaxial cylindrical geometries used to evaluate “standard rheometer”.

CC narrow, smooth CC wide, smooth CC narrow, sandblast

Ri (mm)

Ro (mm)

h (mm)

13.335 8.329 13.331

14.458 14.458 14.457

40.001 25.029 40.002

Fig. 6. Illustration (a): raw data in rheometer for concrete with μp = 25 Pa s, τ0 = 385 Pa, Ri = 100 mm, Ro = 145 mm and h = 199 mm. Illustration (b): “right” and “wrong” interpretation of data as a consequence of the transformation equations.

Please cite this article as: O.H. Wallevik, et al., Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.05.003

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By plotting the measured torque T as a function of rotational velocity N (as done in Fig. 6a), one can connect these measured values with a straight line: T = G + H N. From its slope H and its point of intersection with the ordinate G, one can calculate the plastic viscosity μp and the yield stress τ0 by the above-mentioned Reiner–Riwlin equation (i.e. Eqs. (4) and (5)). Here, the presence of plug has been ignored altogether by putting Rs = Ro in the two above equations. This will generate some error in the analysis. By Eqs. (4) and (5), the obtained plastic viscosity is μp = 29.3 Pa s and yield stress τ0 = 354 Pa. That is, the plastic viscosity is overestimated by 4.3 Pa s (same error as before by Eq. (2)), and the yield stress is underestimated by 31 Pa. Previously by Eq. (2), the yield stress was overestimated by 117 Pa, thus Eqs. (4) and (5) represent a significant improvement. 4. Choice of rheological model In most cases, cement-based materials can be described by means of the Bingham model [48–50]. Although the Bingham model is commonly used for cement-based materials, several authors have reported nonlinear rheological behavior of special cement-based materials [47, 51–54,33]. In most cases, the material showed shear-thickening behavior due to the high shear rates applied and/or a very low water content [52]. In these cases, the application of the Bingham model may lead to inaccurate results, requiring the incorporation of a third parameter. This third parameter can be a power function “n” for the shear rate, creating the Herschel–Bulkley model Eq. (6), or a second order term in the shear rate, typically with coefficient “c”, leading to the modified Bingham model Eq. (7). Shear-thinning occurs when n b 1 or c/μ b 0. Shearthickening is described by n N 1 or c/μ N 0. Logically, when n = 1 or c/ μ = 0, the Bingham model is obtained. Extended versions of the Reiner–Riwlin equation have been proposed to deal with such non-linear models [33,47]. τ ¼ τ0 þ K ⋅γ


n

ð6Þ

τ ¼ τ0 þ μ ⋅ γ þc⋅γ





2

ð7Þ

The Bingham, Herschel–Bulkley and modified Bingham models are illustrated in Fig. 7. Including an additional term into the rheological model increases the sensitivity of all parameters to small errors in measurement. Therefore, non-linear rheological models should only be considered when necessary. Apart from the impact on the shape of the curve, and additional difficulties in defining viscosity, which should be taken as the slope of the curve and is dependent on the shear rate, the estimated value of the yield stress also depends on the choice of the rheological model. In case of shear-thickening fluids, applying Bingham, modified

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Bingham and Herschel–Bulkley to the same set of data always leads to the lowest yield stress when applying the Bingham model and the highest yield stress when using the Herschel–Bulkley model. On the other hand, in the case of shear-thinning material, the opposite is valid. Feys et al. [33] compared the yield stress values for SCC mixtures obtained with the three different rheological models to the yield stress value obtained from slump flow measurements that is proposed in [18]. The authors concluded that the ratio of the yield stress measured using a concrete rheometer to that estimated from the slump flow values as a function of shear-thickening (with increasing “n” from Herschel–Bulkley) was only constant when the modified Bingham model is used (Fig. 8). It can thus be argued that the modified Bingham model, in case of non-linearity of the shear stress–shear rate data, delivers the most stable value for determining yield stress [33]. 5. Measurement errors of rheological behavior In this section, three major sources for errors in measurement or interpretation are discussed: thixotropy, plug flow and particle migration. 5.1. Errors due to time-dependent behavior—thixotropy and structural breakdown As mentioned before, time-dependent phenomena like the thixotropic behavior and structural breakdown [39–41] significantly complicate rheological measurements, since at each shear rate, the rheological properties are different. As thixotropy is a time-dependent phenomenon, the rheological properties need time to achieve their equilibrium values, whether it is through thixotropic rebuild, thixotropic or structural breakdown [39,55]. However, awaiting equilibrium at each shear rate may become a time-consuming process to determine the rheological properties, and may cause other effects to influence the result, like workability loss or even particle migration [45]. In order to reduce potential errors associated with thixotropy, the following strategy can be applied. Since breakdown takes significantly less time than build-up (apart from some exceptional cases), it is suggested to break down the internal structure of the cement-based material just before performing the measurement [56]. Pre-shearing is carried out at the highest shear rate introduced during the measurement. The rheological properties are assessed immediately after the pre-shear period to avoid any negative effect due to particle migration, structural rebuilding, or workability loss. Stepwise decrease of rotational velocity is carried out, and each step equilibrium can be verified by plotting torque versus time and assuring that, on average, the torque is constant for the duration of testing. If torque shows a decreasing trend at a given rotational velocity, the data point should be eliminated to avoid erroneous conclusion of shear-thickening (Fig. 9). 5.2. Errors due to plug flow Plug flow is the direct consequence of the yield stress of the material. As the shear stress depends on 1/r2, it could be that a part of the material in a concentric cylinders rheometer is not sheared, as the shear stress becomes lower than the yield stress at a given distance away from the center of the rheometer, as indicated in Fig. 10. Not correcting for plug flow during rheological testing can lead to a wrong conclusion of the presence of shear-thinning, an under-estimation of yield stress and an over-estimation of plastic viscosity. In this case, the Reiner–Riwlin equation must be adjusted by replacing Ro by the plug radius (Rp). The plug radius can be calculated if the yield stress of the material is known:

Fig. 7. Bingham, Herschel–Bulkley and modified Bingham model applied to the same rheological result.

sffiffiffiffiffiffiffiffiffiffiffiffiffiffi T Rp ¼ 2πτ 0 h

ð8Þ

Please cite this article as: O.H. Wallevik, et al., Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.05.003

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Fig. 9. Non-equilibrium (shaded) in torque measurements (left) can lead to wrong conclusion of shear-thickening (right).

with Rs = min(Ro, Rp) and ω is the angular velocity of the rheometer, regardless whether the inner or outer cylinder rotates (Fig. 10). As can be seen in Eq. (9), the shear rate depends on the geometry of the rheometer, the plug radius and the (unknown) rheological properties of the concrete. An iterative procedure, in which an initial set of rheological properties is used, is necessary to obtain the real rheological properties. A similar strategy can be followed for the modified Bingham model, but due to the complexity of the mathematics and the additional parameter that needs to be determined, the iterative procedure to fully account for plug flow for non-linear rheological models becomes very sensitive to small imprecisions in the data. 5.3. Errors due to particle migration Coarse particles tend to move away from the zone with the largest shear rate (gradient), which is near the inner cylinder in a coaxial cylinders rheometer [45]. If the layer near the inner cylinder becomes depleted of (coarse) aggregates, it will show significantly lower rheological properties. In that case, due to particle migration, the test material becomes heterogeneous, and the rheological measurements would be invalid. The risk for particle migration increases with the increase in measuring duration, rotational velocity (shear rate), gap size in the rheometer and yield stress of the material as well as the decrease in plastic viscosity. An increase in increased gap size and yield stress can increase the plugged zone where particles can reach a larger packing density than in the sheared zone [57]. One way to assess particle migration is to determine the thickness of the sheared zone, based on the plug flow identification (Fig. 11). If for the major part of the rheological measurement, the thickness of the sheared zone is smaller than or near the maximum particle size of the material, the results may indicate significant particle migration, meaning that the measurements are not performed on a homogeneous material. Rheological results should be analyzed carefully to avoid using and reporting invalid data.

Fig. 8. Yield stress obtained with Bingham model (a), Herschel–Bulkley model (b) and modified Bingham model (c), relative to yield stress derived from slump flow values according to [18]. Results show that only the modified Bingham model appeared to be independent of the non-linearity of the rheological measurement (n of Herschel–Bulkley) [33].

As the plug radius depends on the measured torque value, it will be different for every measurement point in the data set. For the Bingham model, based on the Reiner–Riwlin equation, the shear rate at the inner cylinder can be calculated as follows:




γ ðRi Þ ¼

2 R2i

1

1 − 2 R2i Rs

!−1  ωþ

  τ0 Rs τ0 ln − μ Ri μ

ð9Þ Fig. 10. Definition of plug radius (Rp) and the liquid–solid boundary (Rs) [33].

Please cite this article as: O.H. Wallevik, et al., Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.05.003

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Fig. 11. Boundary between sheared and unsheared zones indicates whether the thickness of the sheared zone is sufficiently large. Measurements performed in a coaxial cylinders rheometer with Ri = 63.5 mm, Ro = 143 mm, and a maximum size aggregate of 12.5 mm [57].

6. Use of numerical simulations to determine rheological parameters 6.1. The numerical transformation procedure—NTP As mentioned earlier, there are only two rheometer geometries that have analytical transformation equations and are suitable for cementbased materials (having particles). These are the concentric (or coaxial) cylinder and the parallel rotating plate geometries. If the geometry of a rheometer is not similar to one of these two types, the determination of the real rheological properties becomes more challenging, as no analytical transformation exists. An example of such device is the Coplate 5 viscometer [44], which consists of a mixture of the cone, coaxial cylinders and parallel plate systems. Its geometry is shown in Fig. 12. Due to its geometric complexity, the Coplate 5 setup generates a rather complex flow and boundary conditions. As such, an algebraic equation cannot be formed to convert the measured data to fundamental physical quantities, for example to the yield stress τ0 and plastic viscosity μp. That is, a new type of “Reiner–Riwlin” equation cannot be obtained for the Coplate 5 system. Therefore, an alternative approach must be made using numerical simulations. This consists of doing a series of simulations in such manner that the G and H values can be mapped to τ0 and μp values. Such approach could be named the numerical transformation procedure (NTP). An example of NTP is as follows: for each given value of yield stress τ0 and plastic viscosity μp, simulations are made at N = 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 rps. These six simulations will give six different torque values of T1, T2, T3, T4, T5 and T6, respectively (here, applied on the whole top plate). Thereafter, one can connect (or rather do a best fit in the least-squares sense) these torque values with one straight line, in

Fig. 13. Mapping of G and H values to τ0 and μp [44].

which the slope is H and the point of intersection with the ordinate is G. Thus, with one such set of simulations, a correlation between specific values of τ0 and μp to G and H values is obtained. By repeating this step for a wide variety of τ0 and μp, one can generate a systematic map between τ0–μp and G–H. An example of outcome of the above example of NTP is shown in Fig. 13. This illustration is the result of about 700 simulations made using the software VVPF 1.0 [45], which were automatically controlled and managed by several python and bash scripts. As shown in Fig. 13a, there is a one-to-one relationship between μp and H. However, due to the complexity of the flow, this is not so for the relationship between G value and τ0, shown in Fig. 13b. More precisely, as the plastic viscosity decreases (or more correctly, as the ratio τ0/μp increases, and thus generating more plug in the system), the relationship between G and τ0 becomes more non-linear. More information and detailed examples of how one can use Fig. 13 in testing are available in [44]. More information about the Coplate 5 and numerical procedure is also available in [58]. It should be noted that interdependency of the transformation equations (G to τ0 and H to μp) with the a priori-unknown rheological properties may also occur in other rheometers with more complex geometries.

6.2. Rheological analysis for industrial devices

Fig. 12. The Coplate 5 system during testing: experimental (left) and simulated (right) [44].

Sometimes, a need for rheological analysis is not limited to rheological devices, like the coaxial cylinders or the parallel plate viscometer, but also to industrial tools like the concrete truck mixer. Here, a brief example is given about rheological analysis inside a KARRENA 9/5 drum [59]. Such analysis can be carried out to estimate the degree of mixing capability during transport from a ready mix plant to the building site. This analysis can be done as a function of drum charge volume, yield

Please cite this article as: O.H. Wallevik, et al., Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.05.003

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Fig. 14. Numerical simulation result for the KARRENA 9/5 drum.

stress and plastic viscosity. Information like this is valuable especially for the transport of binder rich SCC where the concrete can exhibit high thixotropy and structural breakdown behavior. An example of numerical simulations for the KARRENA 9/5 drum is shown in Fig. 14. The simulation considers a Bingham fluid in which τ0 is set to zero, and the plastic viscosity μp is fixed to 40 Pa s. The drum rate of rotation is set as N = 0.12 rps, and the number of cells used in this computational fluid dynamic (CFD) calculation is about 370,000. The simulation software is OpenFOAM (www.openfoam.org). The lower left illustration of Fig. 14 shows the surface of the concrete. The color range demonstrates speed range, blue being close to zero m/s, while orange about 0.8 m/s. For the top left illustration, the red color shows the location of concrete, while the blue color location of atmospheric air. Both right illustrations show the shear rate profile (in terms of cross sections), blue being zero shear rate, while red reprepffiffiffiffiffiffiffiffiffiffiffi sents shear rate of 12 s−1. The shear rate is calculated by γ¼ 2 ε:ε. As shown in the two right illustrations of Fig. 14, the shear rate varies as a function of location within the drum. To quantify the shear rate condition, it is better to use the volume averaged shear rate like explained in [59]. With such value, a better understanding is obtained about the overall shear rate condition within the drum. Fig. 15 shows the shear rate (volume averaged) as a function of charge volume and plastic viscosity. There, it is clearly shown how the shear rate (and thus, capacity for mixing) decreases in an exponential manner with the increase in charge volume. It also shows how little effect the plastic viscosity has on shear rate, relative to volume concrete in the drum. More information about this type of simulation is reported in [59].





of serrated surfaces. For concrete rheometers, the degree of roughness of the serrated surface has to be large enough to allow for coarse aggregate to be part of the internal boundary. The designation “protruding vanes” are sometimes used for such type of boundary settings. As the concrete is viscoplastic (i.e. a yield stress fluid) and also bearing in mind that coarse aggregates will be present in the space between the above-mentioned protruding vanes, the concrete and these vanes together behave like a rigid solid. That is, no fluid flow is present in-between the protruding vanes. Experimental observation supports this assumption, which is in accordance with the findings made in [60] (see also [61,62]). The above setting should not be confused with 4 blades-vane rheometers, where well defined flow occurs between the blades, as




6.3. Effect of hydrodynamic pressure in rheological devices To avoid slippage between the material and the rheometer, the internal boundaries of rheometers for cementitious materials have to consist

Fig. 15. Shear rate as a function of charge volume and plastic viscosity μp [59].

Please cite this article as: O.H. Wallevik, et al., Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.05.003

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Fig. 16. Stream lines inside a 4-blades vanes rheometer (relative to the rotating shaft). Fig. 18. Total torque T, torque by hydrodynamic pressure Tp and by viscous stress Tη [64].

shown in Fig. 16. This example is taken from the work done in [30]. In this case, the vane rotates, while the bucket (i.e. outer cylinder) is stationary. It has been shown by Zhu et al. [63], by means of numerical simulations, that the shear rate profiles are not concentric cylinders, but that the shear rate shows significantly higher values near the tips of the blades. Furthermore, it is important to note that when a fluid flow acts perpendicular to a wall boundary, like for the vane rheometer, hydrodynamic pressure will be exerted on the blades wall boundary [30]. By this, hydrodynamic pressure will contribute to torque, similar to the contribution of viscous stresses [30]. The right illustration of Fig. 17 shows iso-plots of the hydrodynamic pressure acting on the vane blades (N = 0.5 rps). For this last-mentioned illustration, the red surface represents 20 Pa gage (contributing to friction), while the blue surface represents −20 Pa gage (contributing to drag) [64]. Both the blue and the red iso-surfaces are contributing to torque, namely torque by hydrodynamic pressure Tp [30,64]. Fig. 18 shows the resulting torque values that are obtained for the case presented in Fig. 17 [64]. Both the torque generated by viscous stress (Tη) and that generated by hydrodynamic pressure (Tp) (“Pressure torque”) are shown. From this illustration, it is clear that the majority of the total torque T = Tη + Tp originates from the effect of hydrodynamic pressure (p), reflected in relatively high Tp value. That is, the effect of hydrodynamic pressure constitutes more than 80% of the overall torque T registered by the rheometer [64]. This result applies for the Herschel-Bulkley fluid. Such result is also produced when the fluid is either Newtonian or Bingham [30]. This highlights the importance of understanding the effect the hydrodynamic pressure inside a rheological device.

7. Recommendations Rheology is a useful tool to determine the influence of changes in the properties of the constituent elements or in variations in the

proportioning of cement-based materials. Rheology allows for a more complete characterization of the fresh properties, compared to standard workability tests. However, the interpretation of rheological measurements is not straightforward, as some errors or inaccuracies may occur, hence affecting the interpretation of the results and leading to wrong conclusions. Based on the discussion presented in this paper, the following remarks can be made: • Use appropriate transformation equations to calculate the rheological properties. Cement-paste, mortar and concrete are complicated materials due to the presence of aggregate and the fact that they are yield stress materials. Standard transformation equations from rheology textbooks may not be applicable. Care should be made to what the rheometer software actually calculates. In some cases, large error can occur as the software may use transformation equations that are not valid. • It is recommended to keep the applied rheological model simple: i.e. the Bingham model, describing yield stress and plastic viscosity. If non-linearity is indeed observed, and is not the result of a measurement error, the modified Bingham model Eq. (7) is recommended instead of Herschel–Bulkley model, as the yield stress estimation appears to be more reliable. • Verification of non-equilibrium of torque values at each rotational velocity, due to thixotropic and structural breakdown, and correction for plug flow should be carried out. Not verifying these two measurement errors can lead to inaccurate estimates of rheological properties. • Particle migration is more difficult to assess. Generally, it is recommended to execute the rheological measurements in short time periods, especially in the case of concrete. Comparing the thickness of the sheared zone to the maximum aggregate size is a good indicator of the validity of the rheological measurements. • For more complex rheometer geometries, or other apparatuses that can be used as a rheometer (such as a concrete truck mixer), the interpretation of rheological measurements is more complicated than for standard coaxial cylinders or parallel plates rheometers. The transformation equations for yield stress and plastic viscosity may depend on the other rheological parameter, the amount of concrete in the concrete truck mixer, or other types of forces that may have additional, non-negligible contribution to the accuracy of the measurements.

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Fig. 17. Iso-plot of the hydrodynamic pressure for a 4-blades vane rheometer.

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Please cite this article as: O.H. Wallevik, et al., Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.05.003