How much is bulk concrete sheared during pumping?

Construction and Building Materials 223 (2019) 341–351

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How much is bulk concrete sheared during pumping? Dimitri Feys ⇑ Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO, United States

h i g h l i g h t s
The amount of shearing in the bulk concrete is affected by

gLL/lp and s0/lp.


Mixtures with higher w/cm and with fly ash are less prone to shear-induced changes.
In specific conditions, Conventional Vibrated Concrete can be sheared inside pipes.

a r t i c l e

i n f o

Article history: Received 16 May 2018 Received in revised form 25 June 2019 Accepted 29 June 2019

Keywords: Pumping Rheology Shearing Concrete Lubrication layer

a b s t r a c t Pumping is an efficient procedure to place concrete inside formworks. Practical guidelines have been developed to facilitate this process for over half a century, and in the last decades, a more scientific approach has been applied to study the flow behavior of concrete in pipes. With the development of self-consolidating concrete (SCC), some substantial differences in the flow patterns of SCC and pumpable conventional vibrated concrete (CVC) have been discovered. Generally, SCC is said to be sheared during pumping, while for CVC, the shearing is only concentrated in the lubrication layer and the bulk concrete flows as a plug. This paper discusses the factors affecting the shear rate in the bulk concrete, and the additional flow rate caused by shearing the bulk concrete. The discussion is based on theoretical analyses and experiments described in literature. Increasing the ratio of the viscous constant of the lubrication layer to the viscosity of the bulk concrete increases the shearing in the bulk concrete. This appears to be the case for mixtures with lower w/cm. Increasing the bulk concrete yield stress to viscosity ratio, by using less flowable concrete mixtures, increases the plug flow and thus decreases the shear rate in the bulk concrete. However, the simple distinction between SCC is sheared and CVC remains unsheared is not valid. For certain sets of parameters, CVC can be sheared as well. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Pumping is a quick and efficient procedure to place concrete into formworks. Although concrete pumps have been employed for over half a century, it is only in the last couple of decades that more scientific insight into the procedure is being obtained. Major accomplishments enabling better understanding of pumping of concrete have been achieved with the introduction of interface rheometers (wrongly named tribometers in current literature) [1–5]. In contrast to regular concrete rheometers, interface rheometers allow the lubrication layer to form near a smooth wall, mimicking the behavior of concrete flowing near the pipe wall. Shear-induced particle migration causes a depletion of particles in the zones with the highest shear rates [6–8]. Coarse aggregates

⇑ Address: 128 Butler-Carlton Hall, 1401 N. Pine Street, Rolla, MO 65409, United States. E-mail address: [email protected] https://doi.org/10.1016/j.conbuildmat.2019.06.224 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

will migrate primarily, but a reduction of large sand particles in the lubrication layer cannot be excluded. By characterizing the lubrication layer, whether this is by means of an interface rheometer or by wet screening (micro-)mortars, analytical calculations and numerical simulations of the pressure – flow rate relationship and the velocity profile can be performed [1,2,9–15]. By imposing a Bingham behavior for both the bulk concrete and the lubrication layer, a bi-modal combination of two homogeneous materials is assumed for the calculation of pressure, flow rate or velocity profiles. In reality though, a continuous concentration gradient, different for each particle size, is more likely to be found if direct observations were possible. Nevertheless, different analytical models have been successfully applied, predicting concrete pumping pressure relatively accurately, such as Eq. (1), developed by Kaplan [1,9], valid when a part of the bulk concrete is sheared:

0 1 Q R R 2 @pR2  4lp s0;LL þ 3lp s0 Dp ¼ gLL þ s0;LL A R 1 þ RgLL 4lp

ð1Þ

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D. Feys / Construction and Building Materials 223 (2019) 341–351

Nomenclature Symbols Dp Q Qconc Qrel R Rb

c_

c_ b

pressure loss per unit of length (Pa/m) total flow rate (m3/s) flow rate of bulk concrete (m3/s) relative flow rate: ratio of bulk concrete to total concrete flow rate Qconc/Q (-) pipe radius (m) radius at boundary between lubrication layer and bulk concrete (m) shear rate (s1)

When exposed to more extended pumping times, the fresh properties of the concrete change [16–18]. Typically, viscosity is reduced, but the effect of pumping on yield stress is not fully clear yet. The magnitude of the applied shear rate in the concrete is expected to have a significant effect on the change in rheological properties, due to increased breakdown of flocculation and hydration linkages between the particles, with increasing shear rate [18– 21]. But what is the magnitude of the shear rate in the concrete? Is the concrete even sheared? Typical distinctions are made between conventional vibrated concrete (CVC) and self-consolidating concrete (SCC). The former is assumed not to be sheared, the latter is said to undergo more elevate shear rates compared to other placement methods [19]. The concrete remains unsheared if the applied shear stress at the boundary between the lubrication layer and the concrete remains smaller than the yield stress of the concrete. The shear stress at the boundary can be calculated based on the wall shear stress as follows:

sb ¼ Rb sw =R ¼ DpRb =2

ð2Þ

In case the bulk concrete remains unsheared, all shearing is happening in the lubrication layer. Assuming a lubrication layer thickness of 2 mm and a pipe diameter of 100 mm, this means that less than 8% of the total volume is sheared. In this case, changes in rheological properties due to pumping should not be extensive, apart from the effects of pressure on the change in the air-void system and the increase in temperature caused by viscous heat dissipation. However, as soon as the boundary shear stress exceeds the yield stress, bulk concrete will begin to shear. The amount of shearing will however not only depend on the concrete yield stress, but also on its viscosity, the lubrication layer properties and the flow rate, as they all influence the pressure loss. This paper focuses on the different mechanisms which influence the shear rate in the bulk concrete during pumping, as well as the contribution of concrete shearing to the total flow rate. By gaining this insight, a better assessment of the potential for changes in concrete rheology due to pumping can be made in laboratory investigations. The discussion is based on a series of pumping tests, which are described in previous publications of the author. 2. Experimental data This section gives a brief overview of how the experimental data were obtained. More details can be found in [10]. 2.1. Concrete mixtures The pumping tests were executed on a total of 25 concrete mixtures: three CVC, 18 SCC, and four mixtures in between CVC and SCC, labeled highly-workable concrete (HWC). The distinction on the nomenclature is based on the designed initial slump flow:

c_ w gLL lp s sb s0 s0,LL sw

shear rate at the boundary between bulk concrete and lubrication layer (s1) shear rate at the pipe wall (s1) viscous constant of the lubrication layer (Pa s/m) plastic viscosity of the concrete (Pa s) shear stress (Pa) shear stress at boundary between lubrication layer and bulk concrete (m) yield stress of the concrete (Pa) yield stress of the lubrication layer (Pa) shear stress at the pipe wall (Pa)

between 450 and 600 mm is HWC, above 600 mm is SCC. All mixtures were delivered in batches of approximately 1.25 to 1.5 m3 by a local ready mix company. For the HWC and SCC, the reference w/ cm was 0.295, the paste volume 375 l/m3, and the binder was a commercially available blended cement containing 8% silica fume. The coarse aggregate had a nominal max aggregate size of 20 mm, and the sand to total aggregate ratio, by vol., was 0.5 for the HWC and 0.54 for the SCC respectively. For SCC 18 and 19, a different type of aggregate was used to increase the strength of the mixtures, but the original grain size distribution was approached as close as possible. For the SCC, the target slump flow was 700 mm, unless mentioned otherwise. The CVC mixtures were commercial products of the concrete producer, made with lower paste content, higher coarse aggregate content and higher w/cm. The target strength of the CVC mixtures was 50 MPa, while the HWC and SCC mixtures reached 70 MPa or more in most cases. Table 1 lists some specific properties of the mix designs when deviated from the reference mix design. More detailed information on the mix designs can be found in [10]. 2.2. Concrete pumping The concrete was pumped several times through a loop circuit, each time imposing between 5 and 8 different flow rates, in descending order. The circuit consisted of two 11 m long straight sections of two different diameters. The upstream pipes were 100 mm in diameter, the downstream pipes 125 mm. The concrete from the pipes was redirected in the hopper of the pump during regular testing. For both straight sections, two pressure sensors were installed, approximately 10 m apart. These pressure sensors allowed to calculate the pressure loss in both the smaller 100 mm diameter and the larger 125 mm diameter pipes. In the vicinity of the pressure sensors, strain gauges were attached to the pipe wall, acting as back-up in case the pressure sensors failed. For a more detailed description of the measuring equipment, the reader is referred to [10]. The flow rate was determined by recording the time needed to pump a number of strokes. This time was recorded by a stopwatch, and was derived from the pressure data, as the pressure shocks were clearly visible. For each mixture, in between two pumping tests, a calibration of the flow rate was performed by pumping one full stroke of concrete in a closed reservoir, attached to a load cell. As such, the flow rate data were corrected based on the calibration curves, avoiding the estimation of the piston filling factors [1,2]. The outcome of the analysis delivered the relationship between pressure loss (per unit of length) and the flow rate of the concrete. To facilitate the analysis, second order polynomials were fitted to the data, allowing the determination of the pressure loss at fixed flow rates, for each test, for each concrete [22]. The reference flow

D. Feys / Construction and Building Materials 223 (2019) 341–351 Table 1 Specific properties of mix designs. CVC 1 CVC 2 CVC 3 HWC 1 HWC 2 HWC 3 HWC 4 SCC 1 SCC 2 SCC 3 SCC 4 SCC 5 SCC 7 SCC 8 SCC 9 SCC 10 SCC 11 SCC 12 SCC 13 SCC 14 SCC 15 SCC 16 SCC 17 SCC 18 SCC 19

Commercial product of ready-mix company - initial slump: 225 mm Commercial product of ready-mix company - initial slump: 245 mm Commercial product of ready-mix company - initial slump: 150 mm Paste volume = 350 l/m3 – initial slump flow: 410 mm Paste volume = 350 l/m3 – initial slump flow: 520 mm Reference HWC – initial slump flow: 550 mm w/cm = 0.25 – initial slump flow: 515 mm Reference mixture Increased HRWRA dosage added on-site - initial slump flow 780 mm Increased HRWRA dosage added on-site - initial slump flow 735 mm Reference mixture 25% replacement of cement by fly ash (by mass) Reference mixture, but may show lower paste volume (mixing issue) w/cm = 0.25 w/cm = 0.34 Reference mixture Paste volume = 400 l/m3 Paste volume = 350 l/m3 Air-entrained mixture Mixture containing VMA, but likely shows higher w/cm (see further) Reference mixture S/A = 0.51 S/A = 0.48 Reference mixture – Different source of aggregates w/cm = 0.22 – Aggregates identical to SCC 18

rate used in the analysis is 8 l/s, as this is a flow rate for which a pressure value could be interpolated for every test performed.

crete and the properties of the lubrication layer can be found in [10]. 3. Theoretical analysis 3.1. Calculation of concrete flow rate and shear rate Fig. 1 represents the velocity profile of concrete in a pipe. The area under the velocity profile is the flow rate (Q), which can be divided into two parts. The first part, below the horizontal dashed line in Fig. 1 is the caused by shearing in the lubrication layer. The second part, above the horizontal dashed line is the contribution of the bulk concrete shearing to the total flow rate, calculated as Qconc, according to Eq. (3) [25]. Eq. (3) is the Buckingham Reiner equation describing the flow of a homogeneous yield stress material in a circular pipe. In fact, Qconc represents the flow rate of the concrete at equal Dp if no lubrication layer were present.

Q conc ¼ p

3Rb 4 Dp4 þ 16s40  8s0 Rb 3 Dp3 24Dp3 lp

ð3Þ

If the yield stress of the concrete would be larger than the boundary shear stress (Eq. (2)), the concrete is not sheared and the velocity profile in the bulk concrete would coincide with the horizontal dashed line, causing pure plug flow. The relative flow rate is defined as the ratio of the flow rate caused by concrete shearing to the total flow rate: Qrel = Qconc/Q. Similarly, the maximum shear rate the concrete undergoes can be calculated according to Eq. (4), which stems from the Bingham model and using Eq. (2) to replace the boundary shear stress:

2.3. Concrete characterization After each pumping test, a sample of the concrete was taken to characterize its fresh properties in terms of slump flow (or slump), V-Funnel flow time, sieve stability, density, air content, rheology and interface rheology (tribology). For the purpose of this paper, only the rheological measurements are discussed. The rheological properties of the concrete were determined by means of an ICAR rheometer [10,22]. This device is based on the concentric cylinder principle, for which a vane rotates at predetermined velocities in a bucket of concrete. The vane dimensions were 63.5 mm in radius and 127 mm in height. The bucket radius was 143 mm. The concrete was presheared during 20 s at 0.5 rps, followed by decreasing the velocity from 0.5 rps to 0.05 rps in 7 steps of 5 s each. If torque was in equilibrium for each step, it was averaged. The linear relationship between torque and rotational velocity was transformed into the Bingham parameters, according to the Reiner-Riwlin procedure [23,24]. Plug flow was corrected for if necessary [24]. In a final step, the rheological properties were modified based on a different testing campaign, to resemble rheological properties obtained with the ConTec rheometer [10,22]. If this adjustment was not performed, physically impossible interpretations of the lubrication layer properties were observed [4]. The concrete interface properties were measured by means of the device developed at the Universite de Sherbrooke, as described in [4]. The inner cylinder of the device was a smooth cylinder with a radius of 62.5 mm and a height of 200 mm. At the bottom of the cylinder, a cone was installed to facilitate penetration into the concrete. The reservoir measured 118.5 mm in radius. For each test, the rotational velocity was decreased from 0.9 rps to 0.01 rps in ten steps of 5 s each, preceded by a preshear period of 30 s at 0.9 rps. From the obtained data, the lubrication layer properties: yield stress (s0,LL) and viscous constant (gLL) were derived, taking the contribution of concrete shearing into consideration. Details on the analysis of the lubrication layer properties can be found in [4]. The detailed results for the rheological properties of the con-

343

c_ b ¼

sb  s0 DpRb =2  s0 ¼ lp lp

ð4Þ

It should be noted that for the calculation of Qconc and the maximum shear rate, the radius at which the boundary between the lubrication layer and the bulk concrete is identified (Rb) is based on an assumed lubrication layer thickness of 2 mm. Fig. 2 shows the relationship between the relative flow rate (Qrel = Qconc/Q) and the maximum shear rate in the bulk concrete, both for the 100 and 125 mm diameter pipes. Both Qconc and the shear rate at the boundary are calculated with the experimentally obtained pressure losses and the rheological properties of the concrete (see [10] for values), following Eqs. (3) and (4), respectively. It should be noted that the total flow rate was fixed at 8 l/s. The shown correlations in Fig. 2 will change if the flow rate changes. As can be seen, Qrel and the shear rate are strongly related, as they

Fig. 1. Typical velocity profile when concrete is pumped: the bulk concrete is surrounded by a lubrication layer. If the yield stress of the concrete is sufficiently low, shearing in the bulk concrete contributes to the flow rate in addition to the shearing in the lubrication layer. The vertical dashed lines represent the lubrication layer boundaries (with radius Rb), the horizontal dashed line divides the total flow rate into the contributions of the lubrication layer and the concrete.

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D. Feys / Construction and Building Materials 223 (2019) 341–351

Q rel ¼

Fig. 2. The relative flow rate (Qrel) and the maximum shear rate in the bulk concrete are strongly related mathematically. The solid lines are best-fitting regression lines, forced to pass through the origin.

are both proportional to Dp/lp. However, there are number of points which deviate from the relationship, especially at low relative flow rates. These points represent mixtures with a relatively high ratio of yield stress to plastic viscosity (s0/lp): a ratio of 10 or higher is deemed to have a significant influence on the obtained relationship. The main conclusion is that the shear rate in the bulk concrete is strongly related to the relative flow rate, apart from situations with high s0/lp. Determining which parameters largely affect the relative flow rate is sufficient to understand their effect on the bulk concrete shear rate. Seen the complexity of the data, and the errors associated with determining pressure loss, flow rate, concrete rheological properties and lubrication layer properties, first, a theoretical approach is applied to determine the physical background for the contribution of concrete shearing to the total flow rate. Eq. (5) calculates the relative flow rate, through division of Eq. (3) by Eq. (1) written explicitly for Q.

Q rel ¼

Q conc Q

¼

3Rb Dp gLL þ 16s gLL  8s0 Rb Dp gLL 4

4 0

3

3

12Dp4 R3 lp þ 3R4 Dp4 gLL  8R3 Dp3 s0 gLL  24R2 Dp3 s0;LL lp ð5Þ

As can be seen, Eq. (5) is a complicated equation, from which it is not entirely clear which terms have the largest influence. The following sections describe a theoretical analysis of Eq. (5) to determine the most important factors influencing concrete shearing by performing a series of simplifications. It should be noted that these simplifications are made to better understand which parameters affect concrete shearing, rather than providing a correct equation to calculate concrete shearing. At first, all yield stress values are neglected, mimicking Newtonian materials, and gradually, the contribution of concrete and lubrication layer yield stresses are included and evaluated. Also, the radius describing the boundary between bulk concrete and lubrication layer is assumed to be close to the pipe radius.

12Dp4 R3 lp þ 3R4 Dp4 gLL

 ¼

4l p þ1 RgLL

1 ð6Þ

As can be seen, the equation is substantially simplified and shows the importance of two parameters in determining the relative flow rate. With decreasing pipe radius, while the properties of the material remain constant, the contribution of concrete shearing to the total flow rate decreases, making the contribution of the lubrication layer more significant. Also, with decreasing gLL/lp, the importance of the lubrication layer increases, and the contribution of the concrete shearing decreases. gLL/lp is a parameter related to the degree of shear-induced particle migration which is the cause for the creation of the lubrication layer [4]. Lower viscous constants indicate either a lower viscosity of the material in the lubrication layer, or a higher thickness of the lubrication layer, or both. It should also be noted that the relative flow rate is independent of the total flow rate or pressure loss. Calculating the maximum shear rate in the bulk (Newtonian) concrete can be performed by dividing the boundary shear stress by the viscosity of the concrete. The boundary shear stress can be obtained by combining Eqs. (1) and (2), assuming R ffi Rb for simplicity. Performing a few calculation steps, the shear rate as a function of material and pumping parameters is shown in Eq. (7):

c_ b ¼

pR2 lp pR3 þ Q gLL 4Q

!1 ð7Þ

It can be seen that, in addition to a dependency to the (pipe) radius and gLL/lp, which are the same parameters influencing Qrel, the shear rate is proportional to the flow rate, as expected. 3.3. Effect of concrete yield stress It is well-known that the concrete yield stress has a significant influence on the portion of the concrete being sheared. For CVC, in most cases, the concrete remains unsheared because the applied shear stress is lower than the yield stress. Rewriting Eq. (5), only neglecting the yield stress of the lubrication layer this time (and assuming Rb ffi R), delivers the following equation:

Q rel ¼ 4

3R4 Dp4 gLL

3R4 Dp4 gLL þ 16s40 gLL  8s0 R3 Dp3 gLL

12Dp4 R3 lp þ 3R4 Dp4 gLL  8R3 Dp3 s0 gLL

if DpR=2 > s0

ð8Þ

In a first step, an analysis of orders of magnitude can reveal which terms in Eq. (8) are dominant, and which can be neglected. Therefore, six different cases are evaluated, in which the radius (101 m) and pressure loss (105 Pa/m) remain constant, with their order of magnitude derived from the experiments, and in which the concrete rheological properties and the viscous constant are altered, reflecting different cases (Table 2). In case of SCC, the equation can be approximated to (Eq. (9)). Terms in the nominator and denominator which are at least two orders of magnitude smaller than the largest number, are neglected:

Q rel;SCC ffi

3R4 Dp4 gLL  8s0 R3 Dp3 gLL

12Dp4 R3 lp þ 3R4 Dp4 gLL  1 4lp 8s0 ¼ þ1  l RgLL 12Dp g p þ 3RDp

ð9Þ

LL

3.2. Newtonian materials By setting all yield stress parameters equal to zero in Eq. (5), and assuming that Rb ffi R, the relative flow rate of a hypothetical Newtonian concrete, surrounded by a Newtonian lubrication layer is predicted (Eq. (6)).

As a result, in case of a low yield stress, the Newtonian solution is still visibly present, with a correction term based on the ratio of the yield stress to the pressure loss. It should be noted that the yield stress term is approximately one order of magnitude lower than the Newtonian term, thus only slightly decreasing the relative flow rate. It can also be seen from Eq. (9) that the relative flow rate

D. Feys / Construction and Building Materials 223 (2019) 341–351 Table 2 Orders of magnitude of concrete properties to evaluate the significance of each term in Eq. (8) (orders of magnitude obtained from [10]).

Low viscous SCC High viscous SCC Low viscous HWC High viscous HWC Low viscous CVC High viscous CVC

Concrete yield stress

Concrete plastic viscosity

Lubrication layer viscous constant

101 Pa 101 Pa 102 Pa 102 Pa 103 Pa 103 Pa

101 Pa s 102 Pa s 101 Pa s 102 Pa s 101 Pa s 102 Pa s

102 Pa s/m 103 Pa s/m 102 Pa s/m 103 Pa s/m 102 Pa s/m 103 Pa s/m

345


The radius of the pipe. For low yield stress materials, the larger the pipe radius, the larger the contribution of concrete shearing to the total flow rate. With increasing yield stress though, the influence of the pipe radius becomes more complicated, as it also influences many other terms in Eq. (5). In the end, when the yield stress is sufficiently high, the concrete will remain unsheared. Situations where bulk concrete is unsheared in the larger pipes, and still undergoes shear in the smaller pipes have been indirectly observed through the calculation of the relative flow rate and shear rate, as smaller pressure losses are needed in larger pipe diameters. 4. Implementation on experimental data

is no longer independent of the pressure loss (or the flow rate), but the relative flow rate will decrease with decreasing pressure loss (or flow rate), until the yield stress is no longer exceeded. A lower pressure loss causes a lower shear stress, increasing the ratio of yield stress to shear stress, which results in a higher plug radius, reducing Qconc. Increasing the concrete yield stress from the order of 10 Pa to the order of 100 Pa results in an additional non-negligible term in Eq. (8), increasing the importance of the ratio of pressure loss to yield stress (Eq. (10)).

Q rel;HWC ffi

3R4 Dp4 gLL  8s0 R3 Dp3 gLL

12Dp4 R3 lp þ 3R4 Dp4 gLL  8R3 Dp3 s0 gLL 1  1  4lp 3Dplp 3DpR 8s0 ¼ þ1  þ 1 8s0 RgLL 3DpR 2s0 gLL

ð10Þ

For CVC, regardless of the viscosity, the relative flow rate needs to be determined according to Eq. (8) as none of the terms in the equation are negligible. However, it should also be kept in mind that for a yield stress of the order of 1000 Pa, a radius in the order of 0.1 m and a pressure loss of 105 Pa/m, the wall shear stress is of similar order of magnitude as the concrete yield stress, which physically means that Qrel needs to be close to zero. 3.4. Incorporation of lubrication layer yield stress If the lubrication layer yield stress is incorporated into the formula, the 4th term in the denominator in Eq. (5) can be neglected in case of SCC, as the lubrication layer yield stress is in the order of 1 to 10 Pa. However, starting from a lubrication layer yield stress in the order of 100 Pa, this 4th term in the denominator can no longer be neglected either. Including the lubrication layer yield stress induces another term dependent on the pressure loss (or flow rate).

4.1. Influence of Q The theoretical formulas derived above show the influence of different rheological properties and pumping parameters on the relative flow rate. As soon as the concrete yield stress is taken into consideration, the relative flow rate becomes dependent on the pressure loss, and thus dependent on the flow rate. A number of examples of the dependency of the relative flow rate on the total flow rate are shown in Fig. 3. It should be noted that Qconc is calculated according to Eq. (3), taking the experimentally measured pressure loss as input. It should however be noted that the experimental Dp-Q curves were slightly non-linear, requiring a 2nd order fit to obtain reliable interpolations at fixed total flow rates. Also, a number of experimental errors influence the results, amongst which errors on the pressure loss assessment, as well as on the values obtained from the ICAR rheometer and the interface rheometer. As can be seen, the Qrel vs Q curves are not monotonously increasing, which is expected, as at very low Q, Qrel is higher for flowable mixtures. Some theoretical concepts are demonstrated in Fig. 3. First, gLL/ lp substantially influences Qrel, which can be observed comparing the results for the three SCC mixtures with the gLL/lp values shown in Fig. 3. Secondly, s0/lp also significantly influences the obtained curves. The best example is the HWC mixture. In the large pipes, the boundary shear stress is close to the yield stress at low Q, resulting in nearly total plug flow. However, as Q increases, Qrel increases significantly, which is in accordance with the theoretical concepts described above, as Dp and lp are strongly related for

3.5. Summary Based on Eqs. (5)–(10), specific parameters are identified influencing the contribution of concrete shearing to the total flow rate, and thus the maximum shear rate in the bulk concrete. These parameters are:
The ratio of viscous constant of the lubrication layer to the viscosity of the concrete. A smaller gLL/lp ratio indicates that the concrete was better able to form the lubrication layer. For lower gLL/lp, less pressure is needed to make the concrete flow at a certain flow rate. A lower pressure will induce a lower flow rate in the bulk concrete, according to Eq. (3).
The ratio of concrete yield stress to total pressure loss, which is indicative of the size of the zone in the bulk concrete flowing as a plug. As pressure loss is strongly correlated to concrete viscosity [22,26,27], at least for SCC, one can take the ratio of yield stress to plastic viscosity as an indication of the plug zone.

Fig. 3. Relative flow rate as a function of total flow rate for a CVC, a HWC and three SCC mixtures. The SCC mixtures show significantly different gLL/lp as indicated in the table in the figure. The full lines and full dots are results for the small (100 mm diameter) pipes and the hollow dots/dashed lines represent data from the large (125 mm diameter) pipes.

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D. Feys / Construction and Building Materials 223 (2019) 341–351

flowable mixtures. Similarly, for the CVC mixture, Qrel is zero for a number of points, showing the material flows as a complete plug. However, with increased Q, CVC can become sheared. Lastly, for low yield stress materials, increasing the pipe radius increases Qrel, but if the yield stress becomes significant (as is the case for SCC 19 at 2 l/s), larger pipes cause a larger plug flow at the same Q, reducing Qrel. This distinction can also be clearly seen by comparing Qrel for small and large pipes for SCC on the one hand, and for the HWC and CVC on the other hand. Again, this follows the theoretical equations, stating that Qrel increases with increasing R if the yield stress is low, but if the concrete yield stress increases, Qrel decreases with increasing R. Fig. 4 shows the calculated shear rate in the bulk concrete, by using the measured pressure loss and concrete rheological properties in Eq. (2). As can be seen, the parameters increasing Qrel in Fig. 3 influence the shear rate in the same manner. As predicted, higher gLL/lp and lower s0/lp increase the shear rate in the bulk concrete. A larger pipe radius significantly decreases the maximum shear rate in the bulk concrete. Furthermore, the shear rate in the bulk concrete is, as expected, strongly dependent on the (total) flow rate. The shear rate values vary between 0 and approximately 45 s1 in the small pipes, and between 0 and 30 s1 in the large pipes, taking all tests into consideration.

4.2. Influence of mix design factors on the maximum shear rate in the bulk concrete As shown, the relative flow rate and the shear rate in the bulk concrete are strongly dependent on the total flow rate. Therefore, only the results at a flow rate of 8 l/s are considered in the remaining part of the analysis. The relative flow rate (Qrel) and the shear rate in the bulk concrete are thus calculated based on the (interpolated) pressure loss measured during the described experiments, according to Eq. (3) (and divided by 8 l/s), and Eq. (4), respectively. The results of Qrel and the maximum shear rate in the bulk concrete, as well as the ratios of viscous constant to viscosity and yield stress to viscosity can be found in Table 3. Fig. 5 shows the shear rate in the bulk concrete as a function of the ratio of the viscous constant to the viscosity, for the SCC and HWC mixtures. A low correlation is obtained due to the imprecision in all measurements affecting the calculation: pressure loss, flow rate, concrete yield

Fig. 4. Maximum shear rate in the bulk concrete as a function of flow rate for a CVC, a HWC and three SCC mixtures. The SCC mixtures show significantly different gLL/ lp as indicated in the table in the figure. The full lines and full dots are results for the small (100 mm diameter) pipes and the hollow dots/dashed lines represent data from the large (125 mm diameter) pipes.

stress, concrete viscosity and lubrication layer viscous constant. Although a strong correlation was observed between the predicted pressure losses, based on Eq. (1), and the experimental losses [10], the calculations performed based on the experimental data to calculate the maximum shear rate in the bulk concrete are more sensitive to small errors in each of the determined parameters. To solve this issue and to clarify better the influence of different mix design factors on the shearing in the bulk concrete, the maximum shear rate in the bulk concrete and gLL/lp are averaged for each concrete mix design. This means that the results of four or five tests, performed on each mixture in approximately 30 min intervals, were averaged (see last column Table 3). SCC 2 and 3 were however excluded from this analysis due to their rapidly changing fresh properties over time, spanning a large s0/lp range [18]. The average shear rate in the bulk concrete versus the average gLL/lp are shown in Fig. 6, and a better trend between the shear rate in the bulk concrete with gLL/lp can now be observed. However, some discrepancies can still be seen, e.g. the two results at gLL/lp = 16 m1 (SCC 5) and 18.5 m1 (SCC 14). Compared to their respective trendlines, these points are switching sides when considering the small and the large pipes separately. Some other mixtures also show a similar behavior which can be attributed to errors in pressure assessment. To further improve the analysis, the shear rate results for the large pipes are transformed into shear rates for the small pipes. Considering Eq. (4), and assuming that the effect of the yield stress is negligible, the ratio of the shear rate in the small pipes relative to the shear rate in the large pipes scales to the ratio of the pressure losses and the pipe radii (Eq. (11)). The ratio between the pressure loss in the small pipes relative to the large pipes is 2.27, determined based on the experimental results, shown in [22]. The ratio in shear rates is, according to this theoretical methodology, equal to 1.8.

c_ w;s Dps Rs 2:27Dpl 0:8Rl ffi ¼ ffi 1:8 c_ w;l Dpl Rl Dpl Rl

ð11Þ

From the experiments on the SCC mixtures, the average shear rate ratio is 1.76, with a minimum of 1.19 and a maximum of 2.36. This variation is most likely attributed to the errors in assessing the pressure losses. Multiplying the shear rates in the large pipes by a factor 1.8, and averaging this with the shear rate in the small pipes delivers the results in Fig. 7. The same principle has been applied to the HWC and CVC mixtures, although this is less justified, especially for the CVC. However, two of the CVC showed zero shear rate (plug flow in the bulk concrete) in the large pipes, at 8 l/s. A clear distinction between certain mixtures can now be made. 4.2.1. SCC mixtures with low gLL/lp There are three SCC mixtures with gLL/lp lower than 20 m1, and all three show a maximum bulk concrete shear rate below 20 s1 at a flow rate of 8 l/s. These mixtures are identified as SCC 9, SCC 5 and SCC 14, in increasing gLL/lp order. SCC 9 was the only mixture with w/cm = 0.34; all other mixtures were produced with lower w/cm. SCC 5 was the only mixture with fly ash. When developing the interface rheometer [4], it was noted that decreasing w/ cm increased gLL/lp and mixtures without fly ash showed larger gLL/lp. As a result, SCC 9 and 5 follow the postulated theories. Focusing on the change in rheological properties due to pumping in [18], SCC 9 shows less variation in viscosity due to pumping, compared to mixtures with a lower w/cm. SCC 14 was intended as a reference mixture to which VMA was added. However, during production, some coarse aggregates were clustered in ice, adding more water to the mixture than anticipated. Although the batch sheet and the official w/cm reported do not include this different w/cm, the SP dosage required to adjust the mixture to the desired

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Table 3 Qrel, the maximum shear rate in the bulk concrete, gLL/lp and s0/lp for each test. Note that Qrel and c_ b are calculated based on the pressure loss at 8 l/s. The first number is for the 100 mm pipes, the second number for the 125 mm pipes. The last column shows the average of the discussed parameters for each concrete mix design.

CVC 1

CVC 2

CVC 3

HWC 1

HWC 2

HWC 3

HWC 4

SCC 1

SCC 2

SCC 3

SCC 4

SCC 5

SCC 7

SCC 8

SCC 9

SCC 10

SCC 11

SCC 12

Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1)

Test 1

Test 2

Test 3

Test 4

1.7/1.6 3.3/2.1 18.6 8.0 0.1/0 0.8/0 20.5 13.1 0/0 0/0 20.3 13.8 22.5/27.6 21.4/13.3 26.1 1.9 27.3/24.0 25.6/11.5 35.1 1.3 29.1/21.7 27.5/10.7 38.1 2.2 28.4/29.8 26.5/14.0 42.3 0.8 22.2/30.0 20.7/14.0 42.7 0.7 19.7/19.4 18.4/9.2 46.2 0.9 24.0/23.0 22.3/10.8 50.2 0.6 17.7/27.7 16.7/13.1 33.9 1.1 12.8/21.5 12.0/10.2 21.0 0.8 25.0/18.2 23.4/8.7 30.5 1.1 35.5/33.2 33.0/15.5 45.1 0.8 11.4/11.4 11.0/5.7 17.2 1.3 22.5/30.7 21.0/14.4 24.9 0.8 23.9/29.0 22.3/13.6 28.7 0.9 22.0/25.7 20.6/12.2 44.6 1.1

1.3/0 2.9/0 20.7 9.1 0/0 0/0 19.8 10.6 0.2/0 1.1/0 32.9 15.6 23.8/28.2 22.4/13.5 37.2 1.5 25.8/23.2 24.3/11.2 44.1 1.6 26.9/19.4 25.8/9.9 30.8 3.1 22.2/20.9 20.7/9.9 25.8 0.8 23.8/29.2 22.2/13.7 36.2 0.8 18.5/18.5 17.3/8.8 41.3 0.9 21.1/18.6 19.9/9.0 59.0 1.4 20.0/34.3 18.7/16.0 36.3 0.7 12.7/20.8 11.9/9.8 12.8 0.7 30.4/27.2 28.4/12.9 43.6 1.1 28.3/25.5 26.2/11.9 32.2 0.6 10.7/11.9 10.2/5.8 8.4 1.0 24.1/31.2 22.6/14.7 31.9 1.1 24.9/30.9 23.3/14.6 42.5 1.1 19.7/23.1 18.5/11.1 44.9 1.2

0.3/0 1.4/0 17.5 11.0 0/0 0/0 20.4 15.9 0/0 0/0 41.5 29.8 20.5/19.5 20.1/10.2 28.1 3.6 25.5/20.9 24.0/10.2 45.8 1.7 19.8/11.1 19.3/6.1 22.5 3.3 19.6/19.3 18.4/9.3 26.4 1.2 21.2/25.6 19.8/12.0 37.9 0.6 17.5/17.3 16.3/8.2 41.1 0.8 16.3/11.7 15.8/6.1 36.7 2.3 17.7/27.7 16.7/13.1 41.2 1.2 12.5/22.0 11.7/10.3 15.0 0.6 28.5/23.8 26.7/11.4 41.6 1.5 27.4/22.6 25.5/10.6 30.5 0.6 11.8/12.9 11.1/6.1 9.3 0.7 23.1/31.6 21.6/14.8 33.3 1.0 23.2/28.1 21.7/13.2 42.3 0.9 16.8/18.4 16.3/9.3 32.2 2.5

0/0 0/0 24.6 18.3 0/0 0/0 31.4 27.6 5.5/0 12.5/0 59.4 38.4 18.9/15.4 19.3/8.9 28.7 5.8 23.3/19.0 22.5/9.8 39.6 3.2 19.0/6.9 19.5/4.8 45.3 6.1 18.9/19.2 17.8/9.2 45.9 1.1 19.0/23.9 17.8/11.3 40.6 0.9 15.6/13.2 15.1/6.7 39.8 2.0 16.3/9.6 16.1/5.5 59.7 3.4 16.4/25.6 15.7/12.4 37.5 1.8 12.1/21.2 11.3/9.9 15.2 0.4 25.6/23.0 23.9/11.0 24.8 1.2 27.0/24.5 25.1/11.5 29.9 0.7 11.8/13.1 11.1/6.3 12.2 0.7 20.5/30.3 19.3/14.3 29.3 1.2 18.9/24.1 18.1/11.8 29.2 2.2 14.3/11.7 15.2/7.3 28.0 6.3

Test 5

18.2/18.6 17.2/9.0 35.0 1.4 17.4/22.1 16.2/10.4 44.4 0.6 9.5/4.0 11.1/3.6 59.9 7.6

28.2/27.3 26.2/12.8 44.3 0.7

Average 0.8/0.4 1.9/0.5 20.3 11.6 0.0/0 0.2/0 23.1 16.8 1.4/0 3.4/0 38.5 24.4 21.4/22.7 20.8/11.5 30.0 3.2 25.5/21.8 24.1/10.7 41.1 1.9 25.3/17.4 23.0/7.9 34.2 3.7 21.5/21.6 20.1/10.3 35.1 1.1 20.7/26.2 19.3/12.3 40.4 0.7

20.6/23.3 16.9/13.7 37.2 1.2 20.6/23.0 11.7/10.0 16.0 0.6 27.4/23.0 25.6/11.0 35.1 1.2 29.3/26.6 27.2/12.5 36.4 0.7 11.4/12.3 10.8/6.0 11.7 0.9 22.6/31.0 21.1/14.6 29.9 1.0 22.7/28.0 21.3/13.3 35.7 1.3 18.2/19.7 17.7/10.0 37.4 2.8 (continued on next page)

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Table 3 (continued)

SCC 13

SCC 14

SCC 15

SCC 16

SCC 17

SCC 18

SCC 19

Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1) Qrel (%) c_ b (s1) gLL/lp (m1) s0/lp (s1)

Test 1

Test 2

Test 3

Test 4

Test 5

Average

27.3/25.7 25.4/12.1 31.2 0.8 23.7/17.8 22.1/8.5 22.4 0.9 17.6/30.0 16.6/14.2 27.3 1.1 22.1/28.5 20.6/13.4 45.1 0.9 22.1/30.0 20.5/12.5 28.5 0.6 29.1/31.4 27.1/14.0 41.1 0.8 29.1/31.4 27.0/14.6 36.1 0.6

25.7/23.8 24.0/11.2 26.8 0.9 20.5/20.4 19.2/9.7 19.3 1.0 18.6/31.1 17.5/14.6 35.1 1.1 23.9/30.3 22.3/14.3 38.9 1.0 25.3/30.6 23.5/14.3 37.7 0.6 23.8/22.6 22.3/10.7 41.4 0.9 31.2/35.6 28.9/16.6 61.4 0.7

23.5/23.0 22.0/10.9 26.6 0.9 17.8/18.8 16.6/8.8 18.5 0.7 18.0/25.9 17.0/12.3 36.0 1.2 18.6/23.0 17.4/10.9 27.0 1.0 21.5/24.8 20.1/11.7 33.0 1.0 21.5/20.2 20.1/9.6 39.4 1.0 14.8/29.6 23.2/13.9 45.9 0.9

21.1/18.6 19.9/9.0 26.6 0.9 17.0/16.4 15.9/7.7 13.7 0.6 17.1/27.5 16.1/13.0 37.0 1.0 19.8/22.6 18.6/10.8 39.4 1.2 18.5/21.4 17.3/10.1 30.0 1.0 19.1/18.1 18.0/8.8 26.7 1.3 23.2/28.4 21.7/13.3 42.5 0.8

19.4/18.8 18.4/9.1 29.7 1.5

23.4/22.0 22.0/10.5 26.6 1.1 19.7/18.3 18.4/8.7 18.5 0.8 17.2/27.9 16.3/13.3 33.0 1.2 20.4/24.2 19.2/11.5 35.2 1.2 21.6/25.5 20.2/12.0 35.5 0.9 22.9/22.0 21.5/10.5 36.1 1.1 25.6/29.5 24.0/13.9 43.4 1.1

Fig. 5. Maximum shear rate in the bulk concrete, at 8 l/s, as a function of gLL/lp for each test executed on HWC and SCC.

14.8/25.2 14.2/12.1 29.7 1.6 17.6/16.6 16.8/8.2 25.8 1.8 20.9/24.0 19.7/11.5 48.5 1.4 21.1/18.9 19.9/9.2 32.0 1.4 19.8/22.3 19.1/11.1 31.2 2.5

Fig. 7. Maximum shear rate in the bulk concrete, averaged based on Eq. (11), for each mix design, as a function of gLL/lp. The trendline is determined based on the SCC mixtures only.

slump flow was zero for SCC 14, while for other reference mixtures, between 1.4 and 2.2 l/m3 of a highly efficient SP were required to meet the slump flow requirement. As such, although unknown, SCC 14 is considered to have a higher w/cm compared to the other mixtures.

Fig. 6. Maximum shear rate in the bulk concrete, at 8 l/s, as a function of gLL/lp, averaged from four or five tests executed on each SCC mix design.

4.2.2. SCC mixtures with high gLL/lp Opposite to SCC 9, SCC 8 and SCC 19 were produced with w/ cm = 0.25 and 0.22, respectively. According to the above analysis, these mixtures should show high gLL/lp and high shear rates in the bulk concrete. In Fig. 7, SCC 19 is represented by the data point the most to the right (gLL/lp = 44 m1), and SCC 8 is the point with the highest average shear rate of almost 25 s1 (at 8 l/s). Although these mixtures cannot as easily be distinguished from the other mixtures, the influence of w/cm is confirmed. Other mixtures which are not following the trend well are SCC 10 (gLL/lp = 30 m1 and a shear rate > 23 s1), and SCC 12 (gLL/lp = 37.5 m1 and a

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shear rate less than 20 s1). No clear explanation can be made why SCC 10 deviates, as it is a reference mixture. SCC 12 has a higher yield stress than the other SCC mixtures, which may explain the slightly lower shear rate. It also has a lower paste volume, but this is not considered to play a role. In fact, decreasing paste volume was considered as a factor amplifying the change in rheological properties due to pumping [18]. As can be seen here, the shear rate in the bulk concrete is slightly lower than for all other SCC mix-

tures at equal w/cm. However, for changes in rheological properties, the shear rate in the paste is deemed as the most important factor, as at equal shear rate in the concrete, the shear rate in the paste increases with decreasing paste volume. Air-entrainment and changes in sand to total aggregate ratio do not appear to influence the magnitude of shear rate in the bulk concrete.

4.2.3. HWC and CVC mixtures The average results of the four HWC mixtures are also shown in Fig. 7. They are of the same order of magnitude as the SCC results, although they show slightly lower average shear rate for a given gLL/lp. The average of the three CVC mixtures are also included. Due to high yield stresses, the shear rates are significantly lower than for the other mixtures, and could be considered negligible in most cases. However, if the same comparison would be drawn at lower flow rates, the relative importance of the yield stress would increase for the HWC mixtures, leading to a faster decline of maximum shear rate in the bulk concrete, compared to the SCC mixtures, when decreasing flow rate or pressure loss.

4.3. Influence of mix design factors on Qrel

Fig. 8. Average relative flow rate as a function of gLL/lp. The trendline is determined based on the SCC mixtures only.

Fig. 8 shows, in a similar fashion, the relative flow rate at 8 l/s, averaged based on four or five pumping tests, and averaged for the two pipe radii, as a function of gLL/lp. As demonstrated in Fig. 1, Qrel and the shear rate are strongly related, and the factors influencing the shear rate affect the relative flow rate in a similar fashion.

Table 4 Estimates of the maximum shear rate in the bulk concrete for the experiments reported by Kaplan [1]. The two rightmost columns represent a hypothetical case of pumping through 100 mm pipes.

C=/52/FL C=/28/FL C=/66/FL C+/52/FL C+/38/FL C+/66/FL C-/52/FL C-/38/FL C-/66/FL C=/38/TP C+/52/TP C+/38/TP C+/66/TP C-/52/TP C-/38/TP C-/52/FL/s C=/66/FL/s l 1% l 1.5% BAP 2 l 2% l 0.5% BAP 1 BCS_CPA 1 BCS_CPA 2 BCS_CPA 3 Air base Air 10% l 1%’ Air 6% Air 8% 10%FS_1.5%GT 5%FS_1.5%GT 5%FS_2.5%GT 10%FS_2.5%GT

s0 (Pa)

lp (Pa s)

Dptot at max Q (bar)

sw for 125 mm pipes (Pa)

c_ w for 125 mm pipes (s1)

sw estimated for 100 mm pipes (Pa)

Estimated c_ w for 100 mm pipes (s1)

808 722 1017 378 403 377 473 440 743 775 1314 554 976 696 556 813 483 1200 655 660 900 1137 106 1200 900 580 1423 2116 900 1174 2000 969 1019 829 1378

73 31 71 351 132 121 73 50 59 51 94 50 90 82 78 41 46 50 175 113 270 88 400 40 40 175 99 30 115 70 56 81 80 170 50

27 23 23 29 36 32 22 18 9 16 32 27 20 12 16 22 13 56 47 43 78 40 86 22 40 78 50 60 43 63 63 43 50 57 43

562 479 479 604 750 667 458 375 188 333 667 563 417 250 333 458 271 1167 979 896 1625 833 1792 458 833 1625 1042 1250 896 1313 1313 896 1042 1188 896

Plug Plug Plug 0.6 2.6 2.4 Plug Plug Plug Plug Plug 0.2 Plug Plug Plug Plug Plug Plug 1.9 2.1 2.7 Plug 4.2 Plug Plug 6.0 Plug Plug Plug 2.0 Plug Plug 0.3 2.1 Plug

900 767 767 967 1200 1067 733 600 300 533 1067 900 667 400 533 733 433 1867 1567 1433 2600 1333 2867 733 1333 2600 1667 2000 1433 2100 2100 1433 1667 1900 1433

1.3 1.4 Plug 1.7 6.0 5.7 3.6 3.2 Plug Plug Plug 6.9 Plug Plug Plug Plug Plug 13.3 5.2 6.8 6.3 2.2 6.9 Plug 10.8 11.5 2.5 Plug 4.6 13.2 1.8 5.7 8.1 6.3 1.1

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4.4. Application to kaplan’s data Applying the same principles to the results obtained by Kaplan [Appendices in 1], reveals that approximately 2/3 of the mixtures evaluated in [1] were in pure plug flow, while some mixtures showed a relatively low maximum shear rate at the wall, with a maximum value of 6 s1 (Table 4). This calculation is based on estimates of the total pressure at the highest reported flow rate read from the graphs (column 4 in Table 4). The total length of the circuit is estimated at 150 m, as Kaplan reported total pressure, not the pressure loss per m of length. The wall shear stress is calculated (column 5), and the shear rate is calculated similarly to Eq. (4), but by using R for simplicity (column 6). If the bulk concrete flowed at uniform velocity, the word ‘‘plug” is displayed for the shear rate. It should be noted that the rheological properties of the concrete mixtures, measured with the BTRheom, seem higher than values measured during the experiments at the Universite de Sherbrooke [10,18,22]. The yield stress was in the order of 103 Pa and the viscosity was 102 Pa s. Also, the pipes employed in the research documented in [1] were 125 mm in diameter, increasing the potential for plug flow in the bulk concrete. As an exercise to show that CVC can be sheared during pumping, the total pressure was estimated for hypothetically pumping through 100 mm diameter pipes. Based on the factor 2.27 relating the pressure in the 100 mm pipes to the pressure in 125 mm pipes, deducted in [22], the pressures read in the graphs in [1] were doubled to estimate pressures in a 100 mm pipe circuit. The wall shear stress and shear rate in the bulk concrete were then recalculated, and are shown in the right two columns of Table 4. It should be noted that the values in the two right columns are hypothetical, and not experimental, but it gives an indication of the order of magnitude of the shear rate in the bulk concrete during pumping (up to 101 s1). It also should be noted that the pressure values were estimated for the highest flow rate for every test reported in the Appendices in [1].

5. Conclusions In this paper, the shearing in the bulk concrete during pumping is investigated in an attempt to identify critical factors which increase or decrease the amount of shearing in the bulk concrete. With increased shear rate, more changes in the rheological properties of the concrete should be induced due to pumping. Two main concepts were defined: the maximum shear rate in the bulk concrete, which occurs at the bulk concrete-lubrication layer interface, and the relative flow rate (Qrel). The relative flow rate is the theoretical flow rate caused by the shearing of the bulk concrete, calculated by the Buckingham-Reiner equation, divided by the total flow rate. Both concepts were investigated theoretically and by means of experimental results published in literature by the author. The main concrete parameter which affects the amount of shearing in the bulk concrete is the ratio of the viscous constant to the plastic viscosity (gLL/lp). If the yield stress of the concrete is minimal, Qrel scales to this ratio, dependent on the pipe radius. At fixed total flow rate, the shear rate in the bulk concrete also scales well with this factor. To minimize shearing, and to facilitate pumping in general, gLL/lp should be low. This results in a lower pressure loss at constant Q and constant viscosity, which on its turn results in a lower shear rate in the bulk concrete. Based on the experimental results, the mixture with higher w/cm, and the mixture containing 25% fly ash show lower gLL/lp, and show lower shear rate in the bulk concrete. A second important concrete property is the ratio of concrete yield stress to concrete plastic viscosity (s0/lp). This ratio delivers

an indication of the size of the plug zone. In fact, physically, the ratio of concrete yield stress to boundary shear stress is the true indicator of plug flow. But the boundary shear stress is influenced by both concrete viscosity (which influences pressure loss), total flow rate, and the pipe radius. Increasing the flow rate can cause a concrete flowing as a plug at low flow rate to be partially sheared at higher flow rate. The distinction between plug flow and shearing flow in concrete cannot solely made by categorizing the concrete as CVC or SCC, as the occurrence of shearing is strongly dependent on the flow rate and the pipe radius. Slowly pumping SCC in a large pipe can show less shearing in the bulk concrete than fast pumping of CVC in a small pipe. Of course, with flow rate, pipe radius, and concrete viscosity being constant, the plug flow will increase with increasing s0/lp and decreasing gLL/lp. Acknowledgements The author would like to acknowledge all parties involved in realizing the experiments at the Universite de Sherbrooke: Sodamco Inc. and the NSERC Industrial Research Chair (PI. K.H. Khayat) for the financial support, K.H. Khayat for securing the financial support, Rami Khatib, Aurelien Perez-Schell for their continuous work, and all other graduate students and technical personnel at the Universite de Sherbrooke for their assistance. Declaration of Competing Interest The author declares no conflict of interest. References [1] D. Kaplan, Pumping of Concretes, (Ph-D thesis) (in French), Laboratoire Central des Ponts et Chaussees, Paris, 2001. [2] F. Chapdelaine, Fundamental and Practical Study on Pumping of Concrete, (Phd thesis) (in French), Universite Laval, Quebec-City, 2007. [3] T.T. Ngo, Influence of Concrete Composition on Pumping Parameters and Validation of a Prediction Model for the Viscous Constant, (Ph-d thesis) (in French), Universite Cergy-Pontoise, 2009. [4] D. Feys, K.H. Khayat, A. Perez-Schell, R. Khatib, Development of a tribometer to characterize lubrication layer properties of highly-workable concrete, Cem. Conc. Compos. 54 (2014) 40–52. [5] S.H. Kwon, C.K. Par, J.H. Jeong, S.D. Jo, S.H. Lee, Prediction of concrete pumping: part I-development of new tribometer for analysis of lubricating layer, ACI Mat. J. 110 (6) (2013) 647–656. [6] F. Gadala-Maria, A. Acrivos, Shear-induced structure in a concentrated suspension of solid spheres, J. Rheol. 24 (6) (1980) 799–814. [7] R.J. Phillips, R.C. Armstrong, R.A. Brown, A.L. Graham, J.R. Abbott, A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration, Phys. Fluids A: Fluid Dyn. 4 (1) (1992) 30–40. [8] J. Spangenberg, N. Roussel, J.H. Hattel, H. Stang, J. Skocek, M.R. Geiker, Flow induced particle migration in fresh concrete: theoretical frame, numerical simulations and experimental results on model fluids, Cem. Concr. Res. 42 (4) (2012) 633–641. [9] D. Kaplan, F. de Larrard, T. Sedran, Design of concrete pumping circuit, ACI Mater. J. 102 (2) (2005) 110–117. [10] D. Feys, K.H. Khayat, A. Perez-Schell, R. Khatib, Prediction of pumping pressure by means of a new tribometer for highly-workable concrete, Cem. Concr. Compos. 57 (2015) 102–115. [11] M. Choi, N. Roussel, Y. Kim, J. Kim, Lubrication layer properties during concrete pumping, Cem. Concr. Res. 45 (1) (2013) 69–78. [12] H.D. Le, E.H. Kadri, S. Aggoun, J. Vierendeels, P. Troch, G. De Schutter, Effect of lubrication layer on velocity profile of concrete in a pumping pipe, Mater. Struct. 48 (12) (2015) 3991–4003. [13] N. Martys, C.F. Ferraris, W.L. George, Modeling of suspension flow in a pipe geometry and rheometers, Proceedings of the 8th Int. RILEM Conference on SCC, May, 2016. Washington DC. [14] S.D. Jo, C.K. Park, J.H. Jeong, S.H. Lee, S.H. Kwon, A computational approach to estimating a lubricating layer in concrete pumping, Comput. Mater. Continua 27 (3) (2012) 189. [15] S.H. Kwon, C.K. Par, J.H. Jeong, S.D. Jo, S.H. Lee, Prediction of concrete pumping: part II—analytical prediction and experimental verification, ACI Mater. J. 110 (6) (2013) 657–668. [16] M. Ouchi, J. Sakue, Self-compactability of fresh concrete in terms of dispersion and coagulation of particles of cement subject to pumping Chicago,

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