#### 4.1. Impact of Aggregates’ Volume-Fraction on Rheological Properties of Concrete and Constitutive Mortar

In this study, the authors considered the mortar as the suspending medium (liquid phase) and the aggregates as the suspended phase (solid phase) of the concrete. The measured Bingham parameters for the both mortar and concrete are summarized in

Table 3.

For the sake of clarity, the rheological parameters are also represented using rheographs in

Figure 8.

Based on the composition, the ratios among the solid constituents, the water-to-binder ratio (w/b), and the dosage of superplasticizer were kept constant for the mortars. C42 and S37 with volumetric aggregate content reduced by 5% showed similar rheological behavior to that of C47 and S42; see

Figure 8a. However, this is not the case for mixtures C52 and S47 having 5% higher aggregate contents than the reference mixtures. This holds true also for C47c and S42c with crushed aggregates. For these four mixtures, both yield stress and plastic viscosity tend to increase; in CVC, the yield stress was significantly influenced while for SCC it was the plastic viscosity. Some increase in the rheological parameters of mortars could be observed with increasing aggregate content in concrete and replacement of round aggregates by crushed aggregates. These changes can be likely traced back to a more pronounced adsorption of the cement paste by coarse aggregates in those mixtures due to higher surface area of aggregates > 1 mm. Consequently, the sieved mortar contained less cement paste and water. The composition analysis of the sieved mortars confirmed this hypothesis. First, the authors determined the water content of the sieved mortar by drying. Then the actual and nominal water contents of the mortar were compared. The difference showed the amount of water adsorbed by aggregate surfaces together with fine solid particles. As a result, the additional 5% of aggregates of the mixtures C52 and S47 decreased the content of water in the corresponding mortars by 0.72% and 0.82%, respectively, in comparison to the reference mixtures. The rough surface of basalt aggregates in C47c and S42c also resulted in less water in the mortars: by 0.52% and 0.47%, respectively.

Investigation of the concrete mixtures shows very clear tendencies: an increase in the volume-fraction of aggregates or replacement of round aggregates with crushed ones results in significant growth of yield stress and plastic viscosity for both CVC and SCC. The arrows in

Figure 8b indicate the increase in

$\varphi /{\varphi}_{c}$ for each type of concrete. Moreover, the intensity of shear-thickening (

$c/\mu $) decreases with increasing volume-fraction of coarse aggregates in SCC mixtures. This can be explained by assuming the formation of (hydro-)cluster as the main mechanism for shear-thickening behavior of SCC. For compositions with larger aggregates, the coarse particles damage the clusters formed in the cement paste due to strong inertial forces acting on them and high shear forces occurring among them; thus, they reduce the intensity of shear-thickening [

40]. By increasing the volume of the aggregates and reducing the volume of the mortar, firstly, there are fewer clusters to begin with, and secondly, there are more particles that can break down the clusters formed. In the case of S42c, replacing the round with crushed aggregates results in less intense shear-thickening as well. This can be traced to the higher shear rates developing among the aggregates of irregular shape.

#### 4.2. Concrete Rheology during Pumping

During each stroke of the Sliper, only 0.5 m height of the material is being deformed (“pumped”) during the experiment. By dividing the observed pressure values by 0.5 m, the pressure loss per unit length in a DN125 pipe can be calculated and drawn at different discharge rates and for each composition.

Figure 9 illustrates these data points and the linear correlation between

$\Delta P/L$ and

$Q$ for all mixtures.

The thickness of the lubricating layer

${e}_{LL}$ was analytically calculated by fitting the

$\Delta P/L-Q$ data points in Equation (6) similar to [

41]. The rheological parameters of bulk and lubricating layer were set to the experimental values for concrete and mortar (

Table 3), respectively. Since Equation (6) disregards the non-linear term

$c$ of the modified Bingham model for SCC mixtures, the rheological results were evaluated once more using linear regression, and the approximated Bingham parameters were used to determine the thickness of the lubricating layer analytically. For each

$\Delta P/L-Q$ data point, one

${e}_{LL}$ value can be derived. The average of these values is reported as the thickness of the lubricating layer for each individual mixture in

Table 4.

Note that the values listed in

Table 4 are not the actual thickness of the lubricating layer during pumping. Rather, in combination with the measured rheological parameters of mortar, they can be used as a calibration parameter for predicting the pumping pressure in a full-scale pipeline. Both rheological parameters used in Equation (6) as well as in the flow equation derived by Kaplan et al. [

17] are device-dependent. This means that for the same concrete, two different rheometers can deliver different sets of rheological parameters, and consequently, different

$\Delta P/L-Q$ relationship. Ferraris et al. [

42] showed that the rheological parameters can exhibit even ± 300% deviation depending on the testing device. The first question arises as to which rheometer can deliver the “real” material parameters. Which values can be used to derive a reliable relation between the pumping pressure and discharge rate? The answer is indeed none. Yet, to derive a reliable relation between pumping pressure and discharge rate for a full-scale pipeline based on the “uncertain” rheological parameters, one can use the analytical thickness of Sliper. A similar approach can be employed for a numerical simulation of a full-scale pipeline, see [

37].

#### 4.3. Experimentally Determined Thickness of Lubricating Layer

The actual thickness of the lubricating layer for each mixture can be obtained using the half-cylinder specimen tested in the Sliper; see

Figure 5.

Table 5 summarizes the average values and the corresponding standard deviation for each composition.

For each value reported in

Table 5, at least 100 measurements were considered. The large standard deviation of the experimental thickness is mostly due to particles with a diameter of 1–2 mm that are positioned exactly at the pipe wall and taken into account when calculating average values and standard deviations. It is worth mentioning that the average thickness does not necessarily mark a region absent of particles coarser than one mm, but rather a region with a significantly reduced amount of such particles.

Considering the errors that might be introduced during casting of the samples as well as image analysis, the authors decided to analyze the qualitative pattern of the experimental values obtained. Reliable quantitative measurements are later required to establish a link between SIPM and the thickness and properties of the lubricating layer. According to the outcomes, the following conclusions can be drawn:

With an increasing volume-fraction of coarse particles, the thickness of the lubricating layer decreases: the migration of coarse particles is hindered when the local volume-fraction of particles in the neighboring region reaches

$0.8{\varphi}_{c}$ [

3,

9]. With a larger

$\varphi $, the equilibrium is reached faster and closer to the pipe wall; see Equation (8). Hence, a thinner lubricating layer develops (

${e}_{LL.S37}>{e}_{LL.S42}>{e}_{LL.S47}$ and

${e}_{LL.C42}>{e}_{LL.C47}>{e}_{LL.C52}$) [

3].

With an increasing rate of discharge, the thickness of the lubricating layer increases: at higher discharge rates, shear rate, and its changes with respect to radial axis (

$\dot{\gamma}$ and

$\partial \dot{\gamma}/\partial r$, as described by Equation (7)) increase, and so does the intensity of particle migration. Since higher discharge rates were measured for CVC than for SCC (

${Q}_{max,CVC}=3{Q}_{max,SCC}$), a thicker LL could be determined for CVC (

${e}_{LL,C42}>{e}_{LL,S42}$ and

${e}_{LL,C47}>{e}_{LL,S47}$), despite the fact of self-compacting concrete’s containing in general a higher volume-fraction of fine particles in comparison to conventional concrete (

${\varphi}_{total,CVC}<{\varphi}_{total,SCC}$); see

Figure 9. The total content of fine particles, including binder and fine sand, in S42 and S47 was 4.59% and 4.29% higher than that in C42 and C47, respectively.

Figure 10 illustrates a comparison between experimentally and analytically determined thicknesses of the lubricating layers.

Accordingly, the analytical values are in the scatter range of their experimental counterparts, except for the mixture S47. It is worth mentioning here that the analytical thickness is based on the rheological parameters measured using rheometers with relative measuring systems, coaxial cylinders. The analytical thickness was calculated under the following assumption: the rheological parameters of the concrete bulk and lubricating layer during pumping correspond to the rheological parameters of concrete and its constitutive mortar measured using relative rheometers. However, this assumption is erroneous under the consideration of SIPM. Instead, the rheological parameters of concrete bulk and lubricating layer vary in the radial direction depending on the local volume-fractions of particles. These changes influence the experimental thickness of the lubricating layer formed during pumping. Therefore, the analytical and experimental thickness of the lubricating layer might differ depending on the intensity of the SIPM. In the case of S47 with the highest volume-fraction of solid particles, the rheological parameters differed extensively inside and outside the pipeline. The reduced volume-fraction of solids (

$\varphi /{\varphi}_{c})$ was close to the percolation threshold, and therefore, slight particle migration resulted in dramatic changes of the rheological properties; more information is to be found in

Section 4.5. As a result, the analytical and experimental thickness vary significantly when compared to other mixtures.

It must be noted that the thickness of the lubricating layer also depends on our definition of this layer. If the lubricating layer is defined as the region consisting of fine mortar, its thickness depends on the intensity of SIPM. If the thickness of the lubricating layer is defined as the width in which the velocity increases significantly, studies indicate that the thickness is about 2 mm [

6,

43,

44]. In this case, the composition of the lubricating layer within this 2 mm is not constant but varies based on the intensity of particle migration at different discharge rates. In both cases, a clear image for concrete pumping cannot be obtained without considering SIPM.

#### 4.4. Particle Distribution in Radial Direction

The surface area occupied by aggregates of a different size range was used for representing the particle distribution over the pipe radius.

Figure 11 shows exemplarily these results of particle size distribution for the mixtures S47 and C47. The average volume-fraction was assumed to be equal to the average surface area fraction for each size listed on the right side of each graph. Note that both mixtures have the same particles size distribution.

Generally, if all the particles larger than 1 mm are traced, it is expected that the average area fraction for each group is equal to its volume-fraction in the mixture composition. However, due to the irregular shape of the particles, the tip of a larger particle can be erroneously classified as belonging to a smaller particle size range. The following remarks should be considered when using the present methodology:

The number of traceable particles within the range 1–2 mm was often limited to one-fourth (1/4) of the expected values (expected: ${\varphi}_{1-2}=0.0886$, measured values: $0.0235$ for S47 and $0.0223$ for C47). Therefore, the tracking of particles smaller than 2 mm in this method would not provide any additional information.

The average surface area fractions for the particle groups 2–4 mm and 4–8 mm are larger than the expected values for both mixtures, expected: ${\varphi}_{2-4}=0.0886$ and ${\varphi}_{4-8}=0.1226$. On the contrary, for the particle group 8–16 mm, the average surface area is always less than expected. This is due to the irregular shape of the particles and their random orientation in the target cross-section.

For particle size ranges 2–4 mm, 4–8 mm, and 8–16 mm a clear peak can be observed. It seems that the larger the particles are, the greater the distance of the peak to the pipe wall. Furthermore, the peaks are shifted from the maximum aggregate size for each group. This indicates that both wall-effect and SIPM influenced the radial displacement of the particles.

To increase the accuracy of this method, the particles of each group should have a different texture or color. The aggregates can be composed of quartz aggregates of 2–4 mm, basalt aggregates of 4–8 mm and granite aggregates of 8–16 mm. Alternatively, model concrete containing glass beads of different colors can be used to determine the particle distribution that is resulted from SIPM.

#### 4.5. Evaluation of Surface Profile during Sliper Tests

The deformation and flow pattern of the top surfaces of the concrete mixtures were captured when tested in the Sliper. The average radial velocity of the coarse particles and the radius of the plug region were determined; cf.

Table 6. Additionally, the analytical plug radii were also calculated using

${R}_{Plug}=2{\tau}_{0,B}/\Delta P$ and listed; more details can be found in Equation (6).

Since the reported radial velocities in

Table 6 were determined at different pressure losses, the values were normalized according to the maximum pressure loss measured for S47.

In Newtonian fluids, the velocity profile and discharge rates can be calculated as:

with

${\upsilon}_{z}\left(r\right)$ and

$Q$ as the vertical velocity at radius

$r$ (m/s) and total discharge rate (m

^{3}/s).

$\Delta P$,

$R,$ and

$\eta $ are pressure loss per unit length (Pa/m), the radius of the pipe (m), and the viscosity of the Newtonian fluid (Pa·s). Equation (10) shows that the focal width of the velocity parabola is directly proportional to the ratio between the pressure loss and apparent viscosity

$\Delta P/\eta $. To check whether this holds for non-Newtonian fluids as well, the inverse of plastic viscosity and the normalized radial velocities are compared in

Figure 12a. The results show good correlation between these two parameters. The non-zero ordinate intercept is due to the formation of the plug during concrete flow.

The velocity profiles were calculated using Equation (6) for all mixtures and are shown in

Figure 12b. Based on the graphs, for CVC mixtures, the analytical plug radii are between

$0.13R\mathrm{and}0.37R$ under indicated

$\mathsf{\Delta}P$. However, the experimental plug radii were zero. This is to be expected due to the smaller plug radii on the top surface when compared with sample inner region. For SCC mixtures, due to small yield stress values the analytical plug radii approach zero for all mixtures. This outcome agrees with the experimental radii for the mixtures S37, S42, and S42c.

In the case of S47, with a yield stress of 6 Pa and plastic viscosity of 130 Pa·s, the authors observed distinct plug flow with particle displacements of less than 5 mm during the drop. This mixture had the greatest amount of solid particulate with 83.86% by volume in total and 62% of particles larger than 0.06 mm, without binders. The maximum packing fraction of solids larger than 0.06 mm was determined experimentally as 79.74%, which results in initial

$\varphi /{\varphi}_{c}=0.78$. According to [

3], particle migration stops after a critical deformation of

${\gamma}_{c}$, when

$\varphi /{\varphi}_{c}$ reaches 0.80. The critical deformation

${\gamma}_{c}$ is of order of

${R}_{Pipe}^{2}/10{a}^{2}{\varphi}^{2}$, which in our case results in

${\gamma}_{c}$ of approximately

$17$ for an average particle size of 8 mm. The shear strain inside the sample can be simplified as

where

${H}_{S}$ is the height of the sample equal 0.5 m (upper pipe) and

${d}_{sheared}$ is the sheared gap during each stroke, which corresponds to

${R}_{pipe}-{R}_{plug}$. Here, the plug radius is not constant: the moment the concrete enters the pipeline,

${R}_{plug}$ can be approximated as the analytical plug radius computed using the measured yield stress. Subsequently, the particles migrate toward the centerline, increasing the local volume-fraction and hence the local yield stress [

12,

13,

14]. Any further strokes, pipe movements in Sliper, cause the additional migration of particles and increase of local yield stress and

${R}_{plug}$. At

$t={T}_{c}^{FIPM}$ the particle migration becomes steady, while local yield stress and

${R}_{plug}$ reach equilibrium. In the case of S47, the authors assumed an initial

${R}_{plug}$ of 0.04 cm; cf.

Table 6. The shear strain inside the sample can be approximated to:

Comparison of

${\gamma}_{c}\cong 17$ and

${\gamma}_{sample}\cong 8$ indicates that with three strokes, the particle migration in S47 reaches a steady flow state. Therefore, the yield stress and plastic viscosity of the sample during the stroke specified in

Table 6 were different from the experimental values mentioned in

Table 3. Instead, they were product of the SIPM that happened inside the Sliper device during the first few strokes. S47 is an example of a modern concrete with a high volume-fraction of solid particles, whose rheological properties change significantly during pumping due to SIPM.

Until now most researchers have assumed that the variations in rheological parameters due to SIPM are not significant enough to influence the flow properties inside a pipeline. Thus, the assumption of two immiscible single-phase fluids—concrete bulk and the lubricating layer—with constant rheological parameters was sufficient to predict pumping behavior. However, the results observed in this discussion indicate that for mixtures such as S47 with a high volume-fraction of solid particles, the changes in the local volume-fraction of solids, and as a consequence, the changes in the local rheological properties are severe enough to alter the pipe-flow regime. Therefore, it is of utmost importance that the variations of local rheological parameters due to SIPM be considered in the pipe-flow equations.