#### 3.1. Effect of the Volume Fraction

The effect of the volume fraction of aggregates on the structural build-up of concrete was studied under condition of constant surface area of aggregates per unit volume of paste, which was equal to 7.25 m^{2}/L. The volume fraction $\phi $ was varied from 0.35 to 0.55 in increments of 0.05. For the given surface area, the volume fraction of 0.55 was the limit for testing; the mixtures having a higher aggregate content were too stiff.

Figure 2 presents the evolution of static yield stress

${\tau}_{0}$ over the age of concrete

${t}_{age}$ (period of time elapsed after addition of water to the dry components) for the compositions under investigation.

The results show that in the present case the structural build-up during the first 80 min can be adequately described by Roussel’s linear model [

25]. The values of the initial SYS for concrete ranged from 559 to 3743 Pa, increasing with the aggregate content while for the cement paste the initial SYS was merely 223 Pa. Structural build-up rate

${A}_{thix}$ increased correspondingly from 10.5 Pa/min for the cement paste to 25 and up to 98 Pa/min for concrete, again depending on the aggregate content.

To compare the experimental results with the prediction provided by the Chateau–Ovarlez–Trung model and its modifications, relative values of the initial static yield stress

${\tau}_{0,\text{}rel}$ and the structural build-up rate

${A}_{thix,\text{}rel}$ were calculated and plotted versus the ratio between the volume fraction and the maximum volume fraction; see

Figure 3a. Then similar calculations were performed using the values of the random loose packing fraction instead of the maximum volume fraction; see

Figure 3b.

Firstly, it should be noted that the relative initial SYS and the relative ${A}_{thix}$ have comparable values only for the three lower volume fractions of aggregate ($\phi $ = 0.35, 0.40, 0.45). As the volume fraction increases to $\phi $ of 0.50 and 0.55, and the distance between aggregate particles decreases, the increase in relative ${A}_{thix}$ becomes less pronounced in comparison to that in the relative initial SYS. Primarily, the authors assumed that the reason for that was the measurement technique, since the single-batch approach (SB) was used. Multiple disturbance of a single sample can potentially have a more prominent effect on the obtained results when testing concrete with a high volume fraction of aggregate, especially if the mixture contains coarse aggregates. Both these features lead to a higher level of heterogeneity in the sheared region; hence, we repeated the measurements for the volume fractions of 0.50 and 0.55 using the multi-batch approach (MB). Although the structural build-up rate was found to be slightly higher (57 Pa/min instead of 53 Pa/min for $\phi $ = 0.50, and 95 Pa/min instead of 87 Pa/min for $\phi $ = 0.55), the previously observed trend did not change.

Since the models discussed further were originally designed to characterise the yield stress of the suspensions, they are to be firstly applied to predict the development of the initial SYS with increasing volume fraction of aggregates. Then the applicability of the models for predicting parameter ${A}_{thix}$ will be discussed.

As presented in

Figure 3, the Chateau–Ovarlez–Trung model, i.e., model A, could not adequately describe the experimental data neither in the case using the values of

${\phi}_{max}$, as in the initial form of the equation (Equation (6)), nor in the case of implementing the values of

${\phi}_{RLP}$ instead of

${\phi}_{max}$, as was done by Mahaut et al. [

24], Lecompte et al. [

26] and Perrot et al. [

27].

Trying to achieve better agreement, the authors introduced the influence of the aggregate shape into the equation. For this purpose, the value of 2.5 in the exponent was substituted by the intrinsic viscosity of particles

$\left[\eta \right]$. This parameter represents the individual particles’ effect on the viscosity of suspensions and depends both on the shape and on the volume fraction of suspended particles [

39]. Intrinsic viscosity was considered in the Krieger-Dougherty Law [

18], which was used as a basis for the Chateau–Ovarlez–Trung model. In the end both Krieger and Dougherty [

18] and Chateau et al. [

23] used

$\left[\eta \right]$ = 2.5 to describe the properties of the latexes and of the suspensions of spherical particles in yield-stress fluids, respectively. This value originates from Einstein’s theoretical prediction described in [

17] and represents the intrinsic viscosity of ideal spherical particles in low-concentrated suspensions. However, since the shape of the aggregates used for concrete production normally deviates from that of an ideal sphere, and taking into consideration the research of Hafid et al. [

12], who demonstrated therewith the effect of the particle shape on the relative yield stress of model-fluid suspensions, it was decided to modify the Chateau–Ovarlez–Trung model by increasing the value of

$\left[\eta \right]$.

Szecsy [

40] suggested a nomogram presenting the relationship between the intrinsic viscosity and the circularity of aggregate particles, which was later used by Choi et al. [

22] to improve a model for the prediction of concrete pumping behaviour. In the present research, the average circularity of the aggregate was equal to 0.85, which corresponds to

$\left[\eta \right]$ = 5.6 on Szecsy’s nomogram. The modified Chateau–Ovarlez–Trung model with this value of intrinsic viscosity is shown as model B in

Figure 3. In the case of applying the values of

${\phi}_{max}$, as in

Figure 3a, this model provided sufficiently accurate agreement with the experimental results up to the volume fraction of 0.50. Beyond this threshold, the relative initial SYS was considerably underestimated. In the case of using the values of

${\phi}_{RLP}$ (

Figure 3b), the model overestimated the relative initial SYS.

Finally, the value of

$\left[\eta \right]$ was varied until the best fit of the experimental data was obtained, yielding with

$\left[\eta \right]$ = 5.1 for the random loose packing; see model C in

Figure 3b. For the maximum packing concept, no

$\left[\eta \right]$ value was adequate to provide good agreement of the model and experimental data. It should be added that the intrinsic viscosity of 5.1 is valid for the particles with the sphericity of approximately 0.88.

Thus, in this research, the experimental data showing the relationship between the initial SYS and the volume fraction of aggregates can be described by Equation (7):

where

$\left[\eta \right]$ = 5.1.

It is worthwhile mentioning that the applied value of $\left[\eta \right]$ is still close to the one obtained using Szecsy’s nomogram ($\left[\eta \right]$ = 5.6), considering that many possible sources of error exist. Note that sphericity was determined on the particular samples and its average value was used. While the tested systems are polydisperse, their particle size distributions vary, making the average sphericity of each individual fraction different. In further research, the authors intend to assess the opportunity to optimizing Szecsy’s nomogram for highly polydisperse aggregate compositions in order to improve the accuracy of predicting the intrinsic viscosity.

Furthermore, it should be explained why the modified equation of Mahaut et al. [

24],

$\text{}{A}_{thix,\text{}rel}=f\left(\phi \right)=\sqrt{\left(1-\phi \right)\text{}{\left(1-\phi /{\phi}_{RLP}\right)}^{-\left[\eta \right]{\phi}_{RLP}}}$, cannot provide a fit for the experimental result in this investigation. In their research, the authors relied upon the Roussel’s model

${\tau}_{0}\left({t}_{i}\right)={\tau}_{0}\left({t}_{0}\right)+{A}_{thix}\xb7{t}_{rest}$ and assumed that the effect of aggregates on the yield stress described by the expression

$f\left(\phi \right)$ is time-independent. This assumption seems logical, because

$\phi $ and

${\phi}_{RLP}$ are not subjected to change after the concrete mixture is prepared. Mahaut’s model for the relative

${A}_{thix}$ was proved to be valid for the short resting times and in the case when concrete was stirred before each SYS measurement. However, in the case of longer resting times and static conditions, as encountered in this research, the evolution of the relative SYS with the increasing volume fraction changed over time; see

Figure 4.

Moreover, it was observed that the extent of this change depends the volume fraction of the aggregates. Being almost negligible at $\phi $ = 0.35, it became very prominent at $\phi $ = 0.55. This behaviour can occur for various reasons. The first possible reason is that the properties of the actual constitutive paste in concrete may differ from those of the cement paste, which was prepared separately, and may be dependent on the aggregate content and composition. As discussed in the introduction, higher volume fraction of aggregates, especially of finer ones, should result in higher content of water required for wetting their surfaces; hence, the actual w/b in the constitutive paste is reduced. Additionally, aggregates act as grinding bodies during mixing, leading to better dispersion of cement in the mixture, thus making it more reactive. The second reason is that the finer aggregate particles can possibly affect the kinetics of the structuration processes by acting as a surface for precipitation of the early hydration products. However, we have no experimental evidence at this stage proving any of these hypotheses. They will be the subject of follow-up research. Deeper understanding of the mechanism lying under the time-dependent effects of aggregates on the structural build-up of concrete should ensure the further development of the model for the accurate prediction of ${A}_{thix}$.

#### 3.2. Effect of the Surface Area

The second stage of the research was dedicated to the effect of the surface area of aggregates per unit volume of cement paste ${A}_{ag}^{{V}_{p}}$ on the structural build-up of concrete. Three volume fractions were selected, $\phi $ = 0.35, 0.45, and 0.55, for which ${A}_{ag}^{{V}_{p}}$ was varied as follows: 5.00, 7.25, 10.00 m^{2}/L.

The development of static yield stress

${\tau}_{0}$ with increasing age of concrete

${t}_{age}$ for the compositions studied is depicted in

Figure 5, while

Figure 6 presents the variations in the initial SYS and in the structural build-up rate with increasing surface area of the aggregates per unit volume of cement paste.

The results obtained showed that within the investigated range, growth in ${A}_{ag}^{{V}_{p}}$ leads to a linear increase in both initial SYS and ${A}_{thix}$ for all tested volume fractions. Moreover, the described effect becomes generally more pronounced at higher volume fractions.

It should be noted that adding the results achieved in this chapter to the plot in

Figure 3a leads to higher fluctuation of the data points and their noticeable deviation from the model in the case of

${A}_{ag}^{{V}_{p}}$ = 10.00 for the volume fractions of 0.45 and 0.55; see

Figure 7.

This deviation may be caused by considerably higher contents of fine sand in the respective compositions, which in turn resulted in the enhanced structuration of the concrete mixture. Thus, the behaviour as observed may count in favour of the possibility of physical-chemical interactions between cement paste and aggregate particles. In terms of the model, the higher volume fraction of fine particles can be taken into account by increasing the intrinsic viscosity parameter, which, according to [

39], is higher in concentrated suspensions due to crowding. The dotted line presented in

Figure 6 was obtained with

$\left[\eta \right]$ = 5.6.

The practical importance of the experimental results obtained consists in the possibility of fine tuning the static rheological properties by varying the surface area of aggregates per unit volume of cement paste; see

Figure 8.

For example, concrete compositions with

$\phi $ = 0.45,

${A}_{ag}^{{V}_{p}}$ = 10.00 m

^{2}/L and with

$\phi $ = 0.50,

${A}_{ag}^{{V}_{p}}$ = 7.25 m

^{2}/L were characterized by the similar initial SYS (1405 Pa and 1490 Pa, respectively) and the comparable structural build-up rates, i.e., 49 Pa/min and 53 Pa/min, while having different workability, i.e., spread diameter of 200 mm and 188 mm, respectively; see

Table 2. Thus, varying both

$\phi $ and

${A}_{ag}^{{V}_{p}}$ parameters can provide more freedom in terms of the mix design, allowing the production of concrete compositions with the specified rheological behaviour.