New approach to determine the plastic viscosity of self-compacting concrete

Abstract

The rheology of concrete is best measured with the use of a rheometer. The slump flow test gives a good indication of the flowability of the mixture and is therefore still used extensively to judge the workability of SCC mixtures. However, this test presents some defects. The objective of this paper is to develop a new methodology for measuring the workability of a SCC. In this article, we have proposed a correlation between the plastic viscosity of concrete, the time and the characteristics of the flow final profile from the V-funnel coupled to a Plexiglas horizontal channel. The proposed approach, verified by experimental results, represents a simple, economical and usable tool on building site, and it allows to characterize rheologically the SCC from its flow. The comparison between our approach and the experimental values of the plastic viscosity shows that, in a laboratory or on site, instead of using a rheometer we can use our approach to characterize the rheological behavior of a SCC.

Keywords

rheology / viscosity / V-funnel / flow profile / rheometer / behavior

Introduction

The Self-Compacting Concrete SCC was first developed in 1988 by Okamura [ 1] at the Tokyo University and its use has gradually increased [ 2- 7]. SCC is a specialized concrete designed to: flow freely around obstacles, completely fill formwork and enclose all reinforcing bars without segregation or bleeding [ 8]. It becomes a popular form of concrete usage in a range of applications throughout the world.

The three key properties of SCC are filling ability which represents the highly fluid to ensure flow under self weight, passing ability which represents the passing around obstacles without blocking and resistance to segregation which represents the no separation of phases during the flow or at rest after placing. As the name indicates, this concrete type requires no external consolidation effort while still fulfilling all the requirements of conventional concrete.

One of the most important differences between SCC and conventional concrete is the incorporation of a mineral admixture (limestone filler, silica fume and fly ash...). Thus, many studies about the effects of mineral admixtures on the properties of SCC have been completed. These studies show the advantage of mineral admixture usage in SCC, such as improved workability with reduced cement content [ 9, 10]. Additionally, the mineral admixtures can improve particle packing and decrease the permeability of concrete. Therefore, the durability of concrete is also increased [ 11].

Since concrete is flowable in its fresh state, it is appropriate to use a rheological approach to describe its properties, especially in the case of SCC. To measure the rheology and to interpret the results, a thorough understanding of rheology principles is required. Rheology is the science used to describe the flow and the deformation of materials and it uses fundamental engineering principles to describe and predict the movement between solids and liquids [ 12].

Quantitative characterization of the rheological properties is important to the sustainability of the concrete construction industry for the following reasons: 1) workability of fresh concrete forms one of the bases of concrete mixture design for quality control purposes; 2) flow behavior of fresh concrete impacts the quality of concrete hardened properties [ 13, 14]; and 3) concrete placement which includes transportation, pumping, casting and vibration, is affected by the plastic viscosity and the yield stress of fresh concrete [ 15]. Rheology provides a measure between shear stress and rate of deformation. The corresponding constitutive equation can be employed to describe mathematically the flow of fresh concrete.

This paper presents a correlation between the plastic viscosity of concrete, the time and the characteristics of the flow final profile from the V-funnel coupled to a Plexiglas horizontal channel. The aim is to compare the found values of plastic viscosity using our approach with those measured using the rheometer. This verification consists in the trace of the evolution of the theoretical plastic viscosity depending on the experimental plastic viscosity.

Rheology and workability

The flow is governed by the usual conservation equations of mass, momentum and energy for incompressible fluids in a laminar state (see, e.g., [ 16- 18]). To model the stress-deformation behavior of viscoplastic materials, different constitutive equations have been proposed [ 16]. In a simple shear flow, these equations take the following form (Fig. 1):

Various constitutive equations have been proposed to characterize the rheology of fresh concrete as suspensions, but only Bingham model and Herschel-Bulkley model have received wide acceptance [ 15]. Then, the concrete behavior is entirely characterized by its yield stress t_o (in Pa) and the plastic viscosity µ_p (in Pa.s). These parameters are intrinsic properties of the concrete and could be used to predict its flow. They characterize the total physical effort required to place and compact fresh concrete. The yield value quantifies the effort to start movement while the plastic viscosity quantifies the extra effort to sustain the movement at a reasonable speed [ 20].

The rheology of concrete is best measured with the use of a rheometer. There are a number of rheometers available around the world with a significantly different design and operation parameters. The five most commonly used rheometers were compared at the Laboratoire Central des Ponts et Chaussees (LCPC) in Nantes, France in 2000. The rheometers used in this comparison were the BML from Iceland, the BTRHEOM and CEMAGREF-IMG coaxial rheometer from France, the IBB from Canada and the Tattersall Two Point Tester from the UK. All these rheometers are designed to effectively describe the rheology of concrete [ 21].

To determine the appropriate self-compacting properties, e.g., good passing ability, filling ability and resistance to segregation, various test methods are used. The filling ability of the mixtures was measured using the slump flow, L-box and V-funnel tests. The passing ability and segregation resistance were assessed with the L-box, V-funnel sieve segregation tests. The three key properties cannot be described adequately with one method and a combination of tests is required.

European project EFNARC [ 22] was the first internationally to recognize a set of guidelines and specifications for self-compacting concrete. This European project did not only focus on the test methods but also relates the results to fundamental rheological measurements. These later will establish a scientific basis of the recommended properties [ 23].

According to Billberg [ 8], Utsi [ 24] and, Nielsson and Wallevik [ 25] the final diameter of the slump flow describes the yield stress and the T50 value describes the plastic viscosity of the SCC mixture. Slump flow and T50 time is a test allowing to assess the flowability and the flow rate of SCC in the absence of obstructions. It is based on the slump test described in EFNARC [ 22]. These comparisons show that the slump flow diameter should increase if the yield value decreases. Similarly, the T50 value increases if the plastic viscosity is higher. The large scatter of these results shows that there is no significant relationship between rheology results and empirical results.

Proposed procedure

The slump flow test gives a good indication of the flowability and the stability of the mixture and is therefore still used extensively to judge the workability of SCC mixtures. However, according to Roussel [ 26], the result of a slump flow test is representative of the rheological behavior of concrete only if the sample is representative of the material. This requires, on the one hand, that the sample volume is large compared to the elementary volume of larger particles. On the other hand, the material thickness, in the case of a flow, is large compared to the size of larger particles composing the concrete. This second condition is not always fulfilled in tests of slump flow. It imposes that the thickness at the center (maximum thickness) is at least 5 times greater than the diameter of the largest grain. To improve these concepts, Roussel 2007 [ 27] has proposed a new rheological test: the LCPC box (Fig. 2).

This LCPC box test is not very practice because a change of the operator and the use of a bucket can disrupt the velocity and the concrete flow. Moreover, with this test we have access to the yield stress but not to the plastic viscosity.

Thus, as noted above, the most adopted approach to quantify the rheological properties of a SCC is to experimentally measure the shear stress vs. the rate of shear stress using a concrete rheometer. However, the use of a rheometer on site is a very complex operation because it is too expensive. In addition, to move, manipulate and repair a rheometer, a qualified person is required

Instead of the LCPC box, rheometer and other empirical tests, we have used in our study a simple, fast, economical and usable on site tool. The proposed experimental test is a channel of a length of 0.90 m, which represents the same length as the slump flow table, a width of 0.20 m, which is the same width as the box in L and a height of 0.16 m coupled to a V-funnel (Fig. 3). These dimensions are proposed in order to facilitate the comparison of the used test and empirical testing.

This test shows that: 1) regardless of the concrete rheological behavior, the flow velocity presents a complete independence regarding the operator owing to the use of a standard V-funnel; 2) at any time, we can determine the flow time and the flow profile (Fig. 4), the interest of this observation is to give the opportunity for theorists to analyze the flow numeric profile of the concrete and to compare it to every moment with the flow experimental profile; and 3) a practical correlation between the plastic viscosity and the yield stress of fresh SCC, the measurements of the flow time and the final profile in a Plexiglas horizontal channel (Eq. (1)). See Refs. [ 28, 29].

(1) {\displaystyle \frac{dz}{dt}}={\displaystyle \frac{{\displaystyle \frac{\mathrm{16}H{\mu }_p}{\pi }}\left({\displaystyle \frac{{[\mathrm{2}(z\tan \alpha +d)+e]}^{\mathrm{4}}}{{[(z\tan \alpha +d)\cdot e]}^{\mathrm{3}}}}\right)-\sqrt{{\left[{\displaystyle \frac{\mathrm{16}H{\mu }_p}{\pi }}\left({\displaystyle \frac{{[\mathrm{2}(z\tan \alpha +d)+e]}^{\mathrm{4}}}{{[(z\tan \alpha +d)\cdot e]}^{\mathrm{3}}}}\right)\right]}^{\mathrm{2}}-\mathrm{4}\cdot \left[{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\rho \left(\mathrm{1}-{\left({\displaystyle \frac{z\tan \alpha +d}{d}}\right)}^{\mathrm{2}}-\xi \right)\right].\left[-{\displaystyle \frac{\mathrm{8}H{\tau }_{\mathrm{0}}}{\mathrm{3}}}\left({\displaystyle \frac{[\mathrm{2}(z\tan \alpha +d)+e]}{[(z\tan \alpha +d)\cdot e]}}\right)+\rho gz\right]}}{\rho \left(\mathrm{1}-{\left({\displaystyle \frac{z\tan \alpha +d}{d}}\right)}^{\mathrm{2}}-\xi \right)}},

with d, H, a, e are the geometric parameters (constants) of the V-funnel (Fig. 5); dz/dt is the flow velocity (emptying velocity of V-funnel); µ_p is the plastic viscosity of mixture. t₀ is the yield stress. r is the density. g is the gravity. x is the coefficient of singular head losses

Equation (1) is established from the energy balance between surface S₁ and surface S₀, the singular and the regular head losses, and the conservation of mass flow [ 28, 29]. The solving of this differential equation requires the use of calculation software. In our case, we have used the MATLAB program, choosing the appropriate Runge-Kutta method of order 4. Figure 6 shows a practical example of calculating flow time in the V-funnel using the MATLAB program.

In this example, we used the plastic viscosity and the yield stress as constants, and we calculated the V-funnel flow time. We found a flow time of 13.85 s for a viscosity of 85 Pa.s. With the same procedure, we can also calculate the plastic viscosity from the flow time and the density of concrete (Eq. (2)).

From Eq. (1), the plastic viscosity becomes:

(2) {\mu }_P=\left[\left(-{\displaystyle \frac{\mathrm{8}H{\tau }_{\mathrm{0}}}{\mathrm{3}}}\left({\displaystyle \frac{[\mathrm{2}(z\tan \alpha +d)+e]}{[(z\tan \alpha +d)\cdot e]}}\right)+\rho gz\right){\displaystyle \frac{dt}{dz}}+\rho \left(\mathrm{1}-{\left({\displaystyle \frac{z\tan \alpha +d}{d}}\right)}^{\mathrm{2}}-\xi \right){\displaystyle \frac{dz}{\mathrm{2}dt}}\right]/\left[{\displaystyle \frac{\mathrm{16}H}{\pi }}\left({\displaystyle \frac{{[\mathrm{2}(z\tan \alpha +d)+e]}^{\mathrm{4}}}{{[(z\tan \alpha +d)\cdot e]}^{\mathrm{3}}}}\right)\right].

Using the Matlab program with the appropriate Runge-Kutta method, the main objective of this procedure is to determine the plastic viscosity (Eq. (2)) from the measure of, such as, the V-Funnel time and the density of mixture.

To check the validity of this method on SCC, we compared the results obtained by the experimental measurements using a rheometer with the plastic viscosity calculated by our Matlab program.

To determine the plastic viscosity and the yield stress, we used two approaches: an experimental approach based on the rheometer test and a theoretical approach based on Eq. (2) (by using two tests with two different filling heights “z”).

Experimental study

The experimental study was conducted in three parts. In the first one, the V-funnel coupled to a horizontal channel tests such as flow time, flow length, H_f/H_i ratio and unit weight have been realized. In the second part, the measurement of yield stress and plastic viscosity by a rheometer have been performed on various mixtures of SCC. Finally, the correlation between the experimental plastic viscosity, measured by a rheometer, and the theoretical plastic viscosity, calculated by our approach, is established.

Materials and mixture proportions

Taking into account the suggestions reported in the literature concerning the proportion of SCC mixture [ 30, 31], the preliminary phase is to formulate the self-compacting concretes (SCC1 to SCC 32) from cement CEM I 52.5 R while varying the dosing of limestone filler LF, of silica fume SF, and of superplasticizer SP. The amount of binder is about 470 kg/m³. All concretes are prepared with the same ratio W/B (Water/Binder) of 0.34. The used superplasticizer is SIKA VISCOCRETE KRONO 20, according to European Standard NF EN 934-2 which represents a high range water reducing and a new generation of superplasticizer that greatly decreases water/cement ration to increase the workability and the mechanical properties of concrete. It does not contain chloride or other constituents that can cause corrosion of reinforcement. Therefore, this superplasticizer is suitable for the manufacture of self-compacting concrete elements or prestressed.

The chemical composition and physical properties of Portland cement and mineral admixtures are given in Table 1. The proportions of mixtures are presented in Table 2.

Local crushed sand, with a maximum size of 2 mm, fineness modulus was 2.3, specific gravity of 2.65, water absorptions of 0.81% and sand equivalent was 72.5, and gravel, with a maximum size of 10 mm, specific gravity of 2.65, water absorptions of 1.4% and Los Angeles coefficient of 22, were used.

Experimental procedure

The rheological tests such as V-funnel coupled to a Plexiglas horizontal channel and the experimental values of the yield stress and the plastic viscosity of various SCCs are presented in Table 3 and Fig. 7. The given results are the average of 6 measurements.

The rheometer used in our work is a rheometer R/S manufactured by Brookfield. It works both in imposed speed (rate) and imposed stress (stress). After complete immersion of the mobile in the tank filled with concrete, initially not subjected to any shear (except mixing and placing), the test consists of measuring the evolution, depending on time, of the torque opposing the mobile rotation. Figure 8 shows the geometry of vane spindle.

To remain in the experimental conditions corresponding to a flow under gravity and sufficient to reduce the risk of segregation or sedimentation [ 32], we have chosen a low speed of 0.2 rpm. The data acquisition is stopped after reaching the maximum torque which corresponds to the stress required so that the concrete studied flows.

Results and discussion

Fresh properties of SCCs

Figure 7 shows that there are two concrete families; the first has a flow length equal to Lmax, while the second has a filling gradient lower than the other concretes. This observation is confirmed by the values of yield stress shown in Table 3. This latter shows that the concretes which have a flow length equal to Lmax (900 mm) have a yield stress below to 70 Pa. This is the case of SCC4, SSC5, SCC25, etc. However, the yield stress for other concretes exceeds, in some cases, the 130 Pa. This is the case of SCC8.

In addition, Roussel [ 26] found a relationship between the yield stress, the length and, the initial and final heights of flow (Eq. (3)). The yield stress tends to 0 Pa when the final height H_f tends to the initial height H_i (Fig. 9).This is the case of SCC20, SCC25, SCC26, SCC27 and SCC28.

(3) {\tau }_{\mathrm{0}}={\displaystyle \frac{\rho g{l}_{\mathrm{0}}}{\mathrm{2}{L}_{\max }}}\left[(H_i-H_f)+{\displaystyle \frac{l_{\mathrm{0}}}{\mathrm{2}}}\ln \left({\displaystyle \frac{l_{\mathrm{0}}+\mathrm{2}{H}_f}{l_{\mathrm{0}}+\mathrm{2}{H}_i}}\right)\right],

where r is the density, l₀ is the channel width, L_max is the length of flow, H_f is the final height, H_i is the initial height and g is the gravity.

In the Fig. 9, we have not represented the H_f/H_i ratio whose values are equal to 0 (H_i = 0 mm).

Table 3 also shows that the values of viscosities increase with the increase of the V-funnel flow time (Fig. 10). For example, SCC28 presents a V-funnel flow time of 9 s and a plastic viscosity of the order of 31.9 Pa.s, while SCC8 presents a V-funnel flow time of 35 s and a plastic viscosity exceeding the 143 Pa.s.

These results show that the incorporation of silica fume as a partial replacement by weight of cement leads to an increase in V-funnel flow time values. This is attributed to the fact that the silica fume has a high reactivity because of its fineness and Pozzolanic properties which increase the inter-particles friction. The limestone filler decreases the inter-particles friction by its filling effect, and therefore leads to a decrease of the V-funnel flow time. By these electrostatic and steric effects, the increasing of superplasticizer percentage reduces the V-funnel flow time.

Therefore, the visualization of the flow profile allows to characterize, rheologically, the concrete and hence its yield stress. The V-funnel flow time measurement characterizes the plastic viscosity of a SCC.

Experimental comparison of viscosity

In this section, we compare the found values of plastic viscosity using our approach (Eq. (2)) with those measured using the rheometer (Table 3). The first verification consists in the trace of the evolution of the theoretical plastic viscosity depending on the experimental plastic viscosity (Fig. 11).

The relationship between the values of plastic viscosity calculated using our approach (µ_p,theo) and those measured using the rheometer (µ_p,exp) is found more accurate, which can be seen from Fig. 11. The best fit-curve representing this relationship is given by: µ_p,theo = 1.0832µ_p,exp + 5.4123, determined by proposed regression model of R² = 0.9224. The difference between the two values of plastic viscosities (experimental and theoretical) does not exceed 28 Pa.s.

The comparison between our approach and the experimental values of the plastic viscosity shows that, in a laboratory or on site, instead of using a rheometer we can use our approach to characterize the rheological behavior of a self-compacting concrete.

On the basis of the tests results which we have achieved in Civil Engineering laboratory of Polytech 'Marseille on more than 100 compositions, it can be concluded that the use of this approach (V-funnel coupled to a Plexiglas horizontal channel) allows to characterize the filling capacity of concrete by the visualization of its flow profile (H_f/H_i ratio, flow length).

Moreover, from Eq. (2) we have generalized the calculation method of plastic viscosities in a chart (Fig. 12) based on the V-funnel flow time values, the density and, the initial and final flow height in the Plexiglas horizontal channel (H_i and H_f).

Generally, the plastic viscosity µ_p is written as: µ_p = µ_p,0i + y. To determine the addition coefficient “y”, we proposed the following graph (Fig. 13):

On site or in laboratories, the proposed charts are simple ways that allow the direct determination of the plastic viscosity.

Conclusion

In this paper, we have proposed a correlation between the plastic viscosity of SCC, the flow time in the V-funnel and the geometric characteristics of the flow profile in the horizontal channel. The proposed approach was verified by experimental results (measurements of yield stress and plastic viscosity by a rheometer have been performed on various mixtures of SCC). This is an efficient, simple, fast and economical tool allowing to characterize the concrete flow (by means of plastic viscosity–Eq. (2)) from its rheological characteristics (flow time, flow length, H_f/H_i ratio and unit weight). The found values by experimental measurements and by our theoretical approach are very similar. The best fit-curve representing this relationship is given by: µ_p,theo = 1.0832µ_p,exp + 5.4123, with R² = 0.9224.

Indeed, being based on the results of the tests achieved by our procedure on a set of more than 100 different compositions, it will be sufficient to measure, on site, the V-funnel flow time and to deduce directly, from the charts, the viscosity plastic of SCC.

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