4.6 R ELATIONSHIP BETWEEN RHEOLOGICAL PARAMETERS AND SLUMP
4.6.3 Empirical relationships between slump, density and rheological parameters
There have been several attempts to establish relationship between the yield stress and slump of normalweight aggregate concrete (NWAC) and the details are presented in Section 2.4 (page 39). Figure 4.22 shows a linear relationship between the yield stress and the slump of the non-air entrained LWAC from the current study, excluding the concrete with slump of 75 mm and below in view of the lower accuracy of the BML rheometer and the slump test for low-slump concrete. The data were obtained from Table 4.1 to Table 4.3. There are two outliers from the data that were excluded from the analysis as indicated by blank symbols in the figure. The outliers were probably attributed to incorrect measurements of the slump during the experiment. This is because the slump test is operator-dependant unlike the BML rheometer, which is independent of the operator during the test. The relationship between the yield stress τ0 (Pa) and the slump S (mm) of the non-air entrained LWAC obtained by linear regression (Fig.4.22) is given by:
τ0 = 630 – 2.33S (4.1)
το = -2.33S + 630 R2 = 0.86
0 200 400 600 800
0 50 100 150 200 250 300
Slump (mm)
Yield stress (Pa)
Fig.4.22 – Relationship between yield stress and slump of non-air entrained LWAC (blank symbols indicate outliers that are excluded from analysis)
According to Wallevik J.E. (2003), the average spacing between the aggregates influences the relationship between the yield stress and the slump of the NWAC. He studied concrete with w/c of 0.4, 0.5 and 0.6. The binder∗ content (inclusive of superplasticizer) per cubic metre of concrete in the mixture proportions was 0.320, 0.305 and 0.295, respectively. From there, he obtained three sets of relationship between the yield stress τ0 (Pa) and the slump S (mm) as follows (Fig.2.17):
w/c 0.4: τ0 = 1290 – 5.38S (4.2)
w/c 0.5: τ0 = 925 – 3.77S (4.3)
w/c 0.6: τ0 = 705 – 2.67S (4.4)
From the equations, it is observed that for a given yield stress the concrete with a higher w/c, and lower binder content, has a lower slump. Due to the decreasing binder
∗ According to ACI 116R-00 Cement and Concrete Terminology: Binders – “cementing materials, either hydrated cements or products of cement or lime and reactive siliceous materials; the kinds of cement and curing conditions govern the general kind of binder formed; also materials such as asphalt, resins, and other materials forming the matrix of concretes, mortars, and sanded grouts.”
content in the concrete with increasing w/c from 0.4 to 0.6, the average spacing between the larger aggregates is reduced. This increases the ease with which a self- bearing network of aggregates may be formed during the slump test and prevents further flow of the concrete, resulting in the lower slump. This explains why the concrete with similar yield stress has lower slump when the binder content decreases.
The relationship of the yield stress and slump of the non-air entrained LWAC in the current study, as shown in Equation (4.1), was a close approximation to the Equation (4.4), which is based on the NWAC with w/c of 0.6 from the study by Wallevik J.E. (2003). The binder content per cubic metre of the concrete in the current study was 0.290 (Table 3.5), and was in close proximity to the binder content of 0.295 in the concrete with w/c of 0.6. The slightly higher slope in the Equation (4.4) compared with that of the Equation (4.1) indicates that the concrete has a higher slump for a given yield stress. This might be due to the higher density of the NWAC as compared with the LWAC in the current study, which was discussed in the previous Section 4.6.2 (page 101). This further confirmed that the relationship of the yield stress and the slump of the LWAC in the current study might be influenced by the average spacing of the large aggregate particles in the concrete, as suggested by Wallevik J.E. (2003).
Figure 4.23 shows the relationship between the yield stress and slump of the non-air and air entrained concrete in the current study. The non-air entrained concrete had about 4.5% of air content, while the air entrained concrete had up to 17% of air content. The equation of the relationship for the air entrained concrete is given by:
τ0 = 1510 – 5.09S (4.5)
Equation (4.5) is a close approximation to Equation (4.2), which is based on the concrete with the largest average spacing between the aggregates due to the highest
binder content (Wallevik J.E., 2003). Although the binder content between the non-air and air entrained concrete in the current study was the same, the average spacing between the aggregates in the air entrained concrete was larger than that in the non-air entrained concrete with the increase in air content. This explains the higher slope in the yield stress-slump relationship of the air entrained concrete compared with that of the non-air entrained concrete, resulting in higher slump for a given yield stress.
Fig.4.23 also shows larger scatter of the data for the air entrained concrete with a correlation coefficient of 0.63, while the data for the non-air entrained concrete had a coefficient of 0.86. As shown by the results of Wallevik J.E. (2003), the slope of the yield stress-slump relationship is affected by the average spacing between the aggregates. As the air content was increased, the average spacing between the aggregates also increased. This might result in different slopes for the yield stress- slump relationship of the air entrained concrete at different air contents. However, due to the limited data at each of the air content, it is not possible to observe a clear trend from Fig.4.23.
Besides this, the difference in the slump for a given yield stress between the non-air and air entrained concrete decreased as the yield stress of the concrete decreased, in the relationship between the yield stress and the slump (Fig.4.23). This trend is also observed in other studies (ACI 236A, 2005; Ferraris and Brower, 2001 &
2003a; Wallevik J.E., 2003) (Figs.2.15 to 2.17).
An equation of similar form as Equation (2.20) that relates the yield stress τ0, the slump S and the density ρ of the non-air entrained LWAC in the current study was proposed based on the experimental data as follows:
640
τ0 = ρ (300 – S) – 130 (4.6)
Comparing Equation (4.6) with that of Equations (2.22) (Hu et al., 1996) and (2.23) (Ferraris and de Larrard, 1998a), it is observed that the constant A of 640 from the former equation is more than twice the value of about 300 from the latter two equations. The reason is due to different types of rheometers used. The BML rheometer used in the current study is known to provide a lower yield stress than the BTRHEOM rheometer used in the other study for the same concrete mixture (Fig.2.16), as mentioned in Section 2.4 (page 39).
τo = -2.33S + 630 R2 = 0.86 τo = -5.09S + 1510
R2 = 0.63
0 200 400 600 800 1000
0 50 100 150 200 250 300
Slump (mm)
Yield stress (Pa)
4.5%
6%
8%
10%
11-12%
13-14%
16-17%
Fig.4.23 – Relationship between yield stress and slump of LWAC with various air content (non-air entrained concrete had about 4.5% air content)
Figure 4.24 shows the comparison between the experimentally determined yield stress and the calculated yield stress of the non-air entrained LWAC with a correlation coefficient of 0.81. As for the air entrained concrete, no equation was proposed in view of the poor correlation between the yield stress and the slump due to the influence of the average spacing between the aggregates at different air contents, which also affects the plastic viscosity. More research and data are needed.
R2 = 0.81
0 100 200 300 400 500
0 100 200 300 400 500
Experimental yield stress (Pa)
Calculated yield stress (Pa)
Fig.4.24 – Comparison of experimentally determined yield stress with calculated yield stress using Equation (4.6)