## 3 Results and Discussion
### CFD Simulations  
#### 3.2.1 Adjustment of Bingham Equation Through the Slump-Flow Test  
The values of the Bingham parameters \(\tau_{0}\) and \(\mu\) were obtained through iterative simulations based on the experimental results of the slump-flow test, as shown in Figure 13. In each iteration, a different value of both parameters was assigned until the results of the simulation of the slump-flow test coincided with those experimentally obtained. The initial values for the iterations were defined according to similar research [46; 50; 63; 64].  
The values obtained for both parameters yield stress and plastic viscosity, allowed for defining by the Bingham equation (Equation (1)) for each SCC mixture, as shown in Figure 14a. Such parameters also allowed for defining the viscosity law of each SCC mix (Equation (2)), which are detailed in Figure 14b. Two aspects can be highlighted from the results achieved through CFD simulations:  
* The addition of RCWTB did not affect yield stress (Figure 14a), with all SCC mixes showing a similar value around 120 Pa. Therefore, SCC with contents of this waste up to 3.0% started to freely flow at the same shear stress. This could be expected in view of the \(t_{500}\)-time results obtained in the slump-flow and 16-bar J-ring tests, where 1.5% RCWTB did not affect the free flow of SCC at low slump-flow levels (Figures 7b and 10b). This means that the start of SCC free flow always happened under the same initial conditions (yield stress) regardless of the RCWTB content [63].
* However, RCWTB did noticeably affect the value of the SCC plastic viscosity (Figure 14a). The addition of 1.5% RCWTB increased the viscosity by around 3.5 times (116 Pa\(\cdot\)s vs. 429 Pa\(\cdot\)s), although higher waste amounts did not result in such a large increase, as the viscosity of the \(W3.0\) mix was 517 Pa\(\cdot\)s. The GFRP fibers exhibited a hard movement against shear stresses and also increased the solid concentration within SCC, which hindered the flow of the aggregate particles progressively as the slump flow of the SCC increased [9; 28]. The same phenomena have been found when adding other fiber types to SCC, their long-term effect being more negative than that at the beginning of the free flow [72]. These effects also caused the stabilization of the apparent viscosity to occur at lower shear rates, as can be noted in Figure 14b.  
Figure 13: Example of the simulation of the slump-flow test in the \(RW\) mix.  
Figure 15 shows the relationship based on simple linear regression between the plastic viscosity obtained from CFD simulations and the results of the slump-flow test. It can be seen that the viscosity exhibited a very close relationship with the slump flow, while the relationship with the \(t_{500}\) time had a much lower R\({}^{2}\) coefficient. These statistical relationships support the aspects discussed above. The plastic viscosity conditioned the free-flow behavior of SCC containing RCWTB in the long term, allowing to accurately explain the value of the slump flow, measured when SCC movement ended. However, it was not as successful in explaining the behavior of SCC with RCWTB at the beginning of the free flow, when the negative effect of RCWTB was less noticeable.