## 2 Materials and Methods
### CFD-Simulation Approach  
Once the fresh behavior of SCC containing RCWTB was experimentally characterized, it was simulated using CFD tools through the results of the slump-flow test with the objective of deepening the effect of this residue on the viscosity of SCC. It was also sought to analyze the relationship of viscosity with the passing ability of SCC, measured through the blocking ratios of the 3-bar L-box and 16-bar J-ring tests. The Bingham equation was considered for such simulation, which is defined in Equation (1), in which \(\tau\) is the shear stress in Pa; \(\tau_{0}\) denotes the yield stress in Pa; \(\mu\) refers to the fluid's plastic viscosity in Pa\(\cdot\)s; and \(\dot{\gamma}\) means the shear rate in s\({}^{-1}\). \[ \begin{cases}\tau=\tau_{0}+\left(\cdot\dot{\gamma}\right)&\tau>\tau_{0}\\ \dot{\gamma}=0&\tau\leq\tau_{0}\end{cases}  \tag{1}\]  
Flow3D(r) software (v2023R2 version), developed by Flow Science, was the CFD tool used for the CFD simulations [62]. On the one hand, this software is conceived to simulate free-surface flows. On the other hand, the TruVOF algorithm with which it works allows us to model dynamic free surfaces in a very accurate way. Finally, its interface and post-processing module are simple and intuitive, facilitating data analysis. From all this, this software perfectly enabled us to address the flow conditions of SCC containing RCWTB. The slump-flow test was first simulated. For this purpose, the Abrams cone and the SCC volume were geometrically modeled and imported into the Flow3D(r) software. Subsequently, boundary conditions were defined, which consisted of imposing a flow under the gravity action and establishing the initial motion of lifting the Abrams cone, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test** & **Parameter** & **Class** & **Condition** \\ \hline \multirow{4}{*}{Slump-flow test} & \multirow{3}{*}{Slump flow} & SF1 & Slump flow between 550 mm and 650 mm \\  & & SF2 & Slump flow between 650 mm and 750 mm \\  & & SF3 & Slump flow between 750 mm and 850 mm \\  & & VS1 & \(t_{500}\) time lower than 2 s \\  & & VS2 & \(t_{500}\) time higher than 2 s \\
3-bar L-box test & \multirow{3}{*}{Blocking ratio} & PA2 & Blocking ratio in a 3-bar L-box test higher than 0.80 \\  & & J-ring SF1 & J-ring slump flow between 550 mm and 650 mm \\  & & J-ring SF2 & J-ring slump flow between 650 mm and 750 mm \\
16-bar J-ring test & \multirow{3}{*}{\(t_{500}\) time} & J-ring SF3 & J-ring slump flow between 750 mm and 850 mm \\  & & J-ring VS1 & J-ring \(t_{500}\) time lower than 2 s \\  & & J-ring VS2 & J-ring \(t_{500}\) time higher than 2 s \\  & & PJ2 & Blocking ratio in a 16-bar J-ring test lower than 10 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: SCC classes according to experimental fresh-state tests. as it defined the beginning of the flow of SCC. Finally, a mesh size of 1/3 mm was established, since such size enabled us to balance the accuracy of the simulation and the computational time [63]. Iterative simulations were conducted by fixing values for the parameters \(\tau_{0}\) and \(\mu\) of the Bingham equation and considering time steps of 0.5 s until the end of the test, in order not to excessively increase the computational time. Different values of Bingham's parameters were considered until the simulation results matched the experimental ones with a difference lower than 5% on average, in line with previous studies [64]. The viscosity law (Equation (2); \(\eta_{av}\), apparent viscosity in Pa-s) could also be defined from the Bingham equation. \[\eta_{av}=\mu+\left(\frac{\tau_{0}}{\gamma}\right) \tag{2}\]  
L-box and J-ring tests were then simulated using CFD. Following the geometrical modelling of both the equipment of the tests and the SCC volume, the boundary conditions were fixed. These conditions were the flow under the gravity action and the motion of opening the L-box gate (3-bar L-box test) or lifting the Abrams cone (16-bar J-ring test).