## 2 Materials and Methods
### Numerical Modelling
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Element** & **Parameter** & **Value** & **Unit** \\ \hline \multirow{3}{*}{Sleeper (Bi-block in prestressed concrete)/Joint} & Poisson ratio & 0.20 & [-] \\  & [PERSON]’s modulus & 30 & [GPa] \\  & Density & 1700 & [Kg/m\({}^{3}\)] \\ \hline \multirow{3}{*}{Reinforcing steel} & Poisson ratio & 0.30 & [-] \\  & [PERSON]’s modulus & 200 & [GPa] \\  & Density & 7.85 & [Kg/m\({}^{3}\)] \\ \hline \multirow{3}{*}{UIC60 rail} & Poisson ratio & 0.30 & [-] \\  & [PERSON]’s modulus & 210 & [GPa] \\  & Density & 7800 & [Kg/m\({}^{3}\)] \\ \hline \multirow{3}{*}{Ballast} & Thickness & 0.40 & [m] \\  & Poisson ratio & 0.10 & [-] \\  & [PERSON]’s modulus & 200 & [MPa] \\  & Density & 1800 & [Kg/m\({}^{3}\)] \\ \hline \multirow{3}{*}{Sub-Ballast} & Thickness & 0.30 & [m] \\  & Poisson ratio & 0.20 & [-] \\  & [PERSON]’s modulus & 259.70 & [MPa] \\  & Density & 2200 & [Kg/m\({}^{3}\)] \\ \hline \multirow{3}{*}{Track-bed} & Thickness & 0.60 & [m] \\  & Poisson ratio & 0.20 & [-] \\  & [PERSON]’s modulus & 400 & [MPa] \\  & Density & 2200 & [Kg/m\({}^{3}\)] \\ \hline \multirow{3}{*}{Wedge 1} & Poisson ratio & 0.20 & [-] \\  & [PERSON]’s modulus & 519.40 & [MPa] \\  & Density & 2150 & [Kg/m\({}^{3}\)] \\ \hline \multirow{3}{*}{Wedge 2} & Poisson ratio & 0.20 & [-] \\  & Young’s modulus & 259.70 & [MPa] \\  & Density & 2080 & [Kg/m\({}^{3}\)] \\ \hline \multirow{3}{*}{Landfill} & Poisson ratio & 0.20 & [-] \\  & Young’s modulus & 60 & [MPa] \\  & Density & 1850 & [Kg/m\({}^{3}\)] \\ \hline \multirow{3}{*}{Foundation} & Poisson ratio & 0.30 & [-] \\  & Young’s modulus & 246 & [MPa] \\  & Density & 1850 & [Kg/m\({}^{3}\)] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characterization parameters of the materials adopted in the numerical simulations. A simulation without any type of reinforcement (NRM) was considered. The transition wedges were eliminated, and the BB sleepers were not implemented, being replaced by using a continuous foundation with a 6.19 m depth along the railway and immediately above the embankment layout. Solutions that implement C&D waste, specifically BB sleepers as reinforcement elements, were developed to perform a comparison when implementing traditional solutions in contrast to innovative solutions that, depending on the arrangement along the length of the railway, simulate the response of conventional solutions by improving the stiffness properties of the embankment in the transition zones (Figure 4). The BB sleepers were grouped into two or three groups, following the type of arrangement, in such a way that the number of sleepers per row in each group along the length arranged by the transition wedges of the base model (BM) was kept constant. The studied arrangements are presented below, and parameters such as the horizontal distance (HD), vertically (VD), the number of sleepers (NS), and the levels implemented in each grouping were varied. Figure 4: Horizontal BB sleeper reinforcement arrangement example. Figure 3: Transverse geometric arrangement and components with dimensions defined in the YZ plane viewed facing the joint. The different types of arrangements were chosen due to adopting similar stiffness behavior responses in comparison to traditional solutions, such as transition wedges, and allowing the use of C&D waste constituting friendly environmental solutions.