## 2 Development and Validation of the Scaled-Down PCS Model
### Scaled-Down PCS Model Construction  
The finite element (FE) model developed for this study is depicted in Figure 4. Concrete, bolts, and nuts are modeled using eight-node hexahedral elements with reduced integration (C3D8R). Reinforcement bars are represented by two-node linear truss elements (T3D2), while anchor rods are modeled using two-node spatial linear beam elements (B31). Steel plates are discretized with four-node quadrilateral surface elements with reduced integration (S4R). The interaction between concrete (host element) and embedded elements (reinforcement and anchor rods) is simulated using the embedded element method. The base of the structure and the inclined anchor rods are fixed to prevent displacement and rotation. Surface-to-surface contact is implemented to model interactions between key components, such as cantilever beams and columns, columns and retaining plates, outer longitudinal beams and columns, retaining plates and foundation, and steel plates and cantilever beams. A penalty friction coefficient of 0.4 is assigned to tangential behavior, while normal behavior is represented by hard contact. Binding constraints are applied to prevent relative displacement and rotation between columns and foundation, inner longitudinal beams and cantilever beams, bolts and prefabricated holes, and cantilever beams and external longitudinal beams. The anchor rods are embedded within the internal longitudinal beams. Figure 3: Testing for the scaled-down PCS: (**a**) loading schematic; and (**b**) loading in testing. Figure 2: Scaled-down PCS: (**a**) 3D view; (**b**) geometrical design. In constructing the scaled model, particular attention was given to mesh size selection to ensure both accuracy and computational efficiency. Since ABAQUS 2020 uses dimensionless units, we defined the basic unit as meters. The mesh sizes were set as follows: 0.0034 m for bolts, 0.05 m for perforated steel plates, 0.1 m for anchor rods and reinforcement, and 0.02 m for concrete components. These mesh sizes were chosen to satisfy the dual requirements of precision and computational efficiency, enabling reliable finite element analysis while minimizing computational time. Concrete specimens subjected to loading undergo both tensile cracking and compressive failure [15]. To model the stress-strain behavior of concrete, the Concrete Damage Plasticity (CDP) model available in ABAQUS is employed [40,41]. By incorporating damage variables, the CDP model effectively captures the mechanical response of concrete under monotonic, low-cycle, and dynamic loads, demonstrating favorable convergence. Figure 5 presents the uniaxial compressive and tensile stress-strain curves, as specified by the GB50011-2010 [42] Concrete Structure Design Code. The compressive stress-strain relationship is defined as follows:  
\[\sigma_{c}=\left\{ \begin{array}{ll}\frac{mx}{\frac{x}{\alpha_{c}(x-1)^{2}+x} }&x\leq 1\\ \frac{x}{\alpha_{c}(x-1)^{2}+x}&x>1\end{array} \right. \tag{1}\]  
\[x=\frac{\varepsilon}{\varepsilon_{c,r}},\rho_{c}=\frac{f_{c,r}}{E_{c} \varepsilon_{c,r}},n=\frac{1}{1-\rho_{c}} \tag{2}\]  
where \(\sigma_{c}\) is the tensile stress; \(f_{c,r}\) is the uniaxial tensile strength of concrete; \(\varepsilon_{c,r}\) is the peak tensile strain corresponding to \(f_{c,r}\); and \(\alpha_{c}\) is the parameter for the descending branch of the uniaxial tensile stress-strain curve. The tensile stress-strain relationship is given by  
\[\sigma_{t}=\left\{ \begin{array}{ll}1.2x-0.6x^{6}&x\leq 1\\ \frac{x}{\alpha_{c}(x-1)^{1/2}+x}&x>1\end{array} \right. \tag{3}\]  
\[x=\frac{\varepsilon}{\varepsilon_{t,r}},\rho_{t}=\frac{f_{t,r}}{E_{c} \varepsilon_{t,r}} \tag{4}\]  
Figure 4: Developed FE model of a scaled-down PCS. where \(\sigma_{t}\) is the tensile stress; \(f_{t,r}\) is the uniaxial tensile strength of concrete; \(\varepsilon_{t,r}\) is the peak tensile strain corresponding to \(f_{t,r}\); and \(\alpha_{t}\) is the parameter for the descending branch of the uniaxial tensile stress-strain curve.