## 3 Numerical Example
### FEM Configuration  
The 3D finite element model (FEM) is configured with accounting for the topographic and geological characteristics of the real CGD. The dimensional FEM is modeled with the help of software ABAQUS considering fluid-soil-structure interaction (FSSI). The fluid (reservoir) and foundation (rock) is extended up to 1.5 times [24] of the dam height along each side. The dam body is modeled as a plastic 3D solid element, and the foundation is a modeled homogeneous, elastic and isotropic 3D solid element. The elements for both dam and foundation domains are acted here as the quadratic tetrahedral elements C3D10. Zero pressure is applied at the headless boundary and at the top of the reservoir to consider the damping effect arising from the propagation of pressure waves. Zero displacements are imposed on horizontal translation degrees of freedom at the bellow of the dam and reservoir. Figure 5a shows all dimensions of the dam section, and Figure 5b shows the numerical FEM meshing of the fluid-foundation-dam interaction system. The mesh numbers counted for the FEM in the dam's inside, outside material, foundation, and water were 6776, 41575, 14,012 and 37,260, respectively. Besides showing the whole model, Figure 5b also indicates the axis direction, where the x-axis indicates the direction parallel with the fluid (water) flow, the y-axis denotes the direction perpendicular to the fluid flow, and the z-axis was upward vertically. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Physical Feature of CGD** & **Inside Material** & **Outside Material** \\ \hline Compressive strength (MPa) & 12 & 18 \\ \hline Modulus of elasticity (MPa) & 13,767 & 16,861 \\ \hline The tensile strength (MPa) & 1.3 & 1.6 \\ \hline Poisson ratio & 0.18 & 0.18 \\ \hline Density (ton/m\({}^{3}\)) & 2.3 & 2.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Materials properties (designed) of Bohyeonsan concrete gravity dam (CGD). Figure 4: Bohyeonsan CGD; (**a**) real view; (**b**) data collection point in Bohyeonsan CGD. To illustrate the dam condition for the construction period, the material property is taken from Table 1 following the dimensions and meshing techniques as shown in Figure 5b. After the FEM optimization through RSM (detained in Section 4), the material properties will show the present condition of the CGD. The optimization has been carried out by modal verification with the FEM result and the record data. The FEM was excited by the free field data of the prescribed earthquake and applied to the CGD foundation. Neglecting the less intensive earthquake component, only the horizontal was considered except the vertical component of GM. Assigning the static condition gravity load for the self-weight, the implicit integration was taken along with the non-linear dynamic analysis. The Rayleigh method [41] is adopted here for considering the damping matrix, where 5% damping ratio has been adopted for both the inside and outside dam section (more detailed in [PERSON] et al. [23]). The epistemic uncertainties as shown in Figure 6 such as aging effect, concrete damage plasticity (CDP) model, parametric randomization and water height effect have been incorporated in this study, where the water has been modeled considering an isotropic 3D solid element as an acoustic model with element type quadratic tetrahedral AC3D10. The aging effect and the CDP model have been discussed in detail in the next. Figure 5: (**a**) The geometrical dimension of sectional view, (**b**) finite element model (FEM) 3D model with meshing. Figure 6: Epistemic uncertainties consideration in 3D modeling. The formulation of the FEM system in a two-dimensional discretized dynamic equation is followed here as explained in [PERSON] [42] and [PERSON] [24]. The material property was assigned in FEM as the concrete damage plasticity (CDP) model. The damage condition in both tension and compression can be evaluated by the inelastic potential behavior namely CDP.