# Seismic Responses of GRS Walls with Secondary Reinforcements Subjected to Earthquake Loading
## 3 Finite Element Model  
The objective of this study is to explore the secondary reinforcement effect on the seismic performance of GRS walls. To this end, a series of parametric studies was carried out. The critical factors considered in this study include the secondary reinforcement length and stiffness, the wall height (H), and the vertical spacing of the primary reinforcement layers. To explore the influence of the critical factors, one set of parameters was utilized as a baseline case. The details of the investigated critical factors and baseline case are listed in Table 4.  
Figure 8: Comparison of the calculated and measured values: (**a**) relative lateral facing displacement; (**b**) maximum acceleration; (**c**) maximum reinforcement load. The heights (H) of the three walls were 3, 6, and 9 m, and all three walls had a length of 50 m. The large length of the wall was intended to prevent the influence of boundary deformation in the study area. The width of the finite element model was modeled to be sufficiently large, as will be addressed in the following section. The length of each primary reinforcement was set as 0.7 H beyond the back of the facing and the length of the secondary reinforcement ranged from 0.9 to 1.8 m (0.15 H to 0.3 H). Two vertical spacings of 0.4 m and 0.6 m were used in the layers of primary reinforcement, and the secondary reinforcement layers were placed within the primary reinforcement layers (see Figure 5a). Vertical modular block facings were assumed, and the width and height of the modular blocks were 0.3 and 0.2 m, respectively. The foundation soil was assumed to be underlain by stiff rock with a depth of 10 m. The mesh and the dimension of the numerical model used in this study are shown in Figure 9.  
The backfill, modular blocks, and the interface between the backfill soil and the modular block and the interface between the modular blocks used in the parametric studies were characterized by HSS, the Linear-Elastic model, and the MC constitutive model, respectively, and the parameters were assumed to be the same as the validation of the large-scale shaking table test. The foundation was modeled as linear-elastic, with E = 2 \(\times\) 10\({}^{6}\) kPa, \(\
u\) = 0.2, and \(\gamma\) = 20 kN/m\({}^{3}\). The primary and secondary geogrid reinforcements were assumed to be linear-elastic, and the former was assumed to have a stiffness of 1500 kN/m while the latter was assumed to have a stiffness ranging from 500 to 5000 kN/m. In this study, the wall with a wall height of 6 m, secondary reinforcement length and stiffness of 0.9 m and 500 kN/m respectively, and vertical spacing of 0.6 m under peak ground acceleration of 0.8 g was considered as a baseline case. In the dynamic finite element analysis, the staged construction step of the GRS walls was first conducted to reach the initial equilibrium of deformation and stress before the dynamic simulation step [21; 26]. The GRS walls were then subjected to the validated 1995 Kobe earthquake (north-south component), which was employed as the input motion in the dynamic analyses, as shown in Figure 10. The duration of the Kobe earthquake was obtained after Kramer [38]. The 1995 Kobe earthquake (north-south component) was scaled to peak ground accelerations (PGAs) of 0.2, 0.4, and 0.6 g to evaluate the effects of the PGA on the dynamic response. In order to prevent spurious wave reflection inside the soil body, the artificial boundary must be set up on the actual boundary when conducting the \begin{table}
\begin{tabular}{c c} \hline \hline
**Critical Factors** & **Values** \\ \hline Secondary reinforcement length (m) & 0, 0.9 *, 1.2, 1.5, 1.8 (0.15 H *–0.3 H) \\ Secondary reinforcement stiffness (kN/m) & 0, 500 *, 1000, 1500, 2000, 5000 \\ Wall height, H (m) & 3, 6 *, 9 \\ Vertical spacing, VS (m) & 0.4, 0.6 * \\ Peak Ground acceleration, PGA (g) & 0.2, 0.4, 0.6, 0.8 * \\ \hline \hline \end{tabular}  
* Baseline case.  
\end{table} 
Table 4: Critical factors used in parametric studies. Figure 9: Mesh and dimension of the numerical model.