# Seismic Responses of GRS Walls with Secondary Reinforcements Subjected to Earthquake Loading
## 2 Validation of the Dynamic Finite Element Procedure
### A Field GRS Wall with Secondary Reinforcement  
The cross-section of the field GRS wall with secondary reinforcement is shown in Figure 1. The 11.7 m height vertical wall was constructed on the foundation bedrock, containing backfill (reinforced soil zone and retained soil zone), wall facing, wall cap, embedment soil, backslope, and primary and secondary reinforcement layers. Four types of uniaxial polyethylene geogrids and one type of biaxial polypropylene geogrid were adopted as primary and secondary reinforcements, respectively. The secondary and primary reinforcement lengths were 1.3 m and 18.3 m, respectively. The secondary reinforcement layers were applied between two primary reinforcement layers(see Figure 2). The dimensions of the facing blocks were 0.3 m in width and 0.2 m in height while the wall cap was 0.3 m in width and 0.1 m in height. To minimize the boundary effects on the numerical simulations, the foundation bedrock was created in 72 m width (extended to 36 m in front of the wall facing) and 20 m depth. Table 1 shows the input parameters of the backfill (reinforced soil zone) used in this verification analysis. The input parameters were obtained and modified based on [PERSON] et al. [5], where the cap yield model was adopted to simulate the backfill behavior. In this verification analysis, the behavior of the backfill soil was characterized by the hardening soil (HS) model following the conversion process reported by [PERSON] [28] and [PERSON] et al. [29]. The converting formulations are shown as follows:  
\[G_{ref}^{e}=\frac{E_{ur}^{ref}}{2(1+\
u_{ur})} \tag{1}\]  
\[K_{ref}^{iso}=\frac{(1+2K_{0})E_{ond}^{ref}}{3} \tag{2}\]  
Figure 1: The cross-section of the field geosynthetic-reinforced soil (GRS) wall with secondary reinforcement. Figure 2: Schematic of the secondary reinforcement installation. where \(G^{e}_{ref}\) is reference elastic tangent shear modulus; \(E^{ref}_{ur}\) is reference Young's modulus for unloading and reloading; \(K^{iso}_{ref}\) is reference bulk modulus; \(E^{ref}_{oal}\) is reference tangent stiffness modulus. Four types of primary reinforcements (UX1, UX2, UX3, and UX4) and one type of secondary reinforcement (BX) were characterized as linear-elastic. The stiffnesses for UX1, UX2, UX3, UX4, and BX are 360, 407, 637, 860, and 330 kN/m, respectively. The foundation bedrock and facing blocks were simulated as linear-elastic. The properties of foundation bedrock and facing blocks are listed in Table 2. The backfill (retained soil zone), backslope, and embedment soil were defined using the Mohr-Coulomb criterion (MC), and their parameters are shown in Table 2. The block-block interfaces (\(\delta=57^{\circ}\)), soil-black interfaces (\(\delta=40^{\circ}\)), soil-uniaxial geogrid interfaces (\(\delta=47^{\circ}\)), soil-biaxial geogrid interfaces (\(\delta=40^{\circ}\)), and block-embedment soil interfaces (\(\delta=28^{\circ}\)) were defined using the MC, where \(\delta\) is the friction angle of interfaces. The finite element procedure for simulating the field GRS wall with secondary reinforcement consisted of eight steps: (a) the foundation bedrock was activated and reached an equilibrium under gravitational force; (b) a layer of the backfill (reinforced soil zone and retained soil zone) and facing blocks was activated; (c) primary and secondary reinforcements were applied in the numerical model; (d) corresponding interfaces (e.g., the block-block interfaces and the soil-block interfaces) were activated; (e) 8 kPa of uniform vertical stress was placed at the top of reinforced soil to represent more accurate compaction-induced stress; (f) the model reached the new equilibrium; (g) the model was lifted sequentially by staged constructions until a total height of 11.7 m was reached (repeating the steps of (b)-(f) until a total height of 11.7 m was reached); (h) on the top of the reinforced soil, the backslope was then constructed.