# 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 specimens of backfill soil and foundation, under drained deviatoric loading, were subjected to confining pressures of 30 and 70 kPa. Figure 6 shows the behavior of the foundation and the backfill soil and the calibration results under triaxial tests. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Constitutive** & \(\gamma\) & **c** & \multirow{2}{*}{\(\Phi\) (\({}^{\circ}\))} & \multirow{2}{*}{\(\Phi\) (\({}^{\circ}\))} & \multirow{2}{*}{\(E_{50}^{ref}\)} & \multirow{2}{*}{\(E_{rad}^{ref}\)} & \multirow{2}{*}{\(E_{nr}^{ref}\)} & \multirow{2}{*}{**m**} & \multirow{2}{*}{\(G_{0}^{ref}\)} & \multirow{2}{*}{\(\gamma\) (\(\
u\)?)} \\  & **Model** & **(kN/m\({}^{3}\))** & **(kPa)** & & & & & **(kPa)** & **(kPa)** & **(kPa)** & **m** & \(G_{0}^{ref}\) \\ \hline Backfill & HSS & 14.3 & 2.5 & 37.3 & 7.3 & 5000 & 5800 & 17,000 & 0.5 & \(3\times 10^{4}\) & \(4\times 10^{-4}\) \\ Foundation & HS & 15.8 & 2.3 & 40.5 & 10 & 14,800 & 14,000 & 44,400 & 0.5 & - & - \\ soil & & & & & & & & & & \\ \hline \hline \end{tabular} Note: \(\gamma\) = unit weight; c = cohesion; \(\Phi\) = soil peak friction angle; \(\psi\) = dilation angle; \(E_{50}^{ref}\) = reference stiffness modulus; \(E_{rad}^{ref}\) = reference tangent stiffness modulus; \(E_{rad}^{ref}\) = reference Young’s modulus for unloading and reloading; m = Stress dependence exponent; \(G_{0}^{ref}\) = reference shear modulus at very small strains; \(\gamma_{0.7}\) = small strain at which the secant shear modulus is equal to 0.7\(G_{0}^{ref}\).  
\end{table} 
Table 3: Input parameters of the large-scale test wall for validation analysis (backfill and Foundation). Figure 5: The cross-section of the modular-block geosynthetic-reinforced soil (MB-GRS) wall: (**a**) wall 1; (**b**) wall 2. The reinforcements were assumed to be linear-elastic with a stiffness of 550 kN/m. Previous studies have shown that, under cyclic loading, reinforcements exhibit hysteretic behavior [33]. However, using finite element analyses, [PERSON] [34] found that the seismic response was not affected by the hysteretic behavior and that the effect of reinforcement stiffness could be captured by the secant value [11; 35; 36]. In the present study, the modular blocks and EPS were modeled as linear-elastic. The properties of the modular blocks were E = \(2\times 10^{6}\) kPa and \(\
u\) = 0.2. The properties of the EPS were E = 200 kPa and \(\
u\) = 0.2. The block-block interfaces (\(\delta\) = 35\({}^{\circ}\)), soil-block interfaces (\(\delta\) = 27\({}^{\circ}\)), block-geogrid interfaces (\(\delta\) = 35\({}^{\circ}\)), and soil-geogrid interfaces (\(\delta\) = 34\({}^{\circ}\)) were defined using the MC. The dynamic finite element procedure consisted of two steps: (a) a staged construction simulation step and (b) a dynamic simulation step, which were utilized to capture the static responses and seismic responses, respectively. In the construction simulation, the wall was lifted sequentially, in which 0.2 m thick soil and block layers were placed until a final height of 3 m was reached. The seismic loading was applied to the model base and was activated following the construction simulation step. The seismic motions (north-south component) reported by [PERSON] et al. [27] were used in this simulation. Viscous damping of 5% was considered for the soil element during the dynamic analysis. The MB-GRS wall was modeled by 15-node triangular solid elements. For the model's boundary conditions, roller boundaries (normally fixed) were assigned to both sides of the wall and the bottom boundary was assigned to be fixed in all directions (fully fixed) [36; 37].