# Dynamic Response of Non-Yielding Wall Supporting Over-Consolidated Sand
## 4 Results
### Effect of Backfill Soil Friction Angle  
The effect of the backfill friction angle on the seismic response of the non-yielding wall was investigated by analyzing the control model at five different friction angles. The internal soil friction angles considered were \(30^{\circ}\), \(35^{\circ}\), \(40^{\circ}\), \(45^{\circ}\), and \(50^{\circ}\). Figure 10 shows  
Figure 8: Force diagram showing labeled outputs. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Values** \\ \hline Backfill friction angle, \(\phi\) (\({}^{\circ}\)) & 30, 35, 40, 45, 50 \\ Over-consolidation ratio, OCR & 1, 2, 3, 4 \\ Wall elastic modulus, E\({}_{\mathrm{w}}\) (GPa) & 2.1, 21, 34, 47 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters varied in this study. the variation in maximum and residual normalized incremental deflections at mid-height with backfill friction angle. The figure shows that an increase in backfill friction angle causes a clear rise in the maximum incremental deflection with little impact on the residual incremental deflection. This is a surprising outcome since increasing the friction angle is expected to improve the soil's stability. This trend can be explained by observing the response accelerations of the walls in question. Although not explicitly clear, the unexpected drop in residual deflection at \(\phi=35^{\circ}\) may be linked to lower amplification of seismic energy within the soil-wall system at that specific friction angle. In other words, the system's natural frequency and the dominant frequency content of the input motion at \(\phi=35^{\circ}\), may have caused less resonance and consequently smaller accumulated residual deformations. However, more investigations are required to confirm this finding. Response accelerations of the non-yielding wall at mid-height for three backfill friction angles are shown, together with the base acceleration in Figure 11, which shows the 1 s time increment with the highest response. It can be seen from the figure that the maximum response acceleration in all three cases was larger than the base excitation. The extent of motion amplification can be defined in terms of an amplification factor, which is the ratio of the maximum response acceleration amplitude to the base acceleration amplitude. Figure 10: Variation in maximum and residual wall lateral deflection with backfill friction angle. Figure 9: Time history for the control test run. (**a**) Lateral deflection, (**b**) lateral earth pressure, (**c**) total earth force, and (**d**) location of resultant earth force. Figure 12 shows the amplification factors for the soil and the wall at mid-height. It is clear that the amplification of response is more pronounced for soil-wall systems with larger friction angles. In the models investigated, increasing the soil friction angle could have caused the natural frequency of the soil-wall system to approach the dominant frequencies of the chosen ground motion record. Thus, the surge in the maximum deflection increment with friction angle may be attributed to the larger amplification effects at larger friction angles. Residual deflections above the static values are observed for all friction angles, except for the case of \(\phi=35^{\circ}\). The residual deflection increment did not show a consistent trend as the backfill friction angle varied. Figure 13 shows the maximum transient and residual earth pressures for the non-yielding wall at different backfill friction angles. Static pressures are also shown for comparison. It can be seen in Figure 13a that for all friction angles, the maximum earth pressure exceeded the static soil pressure along most of, or the entire, wall height. Models with \(\phi=40^{\circ}\), \(45^{\circ}\), and \(50^{\circ}\) developed higher maximum pressures in the upper half of the wall compared to the lower half. Models with \(\phi=30^{\circ}\) and \(35^{\circ}\) showed a different trend in which pressures did not decrease at the bottom half of the wall.