# Dynamic Response of Non-Yielding Wall Supporting Over-Consolidated Sand
## 4 Results
### Effect of Backfill Soil Friction Angle
The models with higher friction angles (\(40^{\circ}\), \(45^{\circ}\), and \(50^{\circ}\)) showed maximum pressures larger than those of the models with lower friction angles (\(30^{\circ}\) and \(35^{\circ}\)) at the upper half of the wall. At the bottom half of the wall, the models with higher friction angles (\(40^{\circ}\), \(45^{\circ}\), and \(50^{\circ}\)) showed maximum pressures lower than those of the models with lower friction angles (\(30^{\circ}\) and \(35^{\circ}\)). Residual earth pressures (Figure 13b) were lower than the static values at the upper half of the wall for all friction angles. At the bottom half of the wall, residual pressures  
Figure 11: Base and response accelerations at mid-height at different backfill friction angles. Figure 12: Wall and soil acceleration amplification factors at different backfill friction angles. were larger than the static values. Figure 13b confirms that redistribution of stresses occurs in a non-yielding wall system at the end of a seismic event. Figure 14 shows the maximum, residual, and static resultant earth forces on the wall at varying backfill friction angles. As seen in the figure, the maximum total earth force during base shaking decreased as the backfill friction angle increased. However, the maximum dynamic force increment, which is the change in force above the static condition, increased with increasing friction angle. This suggests that the decrease in total earth force is attributed to the lower static forces associated with stronger soils (larger friction angles). The increase in maximum dynamic force increment can be attributed to the system's amplification of the base signal as explained before. The residual earth force follows a trend similar to the maximum earth force. The total residual earth force decreased with an increasing friction angle, while the residual dynamic force increment increased with an increasing friction angle, except when \(\phi\) was changed from 45\({}^{\circ}\) to 50\({}^{\circ}\). It is important to note that both the maximum and residual forces exceeded the static values at all backfill friction angles considered. On average, the increase from the static force to the residual force was 12.5%. This suggests that non-yielding walls that have experienced earthquakes may develop permanent earth forces beyond the static values. These forces may be critical if the wall is subjected to subsequent seismic events or if the wall is to be analyzed again for future modification or maintenance. Finally, the dynamic amplitude, which is the difference between the total maximum and minimum transient lateral force, increased when the friction angle increased. The elevation above the base of the maximum, minimum, residual, and static resultant lateral earth force is illustrated in Figure 15 for different backfill friction angles. The location of the resultant force is important in the structural design of non-yielding walls, as it allows for the calculation of the critical shear and bending moments acting on the wall. For a wall restrained at the top and bottom, a resultant earth force located at mid-height is expected to produce the largest bending moments. Figure 14 shows that the elevation of  
Figure 13: Variation in critical lateral earth pressure with backfill friction angle. (**a**) Maximum pressure, (**b**) residual pressure. the maximum transient force above the base was larger than that of the static force at all friction angles. This increase was slightly more pronounced at larger friction angles. For example, at \(\phi=30^{\circ}\), the elevation of the total lateral force increased from 0.39H (static) to 0.42H (static + dynamic), an increase of 7.7%. At \(\phi=50^{\circ}\), the elevation of the total lateral force increased from 0.48H (static) to 0.54H (static + dynamic), an increase of 12%. As an average, the location of the total earth force (static + dynamic) may be taken as 0.05H above that of the static case with the same friction angle.