# Dynamic Response of Non-Yielding Wall Supporting Over-Consolidated Sand
## 4 Results
### Effect of Wall Panel Modulus of Elasticity
It is important to note that, in all cases of wall modulus of elasticity, the residual earth force exceeded that of the static condition. Finally, the dynamic amplitude increased significantly from the case of a wooden panel to a concrete panel and was practically unaffected when the concrete stiffness was changed. The location of the maximum, minimum, and residual earth force at varying panel elastic modulus is shown in Figure 23. It can be observed that the location of the maximum earth force ranged from approximately 0.55 H to 0.6 H from the base of the wall. The lower locations correspond to the stiffer walls. Similarly, the elevation of the residual earth force decreased with increasing wall elastic modulus. The location of the residual earth force was lower than that of the maximum force at all the walls' elastic modulus values (it ranged from approximately 0.47 H to 0.53 H). The elevations of both the maximum and residual earth forces were found to be larger than the static case for all panel elastic moduli. The elevation of the minimum earth force was significantly lower than that of the static conditions. Moreover, it increased when the wall stiffness increased. Figure 21: Variation in critical lateral earth pressure with wall elastic modulus. (**a**) Maximum pressure, (**b**) residual pressure. Results from the study on residual strength can be useful for implementation in performance-based design procedures under extreme loading conditions, such as severe earthquakes. Performance-based design approaches consider the ultimate functional goal and establish objectives and performance criteria that would result in achieving that ultimate objective. For the study at hand, it commonly assesses the seismic performance of a retaining wall by comparing the earthquake-induced residual displacements with allowable displacements. Such an approach is more suitable than conventional design procedures because some parameters (e.g., ductility) cannot be properly quantified in a pseudo-static limit-equilibrium analysis [42]. The performance-based design allows for the attainment of desired performance levels that satisfy the stakeholders' needs with greater assurance and reliability because the emphasis is on the damage state, without imposed limits and requirements to conform to pre-specified solutions. The two important soil parameters used in this study are the sand friction angle, \(\phi\), and the sand over-consolidation ratio, OCR. The normal range of the sand backfill friction angle varies between 28\({}^{\circ}\) and 50\({}^{\circ}\), with the lower values corresponding to normally consolidated sand and the higher values to over-consolidated sand [37]. The over-consolidation ratio of sand depends on the degree of compaction and sand's relative density. In the current study, the largest OCR for sand is not measured, rather it was calculated using [PERSON] theory [34]. Details of how [PERSON]'s theory is used to calculate OCR from experimental results can be found in El-Emam [6]. Figure 23: Variation in maximum, minimum, and residual resultant elevation with wall elastic modulus. Figure 22: Variation in maximum dynamic, static, and residual lateral earth forces with wall elastic modulus. Except for the first very low value of 2.1 GPa, the ranges of the moduli of elasticity of the wall (E\({}_{\rm w}\) = 21-47 GPa) represent values corresponding to a wide range of concrete strength f\({}^{\prime}\)c, from as low as 19 MPa to as high as 96 MPa.