# Dynamic Response of Non-Yielding Wall Supporting Over-Consolidated Sand
## 2 Literature Review  
The earliest work on the seismic earth pressure on retaining walls includes the well-known work of [PERSON] [8] in 1926 and [PERSON] and [PERSON] [9] in 1929. This effort led to the development of the Mononobe-Okabe method (M-O method) for estimating the seismic earth pressure behind retaining walls. The M-O method is based on a limit equilibrium analysis in which seismic loads are considered through a pseudo-static approach, in which a rigid wedge of soil is assumed following [PERSON]'s wedge theory. The total force imposed on the wall by the soil is computed considering the force equilibrium of the wedge and assuming that active earth pressures can develop. The M-O method was developed for gravity walls capable of rotating about their base; thus, may not accurately represent the actual seismic loading conditions of non-yielding walls. Other limitations of the M-O method include its use of only peak ground acceleration (PGA) [7], as well as its extreme overestimation of seismic earth pressures at large ground accelerations [10]. [PERSON] and [PERSON] [11] introduced a simplified version of the M-O method that solves the issue of diverging seismic forces at large ground accelerations. In their method, the point of force application was changed from 1/3 of the wall's height (H) from the base to 0.6 H. However, this method still only considers the case of yielding walls. Recognizing that non-yielding walls do not sufficiently displace to allow for full plastic stress conditions in the soil, [PERSON] [12] attempted to solve this problem by employing the theory of elasticity. Using the results of finite element analyses, an analytical solution was developed for the seismic pressure behind rigid non-moving walls sitting on hard rock. It was shown that his solution yielded accurate results when the amplification effects could be neglected and when the frequency of the motion was less than 50% of the natural frequency of the backfill soil layer. [PERSON] found the seismic stress distribution to be parabolic, and related the point of load application to the soil Poisson's ratio and lateral extent of the backfill. For a wide backfill, the point of load application was found to be 0.63H. Seismicforces calculated by this method, in some cases, may be 2-3 times those calculated using the M-O method. [PERSON] and [PERSON] [13; 14] conducted rigorous numerical analyses to estimate the seismic earth pressure behind yielding and non-yielding retaining walls while treating the soil as visco-elastic material. The effect of wave propagation, frequency content, and amplification of the ground motions were accounted for in their studies. Furthermore, the effects of wall flexibility and base rotational stiffness were found to significantly affect the seismic earth pressure. For a rigid wall with a fixed base, the seismic forces were found to be larger than those estimated by the M-O method. Nevertheless, for realistic wall flexibilities and more compliant foundations, seismic forces were found to significantly decrease from the case of a fixed rigid wall. [PERSON] [15] used the results of finite element analyses to develop a simplified method for estimating the seismic earth pressure on non-yielding walls. His method was developed for buried building walls, which are restrained laterally at the top and bottom due to the presence of floor diaphragms. The method assumed the wall rests on a rigid foundation. It considered the frequency content of the motion, the potential amplification of seismic waves, the interaction of the soil with the structure, and the dynamic properties of the soil. The system was represented by a single degree of freedom (SDOF) and the non-linear effects of the soil could be considered. [PERSON]'s method predicts seismic forces larger than those estimated by the M-O method but smaller than those predicted by [PERSON]'s method. [PERSON] [16] presented a comprehensive literature review on the seismic response and design of soil retaining structures.