# Dynamic Response of Non-Yielding Wall Supporting Over-Consolidated Sand
## 2 Literature Review
He suggested that the use of the M-O method is acceptable for basement walls that can move relative to the soil. However, for walls founded on hard rock, the use of [PERSON]'s method is reasonable. [PERSON] et al. [17] developed and validated numerical models to predict the seismic earth pressure behind flexible and rigid walls by modeling the soil as a visco-elastic material. Results from the study showed good agreement with [PERSON]'s method for a rigid wall fixed against rotation. Good agreement was also shown between the results of this study and those of [PERSON] and [PERSON]'s study [18] for flexible walls capable of rotating about their base. [PERSON] and his research collaborators [10; 19; 20] investigated seismic earth pressures behind model basement walls by conducting a series of centrifuge tests on three cases of basement walls. The cases included a non-displacing cantilever wall, a non-displacing basement wall, and a conventional displacing retaining wall. In their studies, it was shown that the M-O and Seed and Whitman methods provide a reasonable upper bound for seismic earth pressures, even in basement walls, when the foundation is compliant. [PERSON] et al. [21] used a kinematic approach to model the behavior of rigid retaining walls with different movement types. The considered cases include rotation about the base, rotation about the top, translation, and no movement. The non-linear response and plastic behavior of the soil in the free field were considered. The authors presented charts showing the expected dynamic lateral earth pressure coefficient for varying horizontal accelerations and wall movements. The locations of the resultant dynamic forces were also presented for the varying cases. They found out that, although the plastic deformations of the free field are much larger than the elastic ones, the distribution of lateral pressure with depth for cohesion-less soil is the same and depends only on the distribution of shear modulus with depth. [PERSON] et al. [22] developed a solution for predicting the total seismic thrust and point of application on a non-yielding wall. The problem was solved considering the dynamics of wave propagation through an elastic medium. Varying parameters included soil Poisson's ratio, soil damping, input motion's frequency, and the rotational stiffness of the wall base. For the case of a non-compliant foundation, the method yields results that agree well with [PERSON] and [PERSON]'s solution [13]. [PERSON] [23] conducted a pseudo-static finite element analysis to estimate the seismic thrust and its point of application on non-yielding rigid walls. He considered a rigid wall restrained against lateral movement and rotation, sitting on a rigid base; a similarly restrained wall sitting on a non-rigid base; and a rigid wall restrained only against rotation, sitting on a non-rigid base. Equations were developed to predict the seismic thrust as a function of the peak ground acceleration for each case and identify the location of the resultant seismic force. Seismic forces projected by this method were found to be approximately 15% to 17% larger than those calculated by [PERSON]'s method [12]. Similarly, [PERSON] et al. [24] conducted a parametric study on the seismic response of non-yielding walls using the finite element method with consideration of the backfill friction angle, the motion intensity, and the wall height. The purpose of the study was to determine whether the phase difference between the maximum wall inertial force and maximum soil thrust during ground shaking is significant. They concluded that the phase difference is practically insignificant. [PERSON] [25] developed an analytical solution using limit equilibrium to estimate seismic earth pressure on massive or non-yielding retaining walls. The boundary conditions were chosen to simulate different bridge abutment arrangements. Finite element models were created to verify the analytical solution. The analytical method produced seismic forces approximately 10% lower than those of the finite element models.