Seismic Displacement of Retaining Walls Using Limit Analysis Approach

Gravity walls are commonly used as earth retaining systems supporting fill slopes adjacent to roads and residential areas, especially to protect the transportation facilities and/or nearby structures in regions prone to earthquakes. Analysis of retaining walls behavior against earthquake is an important task for geotechnical engineers for reasons such as soil complex seismic behavior and inefficiency of quasi-static analyses. Seismic analysis and design of earth retaining walls is a difficult task, which traditionally requires the determination of the dynamic soil pressures induced by the soil seismic motion on the wall.
Understanding the performance of a retaining wall during an earthquake is very important for an economical design and reducing the damages caused by large earthquakes. Calculated displacement of retaining walls has a key role in the optimal performance design of these structures under seismic loadings. The efficiency of a wall after an earthquake depends on its seismic displacement. Excessive displacements may not only cause the wall to collapse, but also cause to damage the adjacent structures. There have been numerous examples of this type of failure in recent earthquakes. Though the quasi static method for rational design methods of retaining structures has been performed for several decades, deformations ranging from slight displacement to catastrophic failure have been observed in many earth retaining structures during the recent major earthquakes.
Many researchers have developed design methods for retaining walls during earthquakes by using different approaches. In this paper, an algorithm for calculation of permanent displacements of retaining walls in seismic conditions is presented. Formulation of this algorithm is based on the upper bound limit analysis. Displacement of the wall is calculated by obtaining its yield acceleration by limit analysis, and then combination of the proposed method with Newmark method. Effect of various parameters on the displacement of the walls is studied.
For the upper bound theorem to be valid, the velocity field in the failure mechanism must conform to the normality flow rule (associated with the yield condition). The term normality rule originates from the geometric property of the potential law where the deformation rate vector is perpendicular (normal) to the yield surface.
When dense sand is subjected to shear, it simultaneously exhibits volumetric changes (dilatancy). These changes, when described by the flow rule associated with the Mohr–Coulomb yield condition, tend to overestimate the true dilatancy. There are two distinct issues that need to be addressed: (1) How does the departure from the normality rule affect the yield acceleration of the structure; and (2) what flow rule should be used to obtain a reasonable estimation of the true displacements of a structure subjected to seismic excitation?
The first question was addressed earlier by recent researchers who indicated that the yield acceleration of a soil structure built of “nonstandard" soil (“nonstandard” soil is one with deformation governed by the non-associative flow rule) can be obtained with sufficient precision by the kinematic approach if internal friction angle and cohesion of the soil is modified. For the second issue, the deformation description is described by the true dilatancy angle to conform the true material behavior and for prediction of the true (finite) displacements, Effect of various parameters on yield acceleration and the displacement of the walls is studied. Internal friction and dilatancy angles of the soils have the most important influence on the results.