Pseudo-Static Stability Analysis of Retaining Walls Using Upper-Bound Approach

Given the extensive use of cantilever retaining walls in construction and development projects, optimal design and analysis of these walls with due attention to static and seismic loads is a typical engineering problem. As a general rule, a designer seeking to use the Upper Bound Limit Analysis and Limit Equilibrium Method to determine the forces acting on a retaining wall should first search for the mechanism of critical failure. During this procedure, the shape of failure surface can be considered to be planar or circular and failure mechanism can be considered to be translational, rotational, or a combination of multiple scenarios. In the present study, the Upper Bound Limit Analysis Method is used to determine the active pressure on the wall. The failure mechanism consists of two triangular wedges used to determine the active pressure on the wall, and a genetic algorithm is used to optimize the failure wedges. The current results show a good agreement with the results of Coulomb and Rankine Method.
The first step for optimal design of cantilever retaining walls is to check their internal and external stability against overturning, sliding, and bearing capacity failure based on a set of assumed dimensions. This initial design should be then completed by checking the wall’s internal stability against shear and bending failures. In case of any change in wall dimensions, the design should be modified such that all factors of safety remain higher than allowable limits and the cost of concrete and steel bars be minimized. All previous works on this subject have only focused on optimizing the structural components of retaining wall, irrespective of the state of its backfill. In the present study, the upper bound limit analysis method was used to determine the shape of critical failure wedges of a retaining wall and its optimal dimensions, and then the formulas provided by ACI 318-05 were used to check its internal stability. The factors of safety against overturning, sliding, and bearing capacity failure were assessed by the limit equilibrium and limit analysis techniques. Given the reciprocal influence of factors of safety and wall dimensions and geometry, the wall’s optimum dimensions the shape of critical failure wedges needed to be determined simultaneously. The results of (upper bound) limit analysis on the stability of retaining wall showed a good agreement with the results of limit equilibrium method and finite element analysis. These results showed that when using limit analysis to determine the most critical instability states of a retaining wall, the critical conditions of failure mechanisms should be checked simultaneously with the optimal structural conditions. This study also used the proposed algorithm to determine the critical direction of earthquake acceleration coefficients. The critical direction of earthquake acceleration coefficient was defined as the direction that maximizes the active force exerted on the wall and minimizes the safety factor for wall stability. The results obtained in this study are in good agreement with the results of similar studies that have been based on limit equilibrium method and finite element analysis. The critical failure mechanism was determined through optimization with genetic algorithm and analysis was validated by comparing the obtained results with the results of other methods. Also, the results show that the geometric dimensions of the wall affect its safety factors and the active pressure on the wall. Consequently, for determination of the most critical state of failure (the lowest safety factors and the highest active pressure), the failure wedges should be optimized while simultaneously determining the optimal wall geometry that can induce the critical state of soil failure. As the results show, in all cases, the values for the safety factors against stability obtained by the Upper Bound Limit Analysis are higher than the allowable values specified by regulations and are in good agreement with the results from the Finite Element Method.
Therefore, the use of the limit analysis method (based on the proposed algorithm) with an allowable safety factor higher than values specified by regulations can return results close to those of the conventional methods commonly used for the design of cantilever retaining walls. The results suggest that complementary studies on the subject may produce allowable safety factors for checking the external stability of cantilever retaining walls through the use of the Upper Bound Limit Analysis Method.