J. Cent. South Univ. (2019) 26: 241−255 DOI: https://doi.org/10.1007/s11771-019-3997-7 Pseudo-static analysis of cantilever retaining walls using upper bound limit analysis approach Asadollah RANJBAR KARKANAKI 1 , Navid GANJIAN 1 , Farajollah ASKARI 2 1. Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran; 2. Iran International Earthquake Engineering Institute, Tehran, Iran © Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract: Given the extensive utilization of cantilever retaining walls in construction and development projects, their optimal design and analysis with proper attention to seismic loads is a typical engineering problem. This research presents a new algorithm for pseudo-static analysis of retaining walls employing upper bound method. The algorithm can be utilized to design and check the external and internal stability of the wall based on the proposed mechanism. One of the main features of this algorithm is its ability to determine the critical condition of failure wedges, the minimum safety factor and maximum force acting on the wall, as well as the minimum weight of the wall, simultaneously, by effectively using the multi-objective optimization. The results obtained by the proposed failure mechanisms show that, while using the upper bound limit analysis approach, the active force should be maximized concurrent with optimizing the direction of the plane passing through the back of the heel. The present study also applies the proposed algorithm to determine the critical direction of the earthquake acceleration coefficient. The critical direction of earthquake acceleration coefficient is 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 those of similar studies carried out based on the limit equilibrium method and finite element analysis. The critical failure mechanisms were determined via optimization with genetic algorithm. Key words: retaining wall; upper bound; pseudo-static analysis; safety factor; multi-objective optimization Cite this article as: Asadollah RANJBAR KARKANAKI, Navid GANJIAN, Farajollah ASKARI. Pseudo-static analysis of cantilever retaining walls using upper bound limit analysis approach [J]. Journal of Central South University, 2019, 26(1): 241–255. DOI: https://doi.org/10.1007/s11771-019-3997-7. 1 Introduction Better performance of cantilever retaining walls, when compared with the gravity retaining walls, makes them a more preferable option for earthquake-prone areas. The assessment of stability and force acting on the retaining walls is a classical topic in geotechnical engineering. The existing literature in the field provides a number of different methods for evaluating the stability of retaining walls [1–4]. In problems pertaining to the stability of retaining walls, the purpose of determining the active and passive forces acting on the walls is to investigate the internal and external stability. Most works carried out on the stability of retaining walls have ignored the passive earth pressure in front of the wall [5–11]. Other researchers have investigated the effect of buried depth of foundation on the stability of the wall. However, in all these studies, the weight of the wall has been ignored [12–15]. As a result of the significant effect of weight and buried depth of the wall on its safety factors, such assumptions create an error in wall stability Received date: 2017-02-14; Accepted date: 2017-06-26 Corresponding author: Navid GANJIAN, PhD, Lecturer; Tel: +98-21-44868401-9; E-mail: n.ganjian@srbiau.ac.ir