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13This paper applied Particle Swarm Optimization (PSO) in three-dimensional (3D) slope 14 stability analysis to determine the shape and direction of failure as the critical slip surface. A 15 detailed description of adopted PSO was presented and a rotating ellipsoid shape was 16 introduced as the possible failure surface in the analysis. Based on the Limit Equilibrium 17 Method an equation of Factor of Safety (FoS) was developed with the ability to calculate the 18 Direction of Sliding (DoS) in its internal process. A computer code was developed in Matlab 19 to determine the 3D shape of failure surface and calculate its FoS and DoS. Then, two 20 example problems were used to verify the applicability of the presented code, the first by 21 conducting a comparison between the results of the code and PLAXIS-3D finite element 22 software and the second by re-analyzing an example from the literature to find the 3D failure 23 surface. In addition, a hypothetical 3D asymmetric slope was introduced and analyzed to 24 demonstrate the ability of presented method in determining the shape and DOS of failure in 25 3D slope stability problems. Finally, a small-scale physical model of a 3D slope under 26 vertical load was constructed and tested in the lab and the results were re-analyzed and 27 Page 1 of 66 Can. Geotech. J. Downloaded from www.nrcresearchpress.com by MICHIGAN STATE UNIVERSITY on 02/18/15 For personal use only. This Just-IN manuscript is the accepted manuscript prior to copy editing and page composition. It may differ from the final official version of record. 2 compared with the code results. All the results demonstrated the efficiency and effectiveness 28 of the presented code in determining the 3D shape of failure surface in soil slopes. 29 30

Over the last few years, particle swarm optimization (PSO) has been extensively applied in various geotechnical engineering including slope stability analysis. However, this contribution was limited to two-dimensional (2D) slope stability analysis. This paper applied PSO in three-dimensional (3D) slope stability problem to determine the critical slip surface (CSS) of soil slopes. A detailed description of adopted PSO was presented to provide a good basis for more contribution of this technique to the field of 3D slope stability problems. A general rotating ellipsoid shape was introduced as the specific particle for 3D slope stability analysis. A detailed sensitivity analysis was designed and performed to find the optimum values of parameters of PSO. Example problems were used to evaluate the applicability of PSO in determining the CSS of 3D slopes. The first example presented a comparison between the results of PSO and PLAXI-3D finite element software and the second example compared the ability of PSO to determine the CSS of 3D slopes with other optimization methods from the literature. The results demonstrated the efficiency and effectiveness of PSO in determining the CSS of 3D soil slopes.

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