The influence of the unsaturated soil zone on 2-D and 3-D slope stability analyses L.L. Zhang a, ⁎ ,1 , Murray D. Fredlund b , Delwyn G. Fredlund c , Haihua Lu b , G.W. Wilson d a State Key Laboratory of Ocean Engineering, Civil Engineering Department, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, China b SoilVision Systems Ltd., Suite 02, 640 Broadway Avenue, Saskatoon, SK S7N 1A9, Canada c Golder Associates Ltd., 1721 — 8th Street East, Saskatoon, SK S7H 0T4, Canada d Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB, Canada abstract article info Article history: Received 23 June 2014 Received in revised form 7 May 2015 Accepted 11 May 2015 Available online 14 May 2015 Keywords: Stability analysis Limit equilibrium Three-dimensional Unsaturated soils Matric suction It is commonly understood that a 2-D slope stability analysis will provide a lower factor of safety than a 3-D slope stability analysis. The difference in the calculated factors of safety between a 2-D and a 3-D analysis is generally less than 15% for simple slope geometries. Most past comparative studies between 2-D and 3-D stability analyses have ignored the effect of negative pore-water pressures (i.e., matric suctions) in the soil zone above the ground- water table. In this paper, a comparison is made between 2-D and 3-D slope stability analyses on soil slopes where a portion of the soil profile has matric suctions. The factors of safety on simple geometry slopes and com- plex geometry slopes (i.e., slopes which have two intersecting slope surfaces), are investigated for a range of shear strength parameters and groundwater conditions. For simple slopes with a low slope angle, the difference in factor of safety between a 2-D and a 3-D slope stability analysis, (i.e., ΔFs/Fs 2-D ), generally ranges from 9% to 16% when ϕ b is equal to 15°. The value of ΔFs/Fs 2-D for a steep, simple slope is generally larger than for a low angle, simple slope. When ϕ b is 15°, the values of ΔFs/Fs 2-D for the simple, steep slope generally range from 12 to 18%. The difference between a 2-D and a 3-D stability analysis was most pronounced for concave geometries where a portion of the soil profile contained unsaturated soils. The values of ΔFs/Fs 2-D for corner angle concave slopes with angles ranging between 180 to 270° can be as large as 20 to 59% when ϕ b is equal to 15°. Two case histories, (i.e., the highwall stability failure at the Poplar River coal mine and the Kettleman Hills landfill slope fail- ure), were used to illustrate the effect of the unsaturated zone on changes in the factors of safety. © 2015 Elsevier B.V. All rights reserved. 1. Introduction Two-dimensional (2-D) limit equilibrium methods (LEMs) of slope stability analysis remain the most common method of analysis in slope engineering practice. The sliding direction is assumed to be paral- lel to the 2-D cross-section model cutting through the slope and the slip surface is infinite in the transverse direction (i.e., plane strain condi- tions). However, most engineering problems have three-dimensional characteristics that cannot be taken into account by conventional two- dimensional plane strain representations. Most natural landslides are three-dimensional in character and the geometries are too complex to be accurately modeled using a two-dimensional representation. Other engineering problems which are inherently three-dimensional include mining pits, tailings and mine rock waste piles, deep excavations with corners, earth and rock fill dams or levees, and municipal solid waste slopes (Fredlund et al., 2012b; Yu et al., 2005). Three-dimensional slope stability modeling provides a more realistic representation of complex geometries. A three-dimensional (3-D) analysis can accommo- date variations in geometry, pore-water pressures, and material proper- ties across a site. Three-dimensional methods of slope stability analysis are usually de- veloped as extensions of conventional two-dimensional approaches (Hovland, 1977; Chen and Chameau, 1982; Leshchinsky and Baker, 1986; Zhang, 1988; Hungr, 1987; Lam and Fredlund, 1993; Chen et al., 2001; Cheng and Yip, 2007; Zheng, 2012). Kalatehjari and Ali (2013) un- dertook an extensive review of 3-D analyses. Past studies have shown that a 2-D slope stability analysis provides a conservative estimate of a 3-D slope stability problem, provided that 2-D stability analysis is calculated for the most critical two-dimensional section (Duncan, 1996). The differ- ence in the factors of safety of a slope between a 2-D and a 3-D analysis is generally less than 15% for simple slope geometries. Adriano et al. (2008) found differences in the critical factor of safety of 15% to 50% between 3-D and 2-D stability analyses based on finite element modeling for concave and convex slopes. There are some reported differences in factor of safety between 2-D and 3-D analyses that are greater than 50% (Chen and Chameau, 1982; Leshchinsky and Baker, 1986). The differences were mainly due to the shape of critical slip surfaces. Engineering Geology 193 (2015) 374–383 ⁎ Corresponding author at: Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB, Canada. E-mail addresses: lulu_zhang@sjtu.edu.cn (L.L. Zhang), murray@soilvision.com (M.D. Fredlund), del_fredlund@golder.com (D.G. Fredlund), hailu@soilvision.com (H. Lu), wwilson2@ualberta.ca (G.W. Wilson). 1 Current address: Shanghai Jiao Tong University. http://dx.doi.org/10.1016/j.enggeo.2015.05.011 0013-7952/© 2015 Elsevier B.V. All rights reserved. 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