Comparison of 2D and 3D Anchor Analysis Methodologies

The current design standards for the use of anchors in slopes is based on two-dimensional (2D) limit equilibrium analyses. Anchors are considered as discrete loads and the 2D anchor, factored based on the spacing distance, corresponds to extending anchors indefinitely in the third dimension. A three-dimensional (3D) analysis offers a more realistic representation of the problem, including the true discrete nature of the anchor point loads. This paper explores the typical differences between analyzing anchors in 2D and 3D, using four typical conceptual models. Slopes with constant cross sections were shown to be adequately represented by the traditional 2D approach. The maximum difference between 2D and 3D models was 21% and becomes negligible for lower anchor spacing values, as expected. A slope with an external load was analyzed to evaluate critical slip surfaces with lower aspect ratios. Slip surfaces with lower aspect ratios presented higher edge effects that contributed to the stability of the slope. The results indicate that optimum design requires the 3D evaluation of field conditions inducing low aspect ratios, such as concave and convex surfaces, weak layers, and external loads. INTRODUCTION Slopes may be stabilized using a variety of solutions, including anchors. When performing an analysis, geotechnical engineers often follow the traditional two-dimensional (2D), Limit Equilibrium Method (LEM). It is important to understand the consequences and limitations of the assumptions on which the 2D LEM is based. There are numerous studies on anchors that show the importance of considering the actual three-dimensional field conditions. Desai et al. (1986) proposed a three-dimensional procedure based on the Finite Element Method and considering elastoplastic behavior and interface elements, to account for stress and displacement distributions, the relative motion between the anchors and the soil mass, and nonlinear soil behavior. Several important stabilization mechanisms were explained. The role of grout injection was evaluated in terms of the produced normal stresses along the anchor-soil bounding surface. The approach was shown to reproduce adequately experimental tests on a sand, proving realistic stress distributions around the anchor. Nonlinear soil behavior influenced to a large extend relative interface motions. Michalowski (1989) applied an upper-bound limit analysis in 3D to slope stability analyses. Anchors were not specifically considered in this study, but the consideration of locally loaded conditions shed light on important modeling aspects. The manner how the slide mechanism becomes three- dimensional as the slope is locally loaded was demonstrated. This emphasizes the fact that anchors should produce field conditions that require 3D analysis approaches.