Optimal profile for concave slopes under static and seismic conditions

Abstract

This study presents a methodology to determine the stability and optimal profile for slopes with concave cross section under static and seismic conditions. Concave profiles are observed in some natural slopes suggesting that such geometry is a more stable configuration. In this study, the profile of a concave slope was idealized by a circular arc defined by a single variable, the mid-chord offset (MCO). The proposed concave profile formulation was incorporated into a limit equilibrium–based log spiral slope stability method. Stability charts are presented to show the stability number, MCO, and mode of failure for homogeneous slopes corresponding to the most stable configuration under static and pseudostatic conditions. It is shown that concave profiles can significantly improve the stability of slopes. Under seismic conditions, the impact of concavity is most pronounced. Good agreement was demonstrated upon comparison of the results from the proposed method against those attended from a rigorous upper bound limit analysis. The proposed methodology, along with recent advances in construction technology, can be employed to use concave profiles in trenches, open mine excavations, earth retaining systems, and naturally cemented and stabilized soil slopes. The results presented provide a useful tool for preliminary evaluation for adopting such concave profiles in practice.

Optimal Pitwall Shapes to Increase Financial Return and Decrease Carbon Footprint of Open Pit Mines

“…They show that logspiral profiles exhibit higher FoS than their planar counterparts for any value of c, and φ considered with the highest gain for inclinations midway and the vertical line, i.e., for OSA ∼ 4 + 2 . Since then, other researchers [9][10][11] have independently investigated the stability of concave profiles excavated in a uniform c-φ geomaterial, employing different methods, namely the slip line method [9], limit equilibrium methods [10], and the finite element method for the assessment of slope stability. They all reached the same conclusion concerning the superior stability of non-linear concave profiles.…”

“…They all reached the same conclusion concerning the superior stability of non-linear concave profiles. However, a key limitation of these studies is the assumption of a specific shape, either a circle [10] or a logspiral [8] or a curve stemming from the slip-line field theory and the associated characteristic equations [9], so that the shape claimed to be optimal is found as the shape associated to the highest stability number among curves belonging to a very restricted family. It is obvious that these profiles are instead sub-optimal and the shape of the truly optimal profile cannot be inferred from the aforementioned studies.…”

“…In fact, in the case of a profile to be excavated in a uniform c-φ geomaterial, the optimal shape calculated by OptimalSlope [12] turns out to be partly concave and partly convex (see Fig. 2c) so significantly different from the purely concave shapes considered in [8][9][10][11]. Another perhaps even more important limitation resides in the assumption of uniform slope present in all the aforementioned methods that prevent the application of these findings to real open pit mines which are typically featured by complex lithologies involving multiple rock formations of different mechanical strengths and various geological discontinuities.…”

“…Also, the formulation has been extended Fig. 2 Slopes of different shapes: a a concave, planar, and convex slope profile with the same overall slope angle; b profiles excavated into a uniform c, ϕ slope: logspiral optimal profile (gray line) redrawn after [8] and circular optimal profile (black line) redrawn after [10]. Since a circle is a particular case of a logspiral, i.e., a logspiral with a constant radius (rather than variable), an optimal logspiral profile is always more stable than an optimal circular one.…”

Sustainable Slopes: Satisfying Rainfall-Erosion Equilibrium and Mechanical Stability

“…oncave profiles have been presented as a way to optimize both the mechanical stability of slopes (Gray, 2013;Jeldes, et al, 2015aJeldes, et al, , 2015bSokolovskiĭ, 1960;Utili and Nova, 2007;Vahedifard et al, 2016aVahedifard et al, , 2016bZhang et al, 2017) and the water erosion resistance of slopes (Jeldes et al, 2015a;Rieke-Zapp and Nearing, 2005). Jeldes et al (2015a) suggested an approach to combine the mechanical and erosional benefits of concave slopes that includes (1) a procedure to obtain concave contours with the desired degree of mechanical stability, and (2) quantification of the effectiveness of those slopes in reducing erosion and sediment delivery.…”