Design of Stable Concave Slopes for Reduced Sediment Delivery

Abstract

Constructed slopes are traditionally given a planar form. However, natural slopes are more likely to be concave in cross section. In addition, laboratory and computational studies have demonstrated that concave slopes yield less sediment than planar slopes. With current autoguided construction equipment, it is now possible to construct slopes with concave profiles and a more natural appearance, yet a simple method to describe such concave slopes for a given level of mechanical stability does not exist. This article begins with an examination of concave shapes satisfying a desired degree of stability and compares results with those from the FEM and limit-equilibrium method of analysis. An erosion model is used to demonstrate that the concave slopes proposed here yield 15-40% less sediment than planar slopes with the same factor of safety. Finally, a sensitivity analysis suggests that reasonable construction deviations do not compromise the stability of typical concave slopes.

Optimal profile for concave slopes under static and seismic conditions

“…Consequently, when MCO = 0, Y e = 0. However, in concave slopes the critical failure surface may emerge above the toe (i.e., Y e > 0) and such possibility needs to be considered (Utili and Nova 2007;Jeldes et al 2014 the results for a planar profile (i.e., MCO/H = 0). This Case results in the least stable (highest N value) and no reduction in volume (∆A/H 2 = 0) as shown in Fig.…”

“…Engineered slopes and earth structures are commonly built with a planar profile in cross section. However, it has been shown that concave slopes offer higher stability (e.g., Sokolovskiĭ 1960; Utili and Nova 2007;Jeldes et al 2013) and better erosion resistance (e.g., Rieke-Zapp and Nearing 2005;Schor and Gray 2007;Jeldes et al 2014) when compared with the equivalent planar slopes. Utili and Nova (2007) demonstrated the higher stability of concave slopes and argued that such higher stability may also explain the concave shape of perimeter walls of some typical Japanese castles (Nishida et al 2005;Utili and Nova 2007).…”

“…1 shows an example of a natural concave slope located on US-101, north of the Alsea Bay Bridge in Waldport, Oregon. Recent advances in auto-guided construction equipment along with increased precession in three-dimensional mapping technology allow and facilitate construction of such concave profiles in engineered slopes and earth structures (Jeldes et al 2013;Jeldes et al 2014). For geosynthetic-reinforced soil structures, Vahedifard et al (2016a) showed that D r a f t 4 using concave facing profiles can decrease the required tensile strength of the reinforcement by up to 30% under static and seismic conditions.…”

“…Jeldes et al (2013) used the Sokolovskiĭ solution for a weightless medium and presented an approximate solution which transformed Sokolovskiĭ's differential equations into a hyperbolic expression representing the optimal concave profile of slope. Jeldes et al (2014) used the latter approximate solution along with an erosion model and showed that concave slopes yield 15 -40% less sediment than alternative planar slopes with the same factor of safety. Utili and Nova (2007) used two log spirals: one spiral to represent the concave slope profile and the other for the slip surface, in the context of the upper bound limit analysis (LA) method.…”

Incorporating suction in to stability charts for unsaturated soil slopes

“…Some log-spiral concave surface may be more stable than a planar profile (Utili and Nova, 2007). Concave slopes may also have superior erosion resistance compared to planar slopes (Young and Mutchler, 1969a, Young and Mutchler, 1969b, Meyer and Kramer, 1969, Rieke-Zapp and Nearing, 2005, Schor and Gray, 2007 making them preferable within many embankments and cuttings (Jeldes et al, 2014a, Jeldes et al, 2014b. However, there is limited ability to address their stability without resorting to computational tools.…”