Active earth pressures from a log-spiral slip surface with arching effects

Abstract

The distribution of active earth pressures behind retaining structures is typically inferred from simplified Rankine or Coulomb analyses, both of which are triangular in shape and assume a planar slip surface. However, various experiments and numerical models have demonstrated an earth pressure distribution that is non-linear in shape, typically attributed to a phenomenon called 'soil arching'. Existing analytical solutions have typically evaluated arching with planar slip surfaces; however, slip surfaces that form behind retaining structures are often curvilinear, tending to follow a log-spiral shape, particularly when considering wall batter or interface friction between the backfill and wall. In this letter, the arching effect is considered using a log-spiral failure mechanism that has been developed by deriving a first-order differential equation and subsequently solved using a numerical approach. A series of charts are presented accounting for varying soil strengths, interface friction and wall batters.

Discussion: Active earth pressures from a log-spiral slip surface with arching effect

“…Using planar failure mechanism, Paik & Salgado (2003) have developed a closed-form expression for determining the active earth pressure distribution and the resultant earth pressure. With reference to Figs 3(a)-3(d) in Xie & Leshchinsky (2016), the solutions of Paik & Salgado (2003) were found to be in very close agreement with the experimental results and better than that of Coulomb. The solutions of Xie & Leshchinsky (2016) are expected to be better than that of Paik & Salgado (2003) thanks to considering a non-linear failure surface which most likely represents the true shape of the failure surface for finding the maximum magnitude of the active earth pressure; however, the active earth pressure computed by Xie & Leshchinsky (2016) has been found even lower than Coulomb's solution.…”

“…With reference to Figs 3(a)-3(d) in Xie & Leshchinsky (2016), the solutions of Paik & Salgado (2003) were found to be in very close agreement with the experimental results and better than that of Coulomb. The solutions of Xie & Leshchinsky (2016) are expected to be better than that of Paik & Salgado (2003) thanks to considering a non-linear failure surface which most likely represents the true shape of the failure surface for finding the maximum magnitude of the active earth pressure; however, the active earth pressure computed by Xie & Leshchinsky (2016) has been found even lower than Coulomb's solution. In their analysis, the rotation of the principal axes that occur due to arching of backfill soil at any depth z below the horizontal ground was considered by keeping the direction of the major principal stress normal to the ground surface.…”

“…The results presented in Xie & Leshchinsky (2016) are attained using a limit equilibrium (LE) framework with a maximisation procedure to derive potential active, arching pressures behind rigid retaining structures stemming from a log-spiral slip surface. LE inherently involves the analysis of multiple, potentially unstable bodies, restrained externally by a wall, where stresses (or forces) for a given slip surface are typically evaluated using the Mohr-Coulomb failure criteria along its extents without direct evaluation of principal stresses (e.g.…”

“…the Coulomb approach). The work presented in Xie & Leshchinsky (2016) uses an extremisation procedure that evaluates the active resultant stemming from a series of horizontal slices that discretise a potential log-spiral failure mechanism. Ultimately, a maximum active resultant for a series of log-spirals is determined in an iterative process (Fig.…”

“…This consideration does not warrant the satisfaction of Mohr-Coulomb criterion along the failure surface at all depths except when the inclination of failure surface with the minor principal axis makes an angle of 45°+ ϕ/2 (Peng & Chen, 2013). The assumed direction of the principal axes by Xie & Leshchinsky (2016, Fig. 2(a)) is only valid for the planar failure surface making an angle 45°+ ϕ/2 with respect to the horizontal.…”