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

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.