The Arch in Soil Arching

TLDR

Soil arching (bin effect) has traditionally been modeled using Rankine theory, but Krynine proved this approach incorrect in the 1940s. This study replaces the Rankine model with a catenary arch for the minor principal stress path, showing that soil arching develops in two stages—initial stress rotation near a rough wall that raises horizontal pressures above classical predictions, followed by a downward‑dipping arch. The second stage reduces lower wall pressures, yielding a curvilinear distribution centered at 0.42 of the wall height that aligns closely with published data.

Abstract

Soil arching action or “bin effect” is usually quantified by use of a horizontal differential element whose support derives in part from Rankine theory. In the 1940's, Krynine mathematically proved this incorrect. The present analysis substitutes a catenary arch describing the path of the minor principal stress, which thus is complementary to a structural arch, and dips downward instead of upward if supportive. Soil arching action develops in two stages: The first involves rotation of the principal stresses adjacent to a rough wall and causes horizontal wall pressures to significantly exceed those from classical theory simulating a Ko pressure distribution even in loose backfill soil. The second stage reduces pressures on the lower wall to give a curvilinear distribution typically centered at a height 0.42 times the height of the wall and in close agreement with published data.