Arching in Granular Soils

Abstract

Arching is characterized by a stress distribution where the load is transferred from softer to stiffer regions of a structure forming a stable configuration. Since it is a stable arrangement, arching is not a typical limit state problem. However, it can be formulated in a manner that allows using the static theorem of limit analysis to assess the likelihood of arching. Radial stress fields within piles of sand are constructed to search for stress distributions that promote arching. Governing equations are derived for radial stress distributions with regions varying from the yielding stress state to the elastic stress state. The stress fields with an elastic core promote arching, whereas the field where all material is in the active limit state does not support arching. However, if a passive limit state is induced in a sand heap, arching over the central part of the pile base becomes a distinct feature of the fully plastic stress field. Considerations are limited here to wedge-shaped sand heaps, though many of the conclusions are applicable to conical (axi-symmetrical) sand piles. INTRODUCTION Investigation of stress fields in sand piles indicates some characteristics of arching that do not confirm the stereotypical belief that arching is associated with a transfer of load from yielding parts of the structure to the stiffer parts. It appears that equally plausible arching stress fields are ones where the load is transferred through the sand in the stress state at or close to the limit, over the sand that has not reached the yield state or is significantly below the limit. 1 Professor, Department of Civil and Env. Engrg., University of Michigan, 2340 G.G. Brown Bldg., Ann Arbor, MI 48109-2125, U.S.A., e-mail: rlmich@umich.edu 2 Graduate Assistant, Texas AM formerly University of Michigan, U.S.A.