Theoretical and Numerical Analyses of Earth Pressure Coefficient along the Centerline of Vertical Openings with Granular Fills

Granular filling materials are placed into confining structures for various purposes, including but not limited to silos, trenches, mine stopes, and retaining walls for backfill. Stresses in these backfilled openings are commonly estimated using theoretical arching models, with equations that often involve the earth pressure coefficient K (=σ’h/σ’v). Such stress estimation can be dramatically impacted by the magnitude of K, but its value remains debatable. Along the centerline of vertical openings with granular cohesionless fills, the value of K is sometimes obtained by Jaky’s earth pressure coefficient at rest K0, based on the assumption of fixed confining walls, whereas Rankine’s active earth pressure coefficient Ka is regarded more suitable for K as claimed by some others. Recent numerical analyses from the authors have shown that the state of stress close to the center of backfilled openings cannot be solely related to wall movement. It was also shown that the K value can vary between Ka and K0 in backfilled openings with fixed (immobile) walls, depending on the locations and respective values of fill internal friction angle ϕ’ and Poisson’s ratio ν. However, none of the existing works have addressed the mechanisms and answered this fundamental but critical question: which value of coefficient K (K0, Ka, or other) should be used with analytical solutions to assess the stresses in backfilled openings (and why)? After assessing the state of the fill placed in a confined opening, theoretical relationships and specific mechanisms are proposed, for the first time, to evaluate critical values of ν and ϕ’ for defining the at-rest and active states in fills. The approach indicates that when ν or ϕ’ are smaller than or equal to critical values, the value of K near the center line of a backfill opening should be close to Ka; otherwise, K tends to approach K0 defined from ν. The theoretical analysis is complemented and validated (in part) by numerical simulations. The results also demonstrate that Poisson’s ratio can play a major role on the stress distribution within cohesionless fills, and should thus be accurately evaluated.