Novel insights into the dilatancy and non-coaxiality of sand under generalised constant-η loading

Abstract

The present study investigates the behaviour of sand under generalised compression loading. A stress path architecture is devised featuring the repetition of loading and unloading at constant η = q/p′ for a sequence of increasing α_σ′1 and b = sin²α_σ′1; where α_σ′1 is the principal direction of stress, and b = \(\frac{{\left( {\sigma{\prime} 2 - \sigma{\prime} 3} \right)}}{{\left( {\sigma{\prime} 1 - \sigma{\prime} 3} \right)}}\) is the intermediate principal stress ratio. Irrecoverable volumetric and shear strains develop under compression with the former being considerably lower than the latter, exhibiting weaker variations with η and α_σ′1. It is shown that the compression of pre-loaded sand at the same η but different α_σ′1 induces non-coaxiality uncorrelated to excessive plastic contraction. The volumetric and shear strains increase when one of the planes of maximum stress obliquity aligns with the horizontal bedding plane. Furthermore, the compressibility, dε_vol/dp′, oscillates with the increase in α_σ′1 at constant η. The dilatancy, D = dε_vol/dε_q, varies from very large values to zero depending on the stress path and stress history. It is also shown that the variable dε_q/dp′ normalises effectively both the non-coaxiality angle, ξ = α_dε1-α_σ′1, and the dilatancy, D. Specifically, a unique curve describes the relationship between ξ and dε_q/dp′ for a given α_σ′1 irrespective of η, p′, and ψ (state parameter). On the other hand, a unique curve describes the relationship between D and dε_q/dp′ irrespective of the value of the variables η, α_σ′1, b, p′, and ψ, and of the pre-shearing and pre-loading. This inverse proportion relationship indicates the decoupling of the incremental volumetric strains from the incremental shear strains in the compression mode.