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The mean stress tensor is essential to investigate the dynamics of granularmaterial. In this paper, we use Hamilton's principle of least action to derivethe averaged stress tensor of discrete granular assemblies subjected tohydraulic force fields, as well as rigorous conditions for a proper definitionof the Representative Volume Element (RVE). The main goal behind our efforts isto upscale particle physics into a sound stress tensor for systems involvingthe complex interaction between grains and water. We identify the contributionsfrom the unbalanced forces, hydraulic forces, gravity, external forces, andparticle fluctuation to the mean stress tensor. In doing so, it is convenientto separate the influence of different force fields when the granular system issubjected to complex environments, e.g., subaqueous conditions. The obtainedformula is then validated by triaxial test simulations of dry and saturatedgranular systems using the Discrete Element Method (DEM) and theLattice-Boltzmann Method (LBM). The results show that the deduced formula canaccurately calculate the stress tensor of discrete assemblies with variousbody-force fields. We used validated DEM-LBM simulations of submerged granularcolumn collapses to explore the physics happening at the grain scale with thismathematical formalism and showcase its potential. We provide a new perspectivebased on the granular assembly scale to pursue the fluid-solid interaction. Dueto the importance of stress analysis in the constitutive modelling of granularmaterials, this work could help to better obtain the stress-strain relationshipof saturated or submerged granular systems.

Mean Stress Tensor of Discrete Particle Systems in Submerged Conditions