  The mean stress tensor is essential to investigate the dynamics of granular
material. In this paper, we use Hamilton's principle of least action to derive
the averaged stress tensor of discrete granular assemblies subjected to
hydraulic force fields, as well as rigorous conditions for a proper definition
of the Representative Volume Element (RVE). The main goal behind our efforts is
to upscale particle physics into a sound stress tensor for systems involving
the complex interaction between grains and water. We identify the contributions
from the unbalanced forces, hydraulic forces, gravity, external forces, and
particle fluctuation to the mean stress tensor. In doing so, it is convenient
to separate the influence of different force fields when the granular system is
subjected to complex environments, e.g., subaqueous conditions. The obtained
formula is then validated by triaxial test simulations of dry and saturated
granular systems using the Discrete Element Method (DEM) and the
Lattice-Boltzmann Method (LBM). The results show that the deduced formula can
accurately calculate the stress tensor of discrete assemblies with various
body-force fields. We used validated DEM-LBM simulations of submerged granular
column collapses to explore the physics happening at the grain scale with this
mathematical formalism and showcase its potential. We provide a new perspective
based on the granular assembly scale to pursue the fluid-solid interaction. Due
to the importance of stress analysis in the constitutive modelling of granular
materials, this work could help to better obtain the stress-strain relationship
of saturated or submerged granular systems.
