  In this letter, we report on an experimental study which analyzes the
compressive behavior of 2D bidisperse granular assemblies made of soft
(hyperelastic) and hard grains in varying proportions ($\kappa$). By means of a
recently developed uniaxial compression set-up \cite{vu2019_pre} and using
advanced Digital Image Correlation (DIC) method, we follow, beyond the jamming
point, the evolution of the main mechanical observables, from the global scale
down to the strain field inside each deformable grain. First, we experimentally
validate and extend to the uni-axial case a recently proposed micro-mechanical
compaction model linking the evolution of the applied pressure $P$ to the
packing fraction $\phi$ \cite{cantor2020_prl}. Second, we reveal two different
linear regimes depending on whether the system is above or below a cross-over
strain unraveling a transition from a discrete to a continuous-like system.
Third, the evolution of these linear laws are found to vary linearly with
$\kappa$, up to a saturation point around $\kappa=80$\% of hard particles.
These results provide a comprehensive experimental and theoretical framework
that can now be extended to a more general class of polydisperse soft granular
systems.
