  We present 3D DEM simulations of jammed bidisperse granular packings to
investigate their jamming density, $\phi_J$, and bulk modulus, $K$, as a
function of the size ratio, $\delta$, and concentration of small particles,
$X_{\mathrm S}$. We determine the partial and total bulk modulus for each
packing and obtain a transition behavior at specific densities that depends on
the compression level, thus marking the first and second transition of the
system. The highest bulk modulus is found at $X^{*}_{\mathrm S}(\delta = 0.15)
\approx 0.21$ consistent with the maximum jamming density, where both particle
species mix more efficiently. At extreme size ratios, $\delta = 0.15$,
$X^{*}_{\mathrm S}$ divides two structural scenarios for $K$ that depend on
whether small particles are jammed or not jointly with large ones. We find that
along the second transition line, $K$ rises $20\%$ compared to those found at
the first transition. However, their values are still low compared to that
shown at $X^{*}_{\mathrm S}$. This clearly indicates that the jamming of small
particles indeed impacts the internal resistance of the system for low $\delta$
and low $X_{\mathrm S}$. This new result will allow tuning packing bulk modulus
and other properties, such as wave speed, when a specific size and
concentration of small particles contribute to the jammed structure.
