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.
تحميل البحث