Additional jamming transition in 2D bidisperse granular packings

We present a jamming diagram for 2D bidisperse granular systems, capturing two distinct jamming transitions. The first occurs as large particles form a jammed structure, while the second, emerging at a critical small-particle concentration, $X_{\mathrm{S}}^{\ast }\approx 0.21$, and size ratio, ${\delta }^{\ast }\approx 0.25$, involves small particles jamming into the voids of the existing large-particle structure upon further compression. Below this threshold, small particles fill voids within the large-particle network, increasing packing density. Beyond this point, excess small particles disrupt efficient packing, resulting in looser structures. \jp{These results, consistent with previous 3D studies, demonstrate that the second transition occurs at a well-defined point in the $(X_{\mathrm{S}},\delta )$ plane, independent of dimensionality, likely driven by the geometric saturation of available space around particles, void closure, and structural arrangement.