Solar Energetic particles at pileup collisions of the multiple-shock

The ground-level enhancement (GLE) events are often associated with the large gradual solar events such as fast coronal mass ejections (CMEs), but not all fast CMEs lead to GLE events. We suggest that GLE would be associated with processes of the multiple CMEs interactions. Here we proposed a ``multiple-shock'' scenario driven by the ``continuous-CME'' sympathetically, in which the posterior shocks catch up with the preceding shock and have pileup collisions. We simulate the ``multiple-shock'' by applying a dynamic Monte Carlo method in present work. In the ``multiple-shock'' scenario, the seed energetic particles produced by the preceding shock can be injected into the posterior shocks for cascaded acceleration efficiently. We obtain the detailed SEP energy spectrum with different behaviors at the related episodes of the ``multiple-shock'' evolution. As results, we find the pileup collisions of the ``multiple-shock'' dominate multiple``concave'' energy spectral slope in the generated SEP event.