What process occurs when magma rises inside a volcano but the volcano doesn't erupt?

assimilation

Explanation:

Beneath the volcanoes lies the magma chambers and the volcanoes have a channel like that of the cones and the shields and the calderas. The underside of the magma inside the volcanoes created a movement that triggers the eruptions and they can take place below, above and inside the magma chamber. The mixing of the magmas with the rocks spreads to the surrounding rocks and later ion gets assimilated and sometimes the volcano has pathways that surround the magma chambers. The hydrothermal alteration of the rocks also accounts for the eruptions