Translation guide
To pile things into a heap, or to accumulate in a disorderly pile. In Japanese, the verb depends on whether the action is intentional or natural, and whether the focus is on the process or the resulting state.
To deliberately stack or pile objects into a heap.
Literally 'pile up'. Used for stacking things neatly or into a heap. Transitive verb.
He heaped up the fallen leaves in the corner of the garden.
Literally 'make into a mountain pile'. Emphasizes the resulting heap-like shape.
She heaped up papers on the desk.
General verb for 'pile up' or 'stack'. Can be used for heaping, but less specific.
They heaped up stones to make a wall.
To become piled up, often without deliberate action, or to describe the state of being heaped.
To pile things carelessly or into a messy heap.
積む (tsumu) is transitive (someone piles things up), while 積もる (tsumoru) is intransitive (things pile up by themselves). Use 積む when you are doing the heaping, and 積もる when describing the state or natural accumulation.
Avoid directly translating 'heap up' as 'ヒープアップする'. This is not natural Japanese. Use the verbs above depending on context.
Unfinished work has heaped up.
Intransitive verb for things piling up in layers. More formal/literary.
Papers had heaped up on the desk.