big, great, large
little, small
crumpled
ash (AmE,usually figurative), rubbish (BrE), scrap, slag, spoil (esp. BrE), trash (AmE)
the ash heap of history
colliery spoil heaps

compost, manure (esp. BrE)

be piled in
Papers were piled in great heaps on the desk.

collapse in, fall down in, fall in (all figurative)
He collapsed in an exhausted heap on the floor.

in a/the heap
His clothes lay in a crumpled heap on the floor.

on a/the heap, onto a/the heap
Throw the potato peelings on the compost heap.

heap of
a great heap of stones

the bottom of the heap, the top of the heap (figurative)
These workers are at the bottom of the economic heap.

Heap is used with these nouns as the object:
misery, praise, scorn