Why does water rush through pipes when no water is being used?
This sounds like the backwash on your water softener. 

It should be set to cycle at 1 am or so when you wouldn't hear it, but the clock could have been reset from a power outage. Normally, it will trickle for 20-30 minutes as it brines the resin bed and then it will backwash the resin bed with clean water for 10 mins or so. This water must all be dumped to a drain somewhere, possibly in the laundry standpipe. That's where mine dumps to. 

Check your softener settings,and look for a correlation.

Good luck!