Captain discovered propeller damage after operating into AQT and BTI which had soft runways due to the Alaska spring breakup.

Narrative

I was dispatched on a run to AQT. We landed at AQT without event and unloaded our freight. On back taxi for take-off during turn around the aircraft bogged down in the soft dirt but kept moving so I continued the take-off. We flew back reloaded the aircraft and flew to BTI. Upon arrival in BTI the runway was muddy and slushy. We again unloaded; reloaded and returned to base. During the post flight inspection my First Officer noticed that the aft side of the left prop had erosion on it from gravel. I wrote the prop damage up and turned the log over to maintenance. Not being a mechanic myself I didn't know that the prop would have to be replaced. I told the Dispatcher on duty that the AQT runway was soft and that I wouldn't recommend sending another aircraft until it was fixed. I felt that reporting the slush and mud in BTI wasn't needed because it wasn't soft enough to be an operational consideration. I then left for the night.The damage to the prop; whether it occurred in BTI or AQT; occurred due to the soft runway conditions encountered in Alaska in the spring time during break up. When we noticed the damage I didn't fill out any reports because I wasn't aware that the damage was so extensive. This event could have been prevented by having a more open reporting system in place for runway conditions; especially in the spring during break up. This wouldn't prevent all incidents but it could help multiple incidents. We have a hazard/inefficiency/irregularity form that covers many different things; but often when these reports are filed there isn't much follow up. There should be a procedure in place for reporting runway conditions that is easier for the pilots to complete at the end of a long day or in the middle of a busy day. Maybe the procedure should be to call a designated person who has the authority to shut a runway down to company operations; or restrict the conditions when we can operate on that runway.