Fireplaces, Heating Stoves, Flues and Chimneys - What is best to do with removed morter, etc?

We are currently working on removing a chimney that runs through 3 floors of our home. It is going ok, slow, but ok.

One big problem we have is with the morter, chips and pieces of flute that break up. The big bricks we are throwing in our back yard, but the little pieces are a mistery. My husband used our garbage bucket which I vetoed. Then we tried the new tough garbage bags but those are ripping.

Does anyone have any luck with particular garbage bags? Any good solution until we get a dumpster and haul it all away?

Thanks,
Ginny

(Progress report: The first 7 feet went quick. The next 3 were much slower. Now he has reached a subfloor, the space got tighter and the bricks doubled. )

I would think about using the inexpensive vinyl drop cloths. More expensive than garbage bags but much heavier. They could also be re-used later after cleaning. Good luck.