QUESTIONThe home has some areas of unfilled travertine tiles installed, and of course dirt collects in the open pores and gives a dirty look to the tiles. What is the best way to get the dirt out- it doesn't vacuum out.
ANSWERANSWER - I would never recommend installing unfilled travertine or any unfilled stone on a floor or it will collect dirt that could then develop into microbial growth if moisture is present. It would be more practical to fill the voids in the travertine with a cementitious grout. Depending on what color grout you use you can created some very interesting looks with an unfilled travertine.
If a vacuum isn't removing the dirt in the travertine voids it is likely because the dirt has been there for so long and has gotten wet and dried that it is compacted into place. What I would try is to get a detergent into clean water and soak the floor and scrub it with a long bristle scrub brush on an extended handle. Let it set for 10 minutes or so and then scrub again. Now get a wet vacuum to pick up the dirty water. Go through this process again if it didn't remove all of the dirt. Then finally rinse with clean water and vacuum that up. Then after the travertine tile is clean and dry, I would seal it with a penetrating stone sealer so cleaning will be easier in the future. Or fill in the voids with grout so you don't have to go through this another time.