How to Avoid Marble from Shoe Prints
How do I avoid dirty shoe prints on marble, especially safety boots?
At my work site, it's very difficult to make sure everlasting cleaning of the marble, because the floor is wet and always shows shoe prints from the safety boots, that are full of a black colored dust.
I would cover the marble floor completely with either cardboard or something tougher and more resistant.
I've been to job sites before where the floors have been completely covered with material that nothing will penetrate.
Also, you should be careful of spilling water on the floor. It really sounds like your floor needs to be covered, or you will have problems after your work is done.
Look into what types of materials can protect the marble floor. I don't know the names of them right now, but you really need to find out, or you may be responsible for having to restore the marble once you're done with your work.
Restoring a marble floor can be costly, so I recommend covering as soon as possible.
I hope this helps.