Here are few tips on travertine floor cleaning :
Travertine is naturally a porous stone and is classified in grades of 1-9 depending on how porous. The lower grade travertine flooring (the cheaper ones) are full of surface pores. These pores absorb dirt very easily. The best way to avoid having patchy and dirty looking floors is to seal your floors. Depending on traffic, it should be done every 2 years.
The higher grade travertine flooring (the expensive one) will require diamond pad buffing few times per month. If the buffing times are not respected your floor will look dull and tired.
Using bleach or hard chemicals will stain your floors and it will make the floor look dull.
If spillages are not cleaned in good time it will stain the sealant (if there is a sealant).
You should only use qualified & fully insured flooring contractors.
Do not steam clean travertine tiles if there is a sealant on.
Avoid dropping heavy items on your floors – it will crack and you will never be able to find a perfect match tile.
Wash your floor a few times per week using a low PH cleaning agent 2 to 8 PH (lemon gel is the best).
Do not seal your floors yourself. It might look easy but using the wrong sealant can permanently damage the look of your floors and some cheap sealants cannot be removed with normal floor strippers.