Are shell and slate go stones fragile?
From the Wikipedia article on Yunzi stones


  Like glass Go stones, yunzi are very durable. However, like glass stones, yunzi are still at risk for chipping if they are dropped or otherwise come into sharp contact with hard surfaces such as metal, tile, or stone.


The problem you describe is more a property of your (very hard) tile floor. I would suggest acquiring a small area rug and placing it under your board or table when playing to protect your stones. 

I have never enjoyed the pleasure of playing with shell and slate stones, but I suspect that the very properties that make them so beautiful also make them susceptible to chipping from such a hard surface. Being safe seems more prudent than being sorry.