If the slate looking tile is "hard slate" or "porcelain" it is not very porous. If it is "soft slate" is is very porous. Regardless of what the tile is made of, the grout will soak up urine/poo and it is impossible to get it out. Grout that is mixed/poured right will be less porous. However, the soupier the grout the easier to install, then the owner is left with lots of pinholes where the air bubbled out. Drop a few drops of water on the "tile" and see how fast it absorbs. If it sits there in a puddle, the tile is not porous. I would think covering the tile/grout with the enzyme for getting rid of urine would make a difference for the better. No amount of scrubbing will get the odor out of the grout.

Treating pet odors is what I do for a living and I see situations like this on a daily basis. I am going to asume your basement subflooring is concrete which is porous and will absorb urine and its odors. Bleach is the strongest household disinfectant you can use to kill germs and odors and it will do good as a initial clean-up on the surface which is the key word. After the bleach has dried the concrete still has wet urine and odor below the surface that is still off-gassing. The next step is get the concrete as dry as possible by using air movers and dehumidifiers together this equipment will also dry the walls if the cats have been spraying on them. Finally we use a industrial sealer that has a moisture barrier and a odor barrier once applied we guarantee you will never smell any pet urine odor from any area we treat. Kills is designed for smoke odors, as cat and dog urine acids will eventually weaken the product and the urine odor will be back. Enzymes are temporary fixes or are for minor problems per the manufacturers instruction the area has to stay wet for up to 3 weeks for best results and @$20-40 gal do the math bleach is better and stronger. Besides you have already cleaned the area now you have to get it sealed. Oh! and toss the carpet It would cost you more for a pet odor treatment then replacement. Here is a link that might be useful: thepetodorspecialist.com

Even better than Nature's Miracle is Kennel Odor Eliminator by Thornell http://www.amazon.com/Thornell-Kennel-Odor-Eliminator-Gallon/dp/B0002XI7DW My old house POs had cats, lots of them. And no litter box. It's more expensive, but it did in 4 treatments what Nature's Miracle (and others) could not. Now, the one problem you may have (and I did) is that the urine has infiltrated the HW and is into the subfloor. Try TOE first, but if it still smells....then your only option left is to remove the HWF and treat the subfloor. Mine was so bad I removed the entire subfloor because it had sunk into the joists below, but I think I'm a worst case scenario. Good luck. PS....the smell is due to the ammonia salts left behind, which are activated by moisture, hence the stronger smell when the humidity rises. My floor was so bad it changed color (got darker) when it was humid...hopefully yours is not!

That's what I'd recommend also. You may also want to use the product below on your dog.........and be sure to have her vet checked. Her frequent urination could be due to a urinary infection. If the problem is age related they now have success with meds for incontinence. Here is a link that might be useful: diapers