My 2 dogs are terrible for peeing and pooing on the concrete. We live in tropical Nth QLD, so we have heaps of wet rainy days. They drive me nuts. I have spent the whole morning supervising their toileting. If they don't go and the wet grass, I have been crating them. I can't stand the smell of dog waste on the concrete during wet, it just doesn't go away. :p
I would suggest getting a crate and taking your dog out for regular toilets when it's wet. They are most unlikely to soil/wet the crate. I know, this is great for people who have time to dedicate a whole day to watching dogs pee and poo!! See how you go. - Andy.