Mom and Dad had the same problem with their driveway about 15 years ago, and they tried everything--Ortho products, Tide, Avon Skin So Soft, boric acid, you name it. The problem is that whatever you use only gets around the edges of the colony, never into the center of it, and so it never really works.
What finally DID work was boiling water. Mom just got homocidal one day after she'd left part of a load of groceries in the back of the station wagon for the 15 minutes it took to put the first batch away, and came back to find the ants had already gotten into the car and all over her half flat of peaches.
She went in and started boiling water in her great big canning bath-kettles--they hold 5+ gallons of water apiece. When she had both of them at a round boil, she went out and opened the biggest of the nest holes to about a 6 inch diameter with a shovel. Then she made my brother and I help her carry the canning kettles out one at a time and slowly, slowly pour all the boric acid water in the hole. And it definitely took all three of us adults--my brother and I to hold the weight of the kettle, and my mom tilting it to control the flow of the water, to make sure it didn't overflow the hole she'd opened up.
And then she did it twice more that day, just for good measure. She used chalk to mark all the spots around the driveway where ants were fleeing the boiling flood en masse, and she spent a week pouring canning kettles full of boiling water into every last hole.
They've never had any serious ant problems since.
My theory of why it worked is that we forced enough water into the tunnels in a large enough amount that we were able to force it all the way into the heart of the colony by they sheer weight of the water, and the heat did the killing of the ants. Also, because there was so MUCH heat, the slab of the driveway actually worked to hold it in the colony, rather than letting it dissapate in the air--the concrete was warm to the touch well into the evening. I've tried boiling out colonies in gardens and around foundations, and it never worked as completely as it did with that colony under the driveway. I'll bet you'd get a similar effect with your patio.
If you decide to try this, make sure that you have LARGE containers of boiling water to work with--use those huge thermos-server things to keep it hot as you boil it, if you don't have canning kettles to use--until you have at least 8-10 gallons at a time to pour into the colony. And pour only as fast as the hole you're using will take the water. It took us a half hour to pour those kettles into that hole.
