I'm in the same boat with you, jasu. I have a beautiful raised bed 18in. deep that I grew veggies in for a year or two before the roots of the oak trees invaded it. I've been fighting them off (digging them out, that is) ever since. That oak is at least 30ft. away but it is huge so I should have expected it I guess.
The fact is, you water and fertilize your veggie bed generously, and the tree roots will come no matter what you do when they get a taste of those "goodies". Even if you dug a deep trench all around your raised bed and poured concrete in it as a barrier those roots would find their way under it, then up into the bed. All you can do is either cut the tree, or move the bed much further away from it.
I have a big sifter - 2 x 4 frame with hardware cloth stapled in it - and a sharpened shovel. Every fall before I start planting (winter is my growing season here) I sift half the bed. The next fall, I sift the other half. I take away a good big wheelbarrow load of oak tree feeder roots each time.
OR try using Earth Boxes. I have several of them, standing up on cinder blocks so no roots can invade. They have been very productive and my kids give me a new one every Christmas for the last few years, after they saw me laboriously sifting soil in my raised bed. It's a great system, the boxes are made of recycled plastic and with the fitted plastic covers on over the soil they are extremely water efficient and don't grow any weeds, too.
