Are you in FL? With sand? If so, I think you'll be okay. I've seen plenty of palms growing with trunks smack dab next to concrete sidewalks, concrete patios, driveways etc.... You say the concrete is only about 8" deep & 1/2 way around the tree. The roots should go under the concrete & be fine. If you are in FL as I suspect, the sand will allow the roots to breathe.
However, if this happens again, then the best way to handle it is what Philipwonel says.
