Concrete transition
 

My concrete sidewalk is almost 3 inches lower than the driveway, which
crosses it. To avoid a tripping hazard, I put a cement transition in,
making a ramp about a foot in length, but over the years this has broken
up and now I must redo it. There is no sinking involved, they just
built them this way in our neighborhood. I need a material that can
transition from three inches thick to no inches where it blends into the
sidewalk, and will last through freezing winters and pedestrian traffic
(and bicycles; young kids love to launch their bikes off my ramp).

What is the best material for this project? Also, there is a tarred
expansion slot between the driveway and sidewalk, and I want to put
something between my ramp and the driveway so no water can get in there
to freeze and dislocate my ramp.