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.
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The best way is to break out the concrete under the ramp and pour the whole thing as a unit. That way you don't have a feather edge.If you have a hammer drill I would put some pins of 1/2" rebar into the sidewalk part you are pouring up to, to hold that together. Drill them in at an angle and grout them in with some powder from the sakrete, mixed to peanut butter consistancy.
You need more local advice about the expansion joint. It doesn't freeze here so I don't know much about that.
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