gap in concrete between steps and driveway

[Grendel]

I have a gap between the concrete where the concrete steps and concrete driveway come together. The former homeowner looks like they used clear caulk at some point and this is in horrible shape. It also looks like in one area they filled it a little with pea gravel so that the caulk could hold onto something. This looks like in one big area of the gap. Anyway is this the correct idea? Should I go get some pea gravel or something fill the big gaps and put a nice bead of caulk (GE Silicone II concrete and masonry caulk) over the whole area? Or is there something more stable for the bigger areas so the caulk can really hold onto something. Or is caulk not the right idea for this? Once again there are only two or three 1inch area that are big. The rest of the line where the steps and driveway meet is a a little more than a hairline crack that caulk would be perfect on. Thanks