A few months ago I put in a 9ft x 9ft x 6in slab for a hot tub. It turned out great but there isn't a lot of room to walk around it. I want to build a concrete path around the existing slab. The new path will be 42 inches wide and wrap all four sides.
Should I keep the new concrete isolated from the existing slab? The path will be 4 inches thick and I'm planning to put down 4 inches of gravel underneath it.
Concrete is a lot of work & expense. That is necessary to support a hot tub. It generally is not necessary for a walkway. I'd look into using pavers instead. They are available in brick, concrete and stone. You still need a gravel base, plus sand, but the overall process is much more forgiving than concrete - you don't have to get it all done in one pour, and you can much more easily DIY than with concrete.
Yes, you should keep the new sidewalk isolated. I would not connect the two as they're likely to settle differently due to time and varying substrate. If you were to engage the original slab with rebar connections, and the new walkway settles differently, you'll have cracking and tilting. Better to let it settle in a more level way.
Whether you need expansion joints (compressible strips) is a matter of the overall design. If you're wrapping more than two sides, I'd put a thin (1/4") buffer of sill seal foam or similar between to prevent damage due to expansion.
Note that 4" of gravel may be inadequate if there's 12" of organic soil or soupy clay there now. More important than thickness is what the gravel rests on. That's why thickness matters.
