Set 4-foot level on walkway to determine how badly the root has lifted the walkway.
Use pointed shovel to dig down on either side of the walkway to expose the tree root.
Use a pruning saw to cut through root on each side of walkway.
Cut through the asphalt walkway, on either side of the severed tree root, using an electric chipping hammer fitted with a wide chisel blade.
Pry out the asphalt between the two cuts, then dig up the severed tree root.
Tamp down the bottom of the trench with a 10-pound sledgehammer.
Spread into the trench about 2 inches of pack, which is a mixture of stone and stone dust.
Compact the pack with a hand tamper, then add another 2 inches of pack and compact it again. Repeat until the compacted pack is about 2 inches below the asphalt surface.
Use the level as a straightedge to draw a perfectly straight line across the walkway on either side of the repair area.
Next, use a wet circular saw fitted with a diamond-impregnated blade to cut straight across the asphalt.
Pull away the trim-off piece of asphalt. Repeat to cut the opposite side of the walkway.
Install a 2x6 form along each edge of the walkway.
Secure each form on edge with two ½-inch-diameter x 24-inch-long rebars. Use a 3-pound sledgehammer to pound the rebars into the soil directly behind each form. Backfill with soil against both forms.
Use hand tamper to thoroughly compact the area between the forms.
Dump 1 inch of asphalt cold patch over area and spread evenly with a rake.
Compact the asphalt with a hand tamper, then add another inch and compact again. fill Repeat to fill the area with asphalt.
Add one more layer of asphalt cold patch, spreading it about ½ inch higher than the adjacent walkway surfaces.
Compact the cold patch until it’s perfectly flush and even with the walkway on either side of the repair.
Wait two weeks, then remove the forms, backfill with soil and apply an asphalt sealer to the entire walkway, including the patched area.