A city owned tree has cracked a 4' x 3' section of my sidewalk. They will not remove tree, just grind the roots down. I've been advised by tree experts that roots will grow again in 3 to 4 years and break sidewalk again. Quotes for new sidewalk are from $2,500 to $3,500. The broken pieces are large and should fit back together like a puzzle. Can I remove the pieces, grind the tree roots down, add as many layers of gravel and sand to stabilize then put the pieces back and cover with concrete resurfacing product? I can't stand the thought of spending thousands of dollars every few years to replace this dangerous sidewalk. Thanks for any advice!!