I have a house with an extension built in 1969. The extension is a basement space with a tiled terrace on top, which is outdoors. The terrace, which is the roof of the basement, is constructed of lightweight concrete beams with cast concrete, in total about 20 cm thick. The whole structure sags slightly (about 20 mm in the middle) with visible cracks in the ceiling and on the tiles above. When it rains, water collects in the middle that I have to scrape away. I've started chiseling away loose tiles and realize it's time to replace them. Then I see that the tiles are glued to leveling compound (which is more like loose sand now) that in turn lies on a moisture-proof layer of tar and tar paper on top of the concrete.
My plan is to chisel away all the tiles and leveling compound and pour new, but should I remove the tar paper and apply a new one, or choose a modern sealing method such as gluing waterproof membrane on the leveling compound? Can I let the concrete slab continue to sag and assume that it has "settled"? I can prop it up from underneath while the work of laying new tiles is ongoing, or even install a permanent support column. I would prefer to avoid tearing everything down. The terrace is 3.5x8 meters. Grateful for advice and experiences.