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The Danosa web site describes your roof material as Bituminous. They list the types of mastic (glue ) and most interesting is a self stick tape. From the sescription of the tape it is designed for direct exposure to UV. The pinholes you describe sound like the UV protectant wore away and the bituminous substrate became attacked by UV and degraded. These coverings are designed to be under tile, gravel, sand, or some other protection from UV rays from the sun.
The fact that water is oozing when you step on the roof suggest a cellulose pad under the roof membrane, and this pad is acting like a sponge. You need to get that soggy pad removed and dry out the roof deck. Then you can put down new pad and new danosa- glueing it to the old with the mastic. Here is the web site:
Bituminous sheets can be classified according to its finish (sand, polyethylene film, mineral slate or aluminium), as well as by its mastic (oxidised bitumen, modified SBS or modified APP bitumen) and by its reinforcement (fibreglass, polyester felt, etc).
Self-Adhesive Tapes Self-Dan
Self-adhesive tapes 10, 15 or 30 cm wide with metallic self-protection in natural, red or grey colour. Designed for sealing chimneys, pipes, skylights, cracks, etc.
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