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Most likely, the tile was not imbedded into the thin-set soon enough allowing the thin-set to glaze or skin over on the surface. Other possibilities; thin-set was spread to far ahead of tile laying, thin-set was mixed too dry, tile was not properly imbedded into the thin-set.
Gypsum based underlayments are frequently used under vinyl and carpet to smooth out the substrate. When you removed the vinyl was the concrete white? If so, gypsum based underlayments were probably used to prepare for the vinyl and the water in the tile thin-set has softened the gypsum over time and resulted in a bond failure. The gypsum underlayment will have to be completely removed to make the correct repair on your tile floor. Use TexRite Latex Underlayment or TexRite FlowRite, both cement based products, to prepare the substrate before installing ceramic tile.
First, traditional tile setting products do not bond to treated wood; second, outdoor kitchens that will be tiled should be constructed with steel studs or masonry, wood moves entirely too much outdoors to direct bond ceramic tile. Repair? Try the local Big Box for an adhesive in a tube that will bond to the treated wood.
Use an elastomeric caulking material in place of cement grout between the tile riser and the treads. The repetitive stress of expansion over time will pop the tiles off if there is no allowance to absorb this movement. Use TexRite UniFlex to bond the tile in combination with the correct caulking material.
Is the waterproof membrane compatible with cement thin-sets for a direct bond? There are many different waterproof membranes that do an excellent job of waterproofing if installed correctly. Not all waterproof membranes will accept cement based bonding materials, check with the manufacturer for compatibility. Use TexRite HydroRite or NAC Strataflex Waterproof Membranes for complete compatibility with TexRite setting materials
Lack of Movement Joints. Everything expands and contracts from temperature changes. Ceramic tile and concrete expand and contract at different rates when exposed to the same temperature change. Without the proper Movement Joints (soft joints) incorporated into the tile installation temperature changes can put pressure on the tile to the extent that the thin-set bond will fail due to shear and the tile will lift up typically called ‘tenting’. When this expansion and contraction occurs, there must be an outlet to relieve or absorb this movement. If not, the stress will find the weakest point and relieve itself in this area. Use proper Movement Joints according to EJ171 in the TCNA Handbook. Usage ofTexRite HydroRite or NAC ECB membrane as a full floor coverage anti-fracture membrane and bonding the tile with TexRite CeramaFlex to help isolate the movement from the finished tile flooring can prevent loss of bond and "tenting".
Most likely , bond- inhibiting materials were not properly removed from the substrate before installing tile. Paint, drywall mud, wood stain, grease, oil, curing compounds, dirt, old adhesives and cut back residue are considered bond-inhibiting materials that can cause floor failures.