Missing grout + Hollow patio tiles

[alig9]

My patio is laid with travertine tiles. The grout under the tiles around the 3 sides( appx 15 tiles) is missing, the tiles are sounding hollow and some are cracking. Is there anywaterproof grout I could inject into them - I can't afford to have the patio relaid.

 

[rieveleyceramics]

Are these actual travertine which is a form of limestone or an imitative ceramic tile?
If they are travertine then this would be my advice.
Travertine has, due to the way it is formed by lime rich springs, a tendency to have many small holes within it, varying in size. These voids within the tile slabs are often hidden from view but can create weakness with wear and sometimes quite large holes may appear as the surface collapses into them. There are various types and grades of travertine available so hopefully yours will be of better quality without large holes or voids within them.
Nowadays the surface of travertine tiles can be filled with a coloured epoxy resin (Marmox) to seal open surface pores and allow for a polished surface. Previously a lime or portland cement would have been used.

If the tiles are loose and are as you say are along the edge with an open side, they could be easily lifted and having removed the previous failed adhesive layer from beneath along with any attached grout, they can be refixed using a cement based adhesive and regrouted. This is also the case for a ceramic tile.
It should be noted that the adhesive layer and grout are not the same substance, grout is normally of a finer consistency. Also modern adhesives and grout are specifically formulated for different functions and environments and you need to choose the ones best suited.

If you were to use an epoxy filler such as Marmox, in order to create an even finish across the entire patio you would be advised to treat every slab/tile. and not just a section. It may also require having the surface of the tiles ground flat using rotatating diamond grinding discs. This would prove fairly costly and require some expertise.

 

[alig9]

Are these actual travertine which is a form of limestone or an imitative ceramic tile?
If they are travertine then this would be my advice.
Travertine has, due to the way it is formed by lime rich springs, a tendency to have many small holes within it, varying in size. These voids within the tile slabs are often hidden from view but can create weakness with wear and sometimes quite large holes may appear as the surface collapses into them. There are various types and grades of travertine available so hopefully yours will be of better quality without large holes or voids within them.
Nowadays the surface of travertine tiles can be filled with a coloured epoxy resin (Marmox) to seal open surface pores and allow for a polished surface. Previously a lime or portland cement would have been used.

If the tiles are loose and are as you say are along the edge with an open side, they could be easily lifted and having removed the previous failed adhesive layer from beneath along with any attached grout, they can be refixed using a cement based adhesive and regrouted. This is also the case for a ceramic tile.
It should be noted that the adhesive layer and grout are not the same substance, grout is normally of a finer consistency. Also modern adhesives and grout are specifically formulated for different functions and environments and you need to choose the ones best suited.

If you were to use an epoxy filler such as Marmox, in order to create an even finish across the entire patio you would be advised to treat every slab/tile. and not just a section. It may also require having the surface of the tiles ground flat using rotatating diamond grinding discs. This would prove fairly costly and require some expertise.

Thank you for taking the time to respond and offer advice