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Start with a bare floor. Make sure the subfloor is sturdy: if it shifts, the grout could crack. Test the floor for stability by having a helper bounce up and down on their heels on the other side of the room. Little vibration means the floor is stable enough to install marble tiles. If there is marked vibration the flexing of the floor will crack the grout and maybe even a tile. Some floors can be strengthened and stabilized by adding joists and jack supports underneath.
Make sure the floor is level. Marble-tile manufacturers recommend that the floor slope no more than 1/16" for every 3'. Use the longest level available to check. Look for gaps between the level and the floor and use floor leveling compound to level the floor
Using a piece of plywood the thickness of a tile and the thin-set mortar below, undercut any door jambs to accommodate the thickness of the tiles.
Mark the center point of the length of the area where tile will be installed. Repeat the process for the width of the area to be tiled. Then snap chalk lines across the marks: the point at which the lines cross is the center of the room. Check the marks with a framing square to be sure they're at a 90-degree angle, and then spray them with clear acrylic to fix them in place. If the lines are not at 90 degrees from each other adjust one of the lines and resnap the line. Extend the chalk lines up on to the tub surround so that the grout lines there will match the ones on the floor.
Lay out the marble in a dry run. This will help plan for where the tiles will go. Start by placing a tile at one corner of the center point and working all the way to the wall. If there is room for only a sliver of marble at the end, shift the run so that the starting tile straddles the chalk line. Layout the marble tiles in a dry run again to ensure the last tile is wide enough to form a pleasing ending at the edge.
Begin placing marble tiles on the horizontal surface around the tub. When measuring tiles for the edges of the tub surround, keep them long enough to overlap the vertical pieces underneath. To cut the tiles, use a wet saw, rentable at most equipment-supply centers. After cutting, sand the edges with a power sander. Start with coarse 80-grit sandpaper and gradually work up to extra-fine 400 grit. Then polish the edges with a polishing wheel and buffing compound. To measure tiles for placing them in the last row next to a wall, place one tile directly on top of the full tile that is closest to the wall. Then place a second tile against the wall so that the edge rests on the first tile. Mark a line on the first tile, and make the cut along that line. When making notched cuts, lift the tile as the blade nears the corner. That way, you can square off the cut.
Use a notched trowel to apply thinset mortar to the surface of the tub area. Make sure the notches are even. When applying the mortar across gaps in the plywood, place mesh mortar tape (image 1) directly on top of the mortar to prevent cracks in the grout. Position the tiles on the mortar and place spacers between them. To achieve a strong bond, put mortar on the backs of the tiles, a process known as "back buttering" (image 2). Use a piece of plywood the same thickness as a marble tile to help gauge the overlap at the edge.
When applying the backsplash and knee wall, the vertical portions of the tub surround, use mastic adhesive. Back butter the pieces for the backsplash with mastic if you don't plan to tile all the way up the wall. When applying tiles to the knee wall, temporarily attach a 2" by 4" board to the wall to support the weight of the tiles. The uncut tiles should be placed highest on the knee wall. Allow the mastic to cure before removing the support board and finishing the knee wall.
Place one tile on or near the center, depending on the location as determined by your dry run, and trace around the perimeter. Apply thin-set mortar within the borders, and set the tile in place. Push down firmly on the tile setting it thoroughly in the thinset. The tile will act as a reference point when you begin laying out the rest of the floor pieces. Begin applying thin-set mortar to the floor with the notched trowel and apply marble tiles set apart by spacers to keep the grout lines even.
Use a rubber float to force grout into the grout lines between the marble tiles. Hold the float at a 45 degree angle to the lines trying to force as grout as you can between the tile. Wipe excess grout from the surface of the tiles with a damp sponge or cloth rinsing it frequently taking care to not lift grout out from between tiles. When the grout has dried just a bit and has left a haze on the surface of the tiles, buff with a cloth to remove the haze. Follow the grout manufacturer's instructions to the letter for curing. Some types of grout require long curing times to maximize the strength of the grout.
Install thresholds at the edges of the tile.