Ceramic tile is supposed to be the ultimate sanitary system—a floor you could turn a hose on. But every grout seam between tiles is a potential weak link where the water goes when a crack develops. And in bathrooms, the weakest seams are along grouted edges of full and partial tiles that bump up against vanities, toilets and particularly tubs.
Trouble usually starts with a few hairline cracks in grout. They let in a small amount of water, just enough to cause some erosion and make the cracks larger. Unchecked by grout repair or a liquid grout sealer, more water seeps into the joint, then through the grout and under the tile. After that, things can go downhill in a hurry as water breaks the adhesive bond over wood subflooring and begins to rot the plywood. Layers of the plywood sheets separate, which stresses the tile, creates more cracks, and lets in more water. Trapped under the tile, water can also foster mold growth.
Short term, the typical solution is to scrape and clean out the tub seam, let it dry, install new grout, and then be prepared to add caulk as required when the crack opens again. The better solution is to fill the scraped out seam with exterior-grade silicon instead of grout. As the floor under the tub flexes slightly (as almost all do when loaded with water and people), the full-depth silicon will give a bit. A strip of white or clear caulk may look a bit different than the adjacent grout but it will keep the joint sealed and could save the entire tile job.
Too often, installers get it backwards and make the tile system too rigid where seams need flexibility, and too flexible where seams need maximum support. The right approach is to build the subfloor so solidly that tiles can't flex (flexing causes cracks), and to replace rigid grout with flexible caulk at seams that could flex, even in the strongest floor.
In most living space, standard half-inch-thick plywood is more than enough subflooring, installed under finished wood flooring, such as oak, or wall-to-wall carpeting. But those floors are resilient; they give a little when you walk on them. Flooring under ceramic tile has to be stronger, basically like a concrete slab.
There are several ways to take the flex out of a wood-framed floor. You can increase the size of floor joists, or, if you don't have the extra few inches of clearance, either double up smaller joists, or space them closer together. It's pretty simple: to make the floor stiffer, use more wood. If floor joists in the hall outside the bathroom are 2-by-8s, 16 inches on center, you might use 2-by-10s in the bathroom, or 2-by-8s on 12-inch centers. If it's difficult to beef up the entire floor, at least double up joists under the bath tub, particularly under the tub-to-tile seam.
If you don't or can't beef up the floor frame, it's wise to increase the thickness of the subfloor. Instead of half-inch plywood, use at least 5/8-inch, and better yet, 3/4-inch-thick sheets. And don't rely on nails. Use construction adhesive over the joists, and screws through the plywood surface. Over the kind of modest floor span you find in most baths, standard joists covered by glued and screwed 3/4-inch plywood will be extremely rigid. Take the floor joists up a size, and the floor will be like a rock. That's what you want.
On new installations you can also pre-stress the tub-to-tile joint by adding weight to the tub after it's installed. Before the tile is laid and until the grout hardens, add some weight by carefully setting three or four concrete blocks on a doubled-over towel on the floor of the tub. Then when you add water and climb in (showers, obviously, aren't as bad), the extra weight won't have as great an impact on the joint. And combined tub weight can be considerable. A mid-size unit about 5 feet long and 2 feet wide holding 12 inches of water and a 165-pound body can top out at close to 800 pounds — a lot of extra weight in a small area.
Everything changes if you're thinking about a larger whirlpool, spa, or soaking tub. Some can hold hundreds of gallons, and weigh in at over 2,000 pounds without any people. Consult the manufacturer on those projects, which may require oversize framing, steel strapping and other details to keep a surrounding tile floor solid and free from cracks.