You need to understand the properties of the materials you're planning to use.
Rammed earth is earth, chalk, lime and gravel, mixed into the right consistency and proportions for strength and longevity. It's then rammed into a form work to form a solid mass.
As it is earth, it can wash away like earth so it's susceptible to water damage if not properly protected from water. As a garden retaining wall I wouldn't therefore recommend it because it's going to get wet frequently. They can use it on houses because the roof and it's overhang protects the walls from constant moisture.
If it's a particularly high wall you would normally put seep holes into the wall to allow for drainage. Naturally, even with plastic pipe in the hole I would think it'll not last 100 years. So if you're thinking of using rammed earth, I'd definably line the wall with plastic.
Also, earth does crack as it expands and contracts. You fix the cracks with more rammed earth mix. People with these types of houses generally have to patch cracks every few years for this reason. But, it's a very organic material to work with and they would be aware of this... it's a choice you make when you build with it.
You could use cement in place of lime. That may make it last a lot longer and increase it's strength. I've seen this work for some structures and it may require some experimentation being out in the open.
Concrete on the other hand does last a long time if properly prepared.
It also can crack as it naturally expands and contracts. To prevent serious cracking you need to cut it every few meters and fill the gaps with a flexible compound. You might notice that as you drive over some concrete highways you'll hear a bump, bump, bump, noise. That's the wheels going over the horizontal cuts in the concrete designed to allow for expansion and contraction and prevent cracking. If it's a big retaining wall you'll need these cuts.
Concrete is also porous so water can be absorbed. You can imagine that concrete that has absorbed water that freezes won't be good for the concrete right? Because it could cause it to crack, and it does. So you need to get a grade of concrete that is less porous and stronger (and make sure it's thick!). Talk to your concrete supplier if you got this route and make sure you get a stronger grade and that when the concrete is poured it is not too wet.
If I were you I'd consider using a different material all together.
Have you considered brick? You can get some flexible mortars so you won't get the same cracking issues as you would with concrete and it will look more attractive in my opinion.
Another option is to use a hardwood. Down here in NZ we call them railway sleepers. You can stack them, bolt them together and form a pretty nice retaining wall. It's strong and attractive. I'd paint the side where the dirt is touching it to protect the wood, or use a plastic barrier or paint on barrier like mulseal. It probably won't last 100 years but it should last at least 50 if well prepared and looked after.
By the way, some woods like Jarrah can last a very long time without any treatment. We can sometimes get Jarrah poles used by the electric company for the overhead wires. They pull them out of the ground and they are still as good as when they went in over 50 years ago. So, some hardwoods can really last.
A typical bathtub holds around 40 gallons, which equates to 8 pints of water, and since a pints a pound the world around, that means 320 pounds of water+you in the tub plus whatever part of you is above the waterline.
If we estimate the surface area of the bottom of the tub at approximately 4' by 1.5' that's about 6 square feet or 864 square inches.
That means that at most the pounds per square inch on the bottom of the tub will be about .4 - and that's ignoring that part of the weight will be carried by the sides of the tub around to the rim.
Then there's the mortar. 1 cubic inch of mortar comes in at about .08 pounds and 3 of those vertically means .24 pounds bringing the total pounds per square inch on the foam, maximum, to about .64.
So the concern here is - will the foam take the weight - and the only way to find out is to determine if the foam is able to withstand pressure of .64 pounds per square inch without compressing. And also - will the foam's strength deteriorate over time.
These are answers you'll have to find out from the manufacturer. (Although you can test it yourself - use weigh the head of a hammer resting on a scale while the handle rests off the scale and that is probably > 1 pound... then rest it on the foam) But if the foam is rigid enough to take that kind of weight, you'll probably be ok.
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I have only done this once before and I have no idea if it is the correct way but we just poured the concrete onto the floor (shaped so it was cented where the tub bottom is) and then squished the tub into it before it dried.