Tires are also heavy, and then you will need to fill them with something - and if you are stacking them more than a tire high you are going to want to go with ramming them with soil, then covering them with stucco or plaster or some such.
There is a more natural and easier method of doing what you want. And that is using trenches and
berms on contour a.k.a. Swales, then covering the sloping down side and the top of your berm with a permanent ground cover as you initial stabilizing material.
Geoff Lawton is one source big on swales and using them to capture and hold
water. His YouTube videos are here:
https://www.youtube.com/channel/UCL_r1ELEvAuN0peKUxI0Umw swales have been proven to work on all sorts of landscapes and have added benefits of holding rain water in place so it can soak deeper into the soil and recharge ground water.
I red about a man in Mexico who had a bare hill that over decades he hand made swales and trenches and at the bottom of the hill his crop
land went from having to have a deep well to having water close
enough to the surface where the
roots of his crops could get all the water they needed, and it lead to recharging wet season springs and the effects reached out to benefit neighboring farms.
The Chinese Loess hills were at one time completely bare of vegetation due to over harvesting and farming. A few decades ago they decided to reverse that and all they did was take the dusty loess and make it into terraces that were planted with
trees, grasses and lots of other types of plants picked to meet the needs of the soil and ecology. Lots of videos on that:
https://www.youtube.com/results?search_query=chinese+loess
Hard-scape (tires, retaining wall brick,
concrete, etc.) used to hold the shape of your "stairs" will eventually fail no matter what you build it out of, especially if you are trying to do vertical risers (up each step) and no matter what you use, on 15 acres its going to be expensive to move in new material. Using what you have right there (the dirt/soil) will be cost effective, and planting things that you can harvest like fruit trees, berry bushes on the berms will promote long term stabilization of soil and build up of soil, especially if you use the chop and drop method.
Without seeing your hill I can't guess at how many terraces you will need or if you will need
some hard-scape material to give water a way to flow out of one
swale to the next lower one. I don't know what your long range goal is when it comes to planting.
Hope some of that helps.
Cheers
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