Strictly speaking, no.

Without reinforcement, steel or otherwise, you are looking at gravity structures that mostly rely on compressive strength. Any modern application of concrete pretty much calls for reinforcement.

In different terms, once your concrete object (this is a solid concrete object) gets a dimension that is around three times more than the shortest, that’s about as far as you can go with unreinforced concrete. So, imagine a 1x1x3 object scaled as big as you want, that’s near your limit. No thin or narrow objects without your steel.

Legally, you’re still in the city at any depth this side of the center of earth.

If you’re looking for undisturbed soil:

Suburban – houses: 5′.

Suburban – streets: 20′ in most cases, but at low as 60′ for large deep utilities.

Suburban – commercial buildings: 20′ in most cases, but as low as 40′.

Urban – general: 20′ in most cases, but as low as 60′.

Urban – city center – streets: 40′-60′ in most cases, but 120′-240′ is subways are present.

Urban -city center – skyscrapers: 60′-120′ are common, but extend to 300′-400′ below the lowest floor for some caisson foundations.

First, we would need to know if you are talking about a circular or spiral staircase. Circular stair curve gradually and spirals are a tight space.

Given the question, you haven’t designed stairs before.

If you are thinking about a spiral stair just go with a pre-manufactured solution. Things can change with the width and most conventional logic with stairs doesn’t work with spiral stairs because we design them more like deck ladders than stairs.

For circular stairs. I’m not going to go into a lot of systems for the human stride, but instead, keep things simple.

There are three common riser (vertical part of the step) modules to work off of: 6″ (low but long stair), 7″ (average), 8″ (steep stair tight spaces). Remember you get one less tread than risers. So for 10′, 6″ has 19 treads, 7″ has 16 treads, and 8″ has 14 treads.

Now you won’t actually have 10′, so you won’t have the risers at these exact heights. This is to get your tread/riser count. You can easily go back and work out the actual numbers.

If you want a tread size; stick between 11″-12″ and you’ll do fine.

It is generally considered to be 6″. You can get thinner but stone size, shape orientation, and reinforcement quickly become predominant issues.

In other words, the wall starts behaving more like concrete bellow 6″ in thickness and like a shell structure below 4″ in thickness.

Keep in mind when I say they behave in a certain way, I’m saying you need to adjust your materials to fall in line with walls of that thickness.

I think you’re looking for the “modulus of elasticity”.

Yes, but…

If you look at most examples you will notice strictly a framework. A few examples will suspend a bridge or solid form using it or them, as a compression strut.

So you become limited to structures so big the occupied portions look like the struts or a large mass supported by a couple of tendon tied struts.

If you try to cover the thing you get a tensile structure instead.

It could work as a series of platforms, but that may not fit your idea of a building much less a skyscraper.

Ok. Earth is between 7,899.8 (pole to pole) to 7,926.4 (equator through the center to equator) miles. People comfortably walk at about 3mph. This gets you between 2,633 to 2,642 hours. That would be basically 110 days or just less than 4 months.

Of course, this assumes you never stopped walking and kept at the same speed.

Typically we like to limit the weight to about 40 lb/sqft on an unknown 4″ slab.

In most cases you can go to 80 lb/sqft in isolated spots, but unless you know roughly what the soil bearing and reinforcing is for that slab you might be looking at cracking.

Keep in mind that 40lb/sqft is sufficient for a typical passenger car.

There will be people who will give much higher values, but without knowing a number of things you aren’t likely to know you probably need to keep it at or near the 40 lb/sqft.

The process of placing and curing concrete in hot weather is usually called moisture curing. There are two types. One for hot-arid and one for hot-humid environments.

Hot-arid environments are the ones you usually need to worry about. Water is poured onto the surface as needed to keep just enough water to reflect for the first day. After that, you add water until it is visibly wet for the next two days. Many contractors will place tarps, burlap, or straw to limit evaporation. After the third day, it would be allowed to cure naturally unless otherwise directed by the engineer.

Hot-humid environments tend to be less of an issue unless it is above 90F. The surface of the concrete should be periodically checked for drying, bubbles, or unusual separation or striation of the concrete. Generally, water is poured on the surface to cool the concrete. In rare cases, ice may be placed on the surface, but usually, cooled water works well enough. (Don’t use fans or blowers as they will dry the surface too quickly.) Again, after three days the concrete is usually left to cure naturally.

Those are sheet pilings.

They are holding the lateral weight of the hillside up against them.

They are one solution to preventing the hillside from sliding or collapsing into the newly built area.