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I have been drafting the concept of a future world based on current research. I have been contemplating the long lasting transportation tunnels of the future. I am asking about the likelihood of the following building method:

Notes:
Granite is abundant and has extremely high strength and durability.
New carbon based materials are breaking tensile strength records.
There have been breakthroughs in self-healing waterproofing.

Proposed Building Method:

Tunnels cut. Cracks filled and surface covered with self healing waterproofing material. Then coated with abrasion resistant material.

Granite blocks precisely cut for perfect fit in tunnel assembly. 4 hole drilled through the block.(Two through one face, and two through a perpendicular face) Blocks then coated in self-healing waterproofing and abrasion resistant coating.

Blocks moved roughly into position. Carbon based cords weaved through the holes. Cords then pulled tight pulling the blocks into position and cords tied off on themselves.

Would this type of building method be stronger than our current concrete and rebar?

No, it won't work.

The thermal expansion coefficient of granite is $7.9 - 8.4 cdot 10^-6 m/m K$, while for carbon fiber the value ranges around $1.6 - 2.1 cdot 10^-6 m/m K$.

For comparison, steel has $11 - 12.5 cdot 10^-6 m/m K$ and concrete $13 - 14 cdot 10^-6 m/m K$.

Therefore, while steel and concrete will nicely accommodate for temperature variation thanks to their similar expansion/contraction, granite and carbon fiber will not, inducing additional stress in the structure, resulting in loss of the functional bonding.

You will end up with drilled granite walls and loose carbon fibers which would do no work in reinforcing the granite.

No

• Granite does not appear everywhere. It is not the principle substance removed from the vast majority of tunnels (only from the majority of deep tunnels). Shifting to granite as the primary stone for tunnels means quarrying and transporting one of the heaviest types of stone on the planet. That's expensive.




• It also means cutting, (precision!) shaping, and (precision!) drilling one of the hardest types of stone on the planet. That's also expensive. And unlike continuously-poured concrete, you're stuck with layering bricks or blocks of granite. No matter how you secure it, that alone is a significant weakness (think "earthquake." The planet is always shifting).




• Pouring a fluid to fit your mold is much, much simpler than chiseling one of the hardest rocks to fit and drilling holes that must align and accommodate curves. Concrete is easily transported, cheaply available, and flexible in its application. Granite is basically none of those things.




• Concrete is internally reinforceable. Yes, it'll chip more easily than granite. It'll even break more easily than granite. But it's the use of iron rebar that is both the primary strength and the primary weakness — because the metal rusts and expands over time. Replacing the rebar with a non-corrodeable substance would improve this considerably. (I'd like to give a shout-out to @L.Dutch's answer, which points out why carbon fiber wouldn't serve this purpose.)




• And that assumes we don't figure out how to reinvent the Roman concrete used to build Sebastos Harbor 2,000 years ago. It's still there. And Roman concrete is naturally waterproof (it even grows stronger in seawater).

A fascinating article is "The Rock Solid History of Concrete" by Jonathan Schifman for Popular Mechanics. I strongly recommend reading it.

And cost is always an object

Construction methods are always impacted by more than the materials being used — and the cost of any construction method will always be a prime driver of how something is built. Yes, safety, utilization, etc. must all be met. But you don't spend more than you must to do anything. After 150 years (the time you specify in your question), there are many other things that will need replacement. The electrical, plumbing, and ventilation systems, and the transport platform (road, rail, etc.) come immediately to mind — and that assumes that the need for the tunnel exists after 150 years. The U.S. interstate highway system did not exist before 1956 (only 63 years ago) and yet roads have been resurfaced, redesigned, rerouted, and rebuilt considerably during the last 25 years. There are unused railway tunnels all over the country. There are unused, redesigned, and rebuilt subway tunnels all over the world. Perhaps the only kind of tunnel that would need to survive longer than 150 years is a buried aqueduct.

The convenience of concrete makes it nearly impossible to dislodge as the principle building material in the foreseeable future. Reinventing Roman concrete and reinforcing with something other than iron rebar would be a much more economical, practical, and probable future than using granite.

Sure it would be. Granite has a compressive strength of roughly 200 MPa and concrete is usually 70 MPa (using a very quick google search), so that alone is enough to answer your question.

But why would you use Granite? You don't need to have the strongest, best, expensive material to create a tunnel wall. You need a material that will complete the job within safety regulations and you want it to be cheap, fast and easy to use.

So yeah, you could spend a hundred times more money and making a super strong tunnel, covering it with layers of materials to protect it from everything, causing your price to sky rocket and your project to be delayed and eventually abandoned due to the cost and difficultly in manipulating the material. Or you can build it to the safety regulations that have been set using a durable and easy to use material which will fulfill safety standards and not break the bank.

Other answers give far better scientific information than I can and seem to be arriving at the conclusion than your proposition won't work. I'm not going to argue ;-) Since the ground moves about, you could just end up with a 'split' in the tunnel half way down. Both ends are still completely in tact, but there's a 1M 'step' half way down due to surrounding movement. Making a strong tunnel might be a moot point, but let's run with it...

Your future world might have CNC light sabres, contained plasma drills and anti-gravity carrying devices, so might be able to handle and work granite far easier than we can today. That being the case, they could conceivably use granite in the construction of the tunnel, perhaps as the initial support around the drilled tunnel. Inside that goes the more usual concrete 'tube', followed by a decorative internal layer of marble (or granite, if you really must). That way you could have a strong tunnel, with a modestly flexible (and repairable) interior. You could even have an air gap between granite and concrete layers as a space to allow for movement. I'd imagine you could achieve the same with two layers of concrete, but that's not what you asked.

In the future, getting these materials and having them milled or otherwise cut to size and shape will be far cheaper than it is today, and perhaps the aesthetics will be more important than they are today. Maybe 'liquid granite' or 'liquid marble' will be possible, something akin to 'poured stone' as we have today.

On the aesthetics point, the Victorians generally added decorative embellishments to their buildings and machines, and had a sense of 'leaving things for future generations'. I'd suggest we've largely lost that sense in our modern world as we have a far more 'disposable', short-term, money driven culture now. However, if your future world is digging tunnels designed for multiple decades or centuries of use, then they may return to such thinking. If so, doing things that don't necessarily make logical or scientific sense start to become more acceptable.