The primary tldw; is the fact modern concrete uses steel rebar for tensile strength, whereas the Romans relied on architectural techniques to minimize tensile forces on their structures.
Steel rebar is the primary route through which concrete deteriorates.
“University of Utah geologist Marie Jackson… and her colleagues have found that seawater filtering through the concrete leads to the growth of interlocking minerals that lend the concrete added cohesion.” http://unews.utah.edu/roman-concrete/
includes some tasty microscopic photography
Edit: Thanks, civeng, this is a good warning to be aware of validation bias when googling. Here is a paper that cites comparisons of post-tensioned concrete bridges. From the paper:
"As an example, two optimal post-tensioned concrete box-girder road bridges located in an eastern coastal region of Spain were assessed... In addition, maintenance was optimized to ensure that the bridge complied with all the performance requirements during its life-span of 150 years."
- according to two recent independent structural model calculations based on the original plans, the building that collapsed was deliberately designed to meet only 100% to 115% of the original static loads to save money, but not the dynamic loads of rolling vehicles or interior upgrades like granite counter tops and marble wall displays.
Also, there were a few 12" columns, no column caps, and not enough shear wall areas or elevator core tie-in to resist twisting from wind loads or prevent domino column failures.
- any number of events could have started the collapse because there was no safety margin, including water intrusion and previous hurricane wind loads, but it was probably vehicles rolling around the lobby level near the pool.
To answer your question, it would cost more than the building was worth to replace the columns and slabs. The 40-year review for that building really meant a teardown had they redone the structural model. The owners were already looking at a $100,000 to $200,000 bill each for cosmetic repairs. Because of absentee owners (lessors and airbnb), that level of investment for a rebuild doesn't fly.
It's believed that the former building inspector gave a positive building review speech so that cronies could continue selling units, as negative news would have to be reported to potential buyers, killing any sales.
Note that builders who looked at the post-collapse photos even one day afterwards all wrote, "Nothing looks right in those fotos." What bothered them the most were the columns that punched through with no debris stuck to the top (pejoratively called "those toothpicks"), and yards of rebar bundles that also looked too clean.
Not a structural engineer (but I have been site manager for quite a few post-tensioned bridges building sites), you may be confusing pre-tensioned with post-tensioned.
In pre-tensioned there is no difference with "normal" rebar, the steel is in direct contact with the concrete.
In post tensioned you cast the concrete embedding pipes where you later insert the cables, then you tension the cables and inject in the pipes (and around the cables) some sort of corrosion preventing mixture, this used to be a mix of cement + additives (very, very fine, no sand nor other aggregates), but depending on the project it can nowadays be also some mix of grease/wax (in this latter case cables can be de-tensioned, removed, replaced and re-tensioned).
So, unlike the pre-tensioned structures and common rebars the cables in post-tensioned structures the cables are better protected and less likely to suffer corrosion deriving from infiltration of rain or water, so that part of the structure is - in theory - less prone to aging.
Still, the cables only represent a part of the structure, the rest is "kept together" by "common" re-bar steel, and these are - generally speaking - nearer to the surface of the structure, so I would expect properly built post-tensioned structure to have the same life-span of normal reinforced concrete.
IMHO 50 years is a very low threshold for the lifespan of any reinforced concrete structure, including pre-tensioned structures, while post-tensioned should have - at least for the cables - a longer lifespan.
Anecdotally, the first bridges I contributed to build are now around 40 years old and show no particular signs of decay.
The variability based on type of rebar and the environment it is installed in is too high to make statements like that.
Galvanized rebar in concrete in non-marine environment will last hundreds of years. The concrete will probably crumble around it before the rebar corrodes if there's any appreciable moisture and freezing temps. Epoxied rebar will last less, bare rebar less still and improperly installed epoxy rebar will last less than that.
There are tons of 100yo buildings in fairly moist temperate climates with (poorly, by modern standards) reinforced concrete foundation that used bare rebar and are doing just fine.
If you can get an economical, efficient route from co2 to graphene, using graphene flakes in composite materials might be an excellent method of carbon sequestration.
The above is a generalization. See a proper engineer if you are actually building something to get the correct details for your application.