You've put "4th century" as a tag. Does this mean you are only interested in reuse in the 4th century CE? If not, I suggest removing the tag and clarifying in the question what period you are interested in exactly. Also, there may well have been different practices in different regions of the empire. Unfortunately, I suspect primary source evidence might be hard to find.

thanks for the heads up, the saint helena even did happen in the 4th century but i am interested in reuse in 1st century only. fixed the tag and the title, thanks again...

After reading Felicity Harley, "Crucifixion in Roman Antiquity: The State of the Field", Journal of Early Christian Studies, Vol. 27, No. 2, Summer 2019, pp. 303-323 and Matthew W Maslen and Piers D Mitchell, "Medical theories on the cause of death in crucifixion", J R Soc Med 2006;**99**:185–188, I conclude that we know next to nothing with certainty about details of crucifixion. Latter paper contemplates possibility of reuse: "The tip of the nail was bent, suggesting that during its insertion it had perhaps met a hard knot of wood or pre-existing nail left from an earlier crucifixion."

I would do a little further research on the decomposition of wood before basing any serious argument points on the numbers you cite above.

On the point about wood rotting and chipping: This depends enormously on the local environment. Unprotected wood rots in a few years in my New England back yard; It can last for millennia in poorly-oxygenated water or in a desert environment. No general statement is possible, and as given, this is not evidence for or against anything.

@njuffa The presence of an existing "nail" could simply be that the Romans used scrap timber for crucifixions. I doubt timber would be wasted in a dry environment like Judea. Compare that to the 6000 slaves crucified by Crassus after the Spartacus rebellion where they were left on display along a major road into Rome for years - but Crassus was said to be the richest man in Rome and trees are more plentiful in central Italy.

Why wouldn't they be reused?

It is highly likely that whatever St Helena found was already being venerated by the local Christian community and had been for a long time. Any actual discovery the True Cross happened much earlier and we have no record of it. (Consider the similar case of Old St Peter's in Rome: It was built by Helena's son Constantine at the site Christians in Rome had venerated for centuries as Peter's grave.) It would be astonishing if Helena was the first person in Palestine to say, "Gee, I wonder what happened to the cross?" The question is based on a probably false assumption and is unanswerable.

If you want to show that the traditionally assumed origin of any ancient relic is unlikely, you don't need to dig deep - unless you assume the related miracles to be true. On the other hand, if you want to rationally prove that a given relic is true or false, then the question is surely unanswerable due to lack of evidence.

@njuffa "we know next to nothing with certainty about details of crucifixion" ... that seems rather surprising, i mean the crucifixion is a really big deal :|

@Luiz "St Helen found the titulus too, the wood plaque with the inscription INRI in 3 languages" ... that just didn't happen, why would you think the story of the sick women that they used to find the true cross is a thing ?

@MarkOlson i did more research and what you said here is true .. i will link resources below "The question is based on a probably false assumption and is unanswerable."

@Pere so, whenever anyone brings this .. i shall ask for evidence? which they definitely won't be able to provide, other than the well known story.

@MarkOlson about the wood... the story says that they needed to do digging ... which makes it certainly that the wood did decompose ... it was buried in ground after all.

(a) Not that simple... It depends a lot on soil conditions. (b) On what basis do you pick and choose what parts of the story of St. Helena's finding it to credit?

en.wikipedia.org//wiki/Titulus_Crucis I have seen it, it is still there. Even IF it is a medieval copy (carbon dating has issues...), it is a copy of an original that was there since Late Antiquity, besides having reasonable clues about being from 1st century and having being put there by St Helen/Constantine.

book amazon.com/Quest-Cross-Carsten-Peter-Thiede/dp/0312294247