I wonder if generational reputations and transmission of methods from master to apprentice is sufficient.
"Secundus was an apprentice to Marius who was an apprentice to Darius, who built that awesome aquaduct; Marcus was an apprentice to Felix who who was an apprentice to Marcellus, whose shit bridge fell down after twenty years. We're going to hire Secundus instead of Marcus."
Real Roman engineering theory came from Marcus Vitruviouss Pollio's De Archetectura. Considered to be the ultimate reference text for building and engineering projects in Rome in 32bce, It's ten volumes cover how to build everything from temples, to aqueducts, to water mills to machines used for construction. A fascinating read, if you're curious how Romans built things.
De Architectura provides the sort of long-term perspective required to build and engineer projects that were meant to last for centuries, based on experience gathered from centuries of recorded experience.
I'm not sure if De Architectura is the only book that Roman Architects used. But it was certainly the most important.
Hundreds of pages of De Architectura list dimensions of older ancient buildings, the dimension and spacing of pillars, and failures encountered during or after construction. Something along the following lines (not actual text):
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The second Temple at Delos was built in 432bce. It consisted of 13 x 29 doric columns, 6' in diameter, 22' high, spaced on 12' intervals, with two rows in the pro-cella. The cella measured ..... The entrance to the cella was 16' high and 12' wide with a granite lintel measuring 16' x 3' x 2'.
The lintel above the entrance cracked and had to be replaced after an earthquake in 430bce. The front-right architrave cracked in 329bce, but was not repaired. The temple was subsequently abandoned and collapsed completely after an earthquake in 327bce.
The temple of Apollo at Thebes ....
The main architrave cracked while it was being mounted, and further construction was abandoned.
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Given a hundred or so such examples, a Roman architect of a new temple could make somewhat informed decisions about how high, how wide, and how thick he would need to build a new temple, and how afraid he should be when he was commissioned to build a new temple that was higher, wider, or taller.
as far as i know, vitruvius wasn’t original: he aped the meticulous and more successful greeks. the ten volumes regularly refer to greek knowledge or practice to cement its authority. the method of construction that is uniquely roman is mixing concrete and bricks, usually to produce aqueducts. and here the simple theory was: everything in excess. in fact, the romans may have been unique in their construction of military camps. for more on that see de re militari
"Secundus was an apprentice to Marius who was an apprentice to Darius, who built that awesome aquaduct; Marcus was an apprentice to Felix who who was an apprentice to Marcellus, whose shit bridge fell down after twenty years. We're going to hire Secundus instead of Marcus."