"vast build up" is a correct and usable phrase in written English.
It is used to describe a great accumulation of something over time. Example sentence: The vast build up of carbon dioxide in the atmosphere is causing climate change.
This is a problem both for the ecosystem and for power stations, which find the intake pipes for their water cooling systems becoming blocked by a vast build-up of mussels.
Part of the vast collections built up by Arthur M. Sackler were among the offerings.
Fortunes were made, vast estates built up, a whole feudal Hispanic culture evolved.
"I saw the vast industry built up from publicly funded research, and it was never clear to me what value was being added.
Britain's leading fund manager, Neil Woodford, has warned that falling oil prices could prompt a rout in the global bond market as shale companies default on vast debts built up during the US fracking boom.
(It often surprises people who don't know much about banking to hear that banks, whose primary role is to lend, also borrow vast sums of money and build up huge debts, but they do. In 2008, it was the difficulty banks encountered rolling over their debts that almost caused them to collapse).
To protect exports and to build up vast war chests of reserves, many East Asian governments kept their currencies cheap for years after the financial crises.
NINE-FIGURE I.R.A.'S Remember Mitt Romney's $100 million I.R.A? Private equity partners apparently build up vast tax-deferred accounts by claiming that the equity interests transferred to such accounts from, say, their firms' buyout targets are not worth much.
For decades, Arab regimes diverted valuable resources to build up vast security apparatuses justified as necessary to combat Israel.
But even those titans of Wall Street who made the calls to build up vast wealth at the expense of the global economy, his film argues, aren't just two dimensional.
By judicious speculation he began to build up the vast fortune that guaranteed his independence.
