Romans, Chinese and supply depots

Mar 2015
In late 2nd millennium AD Western Europe, in 16th and early 17th century, it was found that the largest armies that could logistically operate together and feed off the land were about 20 000...30 000 men, and that in summer.

Trying to collect bigger forces would run out of locally available food. And for winter, the armies needed to disperse to small garrisons.

In 1660s, Le Tellier started stockpiling food in magazines/supply depots.
And this enabled France of Sun King to collect armies of 50 000...60 000, and deploy them in winter.
Supply depots had been tried before, but nobody had had total armies big enough to need them.

Nobody, that is, in 2nd millennium AD Western Europe.

In 1st millennium BC Western Europe, Roman Republic had fielded 36 000 men at Sentinum in 295 BC... but 80 000 men at Cannae, 216 BC.

Did Romans by the time of Second Punic War establish and stockpile magazines of food like 17th century France would do?

And how about China?
Armies of massed infantry numbering to hundreds of thousands are reported since Warring States period.
True, Chinese historical recorded numbers are somewhat suspect. Zhang Xianzhong gained distinction by officially killing 600 000 000 people. Well, Justinianus slew 1 000 000 000 000.

A period for which better records might exist is middle of 19th century. Traditional Chinese government. No railways, no telegraph.
Armies of both Taiping and Qing were in hundreds of thousands total.
And relatively abundant written records and outside witnesses might exist.
How many men were Taipings and Qing loyalists able to concentrate on single battlefields or sieges and keep fed? And how did they accomplish this? Did they build up supply depots?
Oct 2017
About the Romans, they did have depots. Recently I saw this:

Gabriel writes a lot about Roman logistics in his book about Scipio. For example:
Scipio spent a lot of time preparing Tarraco for the role of the main operational base in the coming campaign. Another characteristic feature of Scipio's operations was providing logistic bases from which military operations were carried out and supported. He was an effective organizer and administrator in the field of supplying the army, and his Spanish campaign in this respect exceeded the campaigns of Napoleon and Duke Wellington (Arthur Wellesley), who to their great disappointment, discovered that Spain is the worst place to feed the army. March without enough provisions and water forces the army to dissipate in small groups in search of food, which makes it difficult to maintain the right pace and strategic direction.
But many of Gabriel's claims about logistics are debatable to me.

It is also worth mentioning that it was possible to maintain a large army without a military depot system. The food could have been provided by civilian merchants for money. In addition, the army could occupy a very large area and draw contributions from it at every harvest.