While reading through the recent forum about the Great Wall of China I saw a few parallels between China's dilemma contending with the Mongols and The Byzantine struggle against similar foes in the Arabs and Turks. China chose a to put up a big wall which despite some limitations did offer some decisive advantages such as control of the battlefield and early warnings. What I want to know is did the Byzantines consider the advantages of long fortifications on its eastern borders? Were there any Byzantine 'Great Wall' projects in planning or put into practice?
I wouldn't be surprised if Byzantium was well acquainted with concept since they had a historical precedent with the Roman walls, they had diplomatic and trade relations with China and may have had knowledge of the Great Wall and had already proved themselves accomplished wall builders after putting up the Theodosian Walls.
The situation for the Byzantines was very different.
In the cases of the Romans versus the Picts/Germans/other peoples, or the Chinese versus the various nomadic peoples to their north, you have a big, strong, rich, centralised empire that has to deal with endemic raiding from less organised but mobile and elusive enemies. These states have resources to throw at the problem (though not infinite ones) and have border control as their main priority.
The Byzantines, on the other hand, were a regional power sitting right next to, depending on the timeframe, far greater world-class empires.
Sure, the Arabs would raid Byzantine territory year after year in the 7th and 8th century. But it was a different kind of raid: the Byzantine problem wasn't finding the raiders and delaying them until overwhelming force could be brought to bear against them. They didn't have overwhelming force. The Caliphate was much bigger and stronger. The Byzantine priority was survival and minimising the damage they suffered.
They were never in a position to expend the massive resources it would take to create giant walls. At times their enemies were weaker and divided, but that usually prompted the Byzantines to try and re-take their lost territory rather than construct big static defences.
That said, in the Balkans they did construct the Long Walls of Thrace in the 5th century, a 56 kilometer stretch of wall west of Constantinople, protecting its peninsula from the Black Sea to the Sea of Marmara. These defences don't seem to have been very effective.