For more info about the Great Wall, I'd suggest looking at other questions that have been asked before.

So, as to your assumption, it's unfortunately a faulty one. The Great Wall (we'll use capitalized letters to refer to the brick and stone structure that existed during and after the Ming dynasty in the 1400s, in contrast to the rammed earth structures that had existed in the area beforehand) was a huge fortification of tall walls with several manned guard stations and garrisons along its length (this tradition of border garrisons actually goes back to the Tang, but that's a different conversation. It's just one I like slipping in). "So it's just some walls. Big deal" you may say. Well, consider what this thing actually looked like with the surroundings (in addition to those guard garrisons I mentioned).

I'm not sure if this is also part of your assumption, but if you are assuming that the Great Wall was not effective against the Mongolian invasions, as the search of previous questions will point out, this is an all too common conflation of time periods and events. The Mongolian invasions happened a good 300 or so years before the actual Great Wall was built, and the majority of the invasions against the Southern Song Dynasty actually didn't involve dealing with the great walls to the north.

If you're referring to the fall of the Ming dynasty, this is a whole different issue. To sum it up: the Manchu tribes that breached the Great Wall didn't actually breach it, they were let in by a general named Wu SanGui at one of the more famous (if not the most famous) passes along the wall, ShanHaiGuan/山海关. It wasn't so much a failing of the Great Wall as it was a case of the country being struck by rebellion and the Manchus actually being let in and aided by this general and garrison (initially, in hopes of ridding the capital of rebel control). The Manchus, as you might be well aware, then set up their own dynasty, the last dynasty of China, the Qing dynasty. So it's not as if they were particularly displeased at the Great Wall "not working".