I've recently done this on a website I launch for a product I was working on called Lightning. On that page what I've done was use the bottom navigation as sort of a page navigation. This is useful if you use a parallax style page which can have a lot of information and you want users to navigate to it quickly.
The main navigation I use it to bring users between different sites within the product. Of course there are many ways to accomplish something like I've done. You can look at websites like Microsoft Surface who also do this but on the right hand side and with dots. I could argue that Microsoft's approach is slightly more complicates since you don't know what each of those dots represent.
I do want to caution though, since a dual navigation can often be confusing. Implement it in a way that would reduce friction and make sure you take into consideration user feedback. I was in the process of updating the one on Lightning for it to feel more like a page navigation rather than a global navigation as it does now.
A dual navigation is also very useful and use it on my personal blog. You have one primary navigation and a secondary one when the primary one is out of view. I make my secondary one pop out from the top, but I've also had it popping out from the bottom for a while. The reason I went from the bottom is so that I wouldn't distract users from my content, but it turns out some users didn't notice the menu at the bottom pop out and many scrolled to the top to find the menu again.