Thanks you guys for your answers, really appreciated.
I haven't solved this issue yet; so any suggestion is still welcome

Indeed, a clean solution would be to add some kind of support for btConcaveShape-derived class, into the existing built-in Bullet internal edge detection routines.
Don, I will try to adapt your source code to my class. I created a custom terrain shape in order to support terrain tiles streaming, but I can't foresee any big issue with that. Thanks for sharing your code, it will really help (I am not such a physic engine expert, just a simple user - might reach the power user stage once I have manage to adapt your code

)
I will keep you informed on the results.
Thanks once again guys !