Basically a no-slip condition is assumed in fluid mechanics. In other words the velocity of the first fluid layer close to the surface is moving with the same velocity as the surface one.

Alternatively a partial (or even a full) slip can occur at the liquid/solid interface under some circumstances. This effect can be characterized by the slip length or the slip ratio (abundant literature on this is available ).

In numerical modelling of fluids in a channel, a full slip boundary condition is equivalent to an infinite domain (or no walls) while a no slip boundary condition implies the existence of boundaries (or walls) and interaction between fluid and wall.

I would like to make sure about the problem you are addressing. In these papers by Hashash, all the slip being addressed to is regarding the slip of tunnel lining to the joints connecting it and also with respect to the medium around it.  Please find the link attached to google book.

Also a full slip and no slip condition is also referred to when cases of rock joints and joint slippage are addressed.

https://books.google.co.in/books?id=qwK7BAAAQBAJ&pg=PA312&lpg=PA312&dq=joint+slip+no+slip+full+slip&source=bl&ots=FXGwx6F2Lc&sig=Qb0sB8ShoZtXVDDc7c1mTecA030&hl=en&sa=X&ved=0ahUKEwj-0KOGgZjOAhVHMI8KHSzIAzgQ6AEIPzAI#v=onepage&q=joint%20slip%20no%20slip%20full%20slip&f=false

Thank all for your help. Now I understand about it.

Best regard,

Quang