Mu, as a coefficient of friction, is applicable to two smooth surfaces interacting with one another. For our purposes, when considering the force wheel chair wheels exert unto the carpet, F=uN is fine.
However, as Matt Leese states in
this thread, traction can increase when two surfaces mesh with one another. In such instances, this occurs because there is contact occurring between the surfaces that is perpendicular to the direction of movement.
Think about a set of spur gears, if you will. Their ability to transmit torque isn't limited by the friction that occurs between those two surfaces because they mesh.
On our robots, belting or file cards or other irregular surfaces often serve a similar purpose. Last season, our robot featured treads with over 1 ft. sq. of surface area contacting the carpet. Because the carpet is made of small loops of fiber and our belting material was made of similar PVC hooks, the materials meshed, giving us superior traction.
Unfortunately, I don't know if there's a single universal formula that applies to the force two meshed surfaces can incur before slipping. I would imagine that, like mu, it is dependent on some experimentally derived constant that varies with each surface.
Sorry I couldn't help more.