Upon further reading, If the support sticks due to friction (load perpendicular to support is less than friction load mu*N), then the restraint with friction stiffness will be applied in the stiffness matrix of the system.

However, if the pipe slips (load perpendicular to support is greater than friction load mu*N), a force (mu*N) opposite the direction of movement will be applied in the force vector of the system.

I believe the question will be, should the stiffness to be used will be (mu*N/sqrt(dx^2+dz^2), (where, x,z being perpendicular to the support axis)?

And I think, the resilient friction restraint approach, does not use the force approach either in the stick or slip condition (it always uses the stiffness approach) from the term itself.

Warm Regards,