This is based upon a real world situation we encountered. Usually assuming 0.002 structural damping is conservative; however, we had a user that used 0.002 and the stack was experiencing vortex shedding. When we investigated, we found that if we reduced the damping to between 0.001 to 0.002 that it correlated well with what they were seeing in the field. In this case they had some very stiff braces at the bottom of the stack, right above the foundation. It seemed as if braces were so stiff that any damping behavior of the foundation was being eliminated.
We felt we should add the very stiff option because there are cases where the stack is braced, welded to a steel deck, etc.. and could actually have damping lower than 0.002. We don't have any specific guidelines that we can offer on when the "Very Rigid" should be used; however, we would suggest that if you have a steel support or some other situation that may negate any damping offered by the soil and foundation that you should consider taking a more conservative approach and indicate "Very Rigid". When a stack gets to the field and has a vibration problem it will be much more problematic, so much better to be safe than sorry.
When the Very Rigid option is selected, then a structural damping of 0.001 is assumed.