Sye123,
You're describing an eigenvalue or modal analysis. I'm not sure that would work. I don't think you can use nonlinear compression only supports with dynamic analysis. Also, while there are assumptions STAAD can make in eigenvalue analysis to allow for variable damping, I don't think STAAD allows you to do the same for the stiffness. Dynamic soil behavior is all about impedance (variable stiffness and damping). I could be wrong, but I think you're stuck with a nonlinear inelastic time-history analysis - which STAAD doesn't handle.