Scattering Analysis Framework
A scattering analysis framework, developed by Bielak and co-workers as part of the effective seismic input method, is adopted as the approach for soil-structure interaction analysis in LS-DYNA. This approach considers soil-structure interaction to be caused by the scattering of the free-field ground motion by the presence of the structure, and the appropriate earthquake forces and the use of an absorbing boundary follow rationally from this viewpoint.
Consider the following two independent states as part of a thought experiment:
(a) soil is excited by an earthquake in the absence of the structure, and
(b) the structure disturbs and scatters the incoming earthquake wave.
Note that both these states cannot occur in reality: it can be either one or the other.
If we take the difference of the foundation motion in the two states, we are left with only the scattered motion, having eliminated both the earthquake source and the incoming wave. The scattered motion — because it is generated solely by the structure — propagates entirely outward from the structure.
Now the unbounded domain can be replaced by a truncated bounded domain, but without only simple boundary conditions, the outer boundary will reflect spurious waves back to the structure. This may be avoided by using an absorbing boundary to reduce the wave reflection and appropriately model the unbounded domain beyond.
We shall use perfectly matched layers as the absorbing boundary, and the scattered-wave formulation will provide the equivalent earthquake forces, termed as the effective seismic input.