Improved two-step method for seismic analysis of structures
25 July 2014
Seismic soil-structure interaction (SSI) analysis requires use of specialty programs such as SASSI2010, which are not suited for general structural analysis for other (non-seismic) load cases and load combinations. Also, due to the computational effort involved, SSI analyses are generally performed using somewhat coarser finite element mesh, whereas static/dynamic analyses for other load cases are typically performed using more refined finite element mesh.
Because of this difficulty, the seismic design forces are obtained using selected outputs from SSI analysis as input to a second analysis that is performed using general purpose structural analysis software. This approach is called two-step method, in which SSI analysis is the first step. The second step of analysis is either equivalent static analysis or response spectrum analysis. In the former inertial loads are applied based on subjective interpretation of SASSI2010 results, which ignores their temporal and spatial distribution and therefore leads to conservative results for sliding/overturning stability evaluations and member design forces. In response spectrum analysis, the SSI-generated Foundation Input Motion (FIM) across the foundation expanse is accounted for determining the envelope of foundation in-structure response spectra (ISRS) at selected locations as the input spectrum. While this is an improvement, this approach does not capture the superstructure response to the actual incoherent foundation motion that contains effects such as SSI-induced rotational motion (i.e., rocking and torsion), basemat flexibility, and cross-directional excitation effects.
This paper presents an improved two-step method that characterizes the incoherent FIM using combination of spatial mode shapes (i.e., admissible shape functions that collectively approximate the total foundation motion at each node). Results are compared with SASSI2010 to judge the method’s accuracy for various response quantities, and sensitivity of results to the number of spatial modes is studied. The results show that the proposed method is quite accurate when a few basemat mode shapes are included in addition to the six rigid body mode shapes (three translations and three rotations due to SSI).
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