Modal pushover analysis for seismic evaluation of bridges

Although nonlinear response history analysis (NL-RHA) is considered to be the most rigorous method to determine responses of a structure due to a strong earthquake excitation, it can only be undertaken by highly qualified engineers and may be too time-consuming for typical structural design and evaluation projects. The nonlinear static procedure, or pushover analysis, thus became a popular method to estimate building responses considering inelastic behavior, although the results are not as accurate as those from NL-RHA. This research aims to extend the nonlinear static procedure, originally developed for analyzing buildings, to analyze bridges. In recent years, there have been attempts to improve the accuracy of nonlinear static procedures, for example, modal pushover analysis (MPA), which includes response contributions from higher modes, improved modal pushover analysis (IMPA), or mass proportional pushover (MPP) procedures. This research first assesses the accuracy of these available procedures when applied to simpler structures like buckling-restrained-braced frame buildings, which have non-degrading behavior. It was found that MPA and IMPA provide good estimates of structural responses, while MPA is slightly easier to implement, so it was chosen to be modified for application to bridges. An extension of MPA procedure was proposed in this study to estimate seismic responses of complex actual bridges that require 3D analyses. In particular, the displacement monitoring point for pushover analysis, which is usually the roof displacement when buildings are analyzed, was proposed to be the point of largest displacement in the vibration mode considered, so that the contributions of torsional and vertical vibrations can be taken into account. The bias and dispersion of the proposed extension of MPA procedure was investigated in a case study of analyzing an existing continuous twin I-girder bridge with PC slab due to a set of twenty large-magnitude-smalldistance (LMSR) ground motions. Two types of bridge bearing supports were considered: (1) steel bearing and (2) rubber bearing with lead core. The MPA estimates were compared to reference ‘exact’ values computed by NL-RHA. The results show that the pushover analysis, despite considering only the fundamental ‘mode,’ can accurately estimate responses due to excitation in the longitudinal direction, but one ‘mode’ pushover analysis is inadequate when excitation is in the transverse direction. In this case, MPA can provide better estimates with bias less than 10% for the studied bridge. The bias in estimating deck rotations due to torsional vibration is larger than in estimating displacements of the deck, or drifts of column piers.