Multidirectional seismic performance evaluation of concrete-filled steel tube pier-continuous beam bridges based on endurance time method

To address the strongly nonlinear response of multi-span continuous girder bridges under multi-directional seismic excitation, this paper proposes an endurance time method (ETM)-based approach for assessing the seismic performance of concrete-filled steel tube (CFST) bridge piers. A refined finite element model of a two-span continuous girder bridge is developed using the high-fidelity FE software ABAQUS with solid-shell elements, incorporating a combined hardening-ductile damage model and a triaxial plastic-damage model for confined concrete. The model is validated against bidirectional shaking-table test data to ensure its accuracy. Subsequently, the ETM analysis technique is introduced. Artificially generated multi-component endurance time acceleration functions are employed to simulate the nonlinear dynamic response and damage evolution of CFST piers under different seismic intensities and directions, to quantify the displacement response and damage level of the piers under various scenarios, and to evaluate the applicability and accuracy of conventional combination rules under multi-directional seismic inputs. The results show that the good agreement between the experimental and numerical responses confirms the reliability of the proposed model. Taking the controlling pier P₂ as an example, under multi-directional seismic excitation, its maximum transverse displacement increases from approximately 26 mm to 32-40 mm, corresponding to drift ratios of 3.99%-5.02%, and in some cases exceeds the critical performance limit of 4%. Furthermore, compared with the ETM-based time-history analysis, the traditional square-root-of-sum-of-squares (SRSS) and 100%/30% combination rules conservatively amplify the axial force of pier P₂ from 316.69-320.39 kN to 407.19-440.55 kN under typical bidirectional loading, resulting in an overestimation of approximately 27%-39%. This discrepancy mainly arises from the phase differences among ground-motion components and the nonlinear structural response, which make it difficult for the conventional rules to adequately capture multi-directional coupling effects and the actual dynamic characteristics, thereby compromising the accuracy of seismic performance evaluation. In practical bridge design, it is recommended that the seismic design of critical components be supplemented by time-history analysis that explicitly accounts for ground-motion phase differences and coupling effects. An integrated application of multiple assessment approaches should be adopted to achieve an improved balance between safety and economy.