Resilience assessment of pile-supported wharves under the effects of sequential earthquake and soil liquefaction incorporating vine copula captured dependence

Pile-supported wharves (PSWs) constructed in seismically active coastal environments are susceptible to earthquake-induced liquefaction and the cumulative effects of sequential seismic events. This study develops a probabilistic framework to assess the seismic resilience of conventional and seismically isolated PSWs subjected to mainshock-aftershock (MS-AS) sequences while accounting for liquefaction-induced soil degradation. A detailed 3D finite element model of a representative PSW is established in OpenSees, where nonlinear pile-soil interaction under liquefied conditions is incorporated through a simplified p-multiplier approach. A dataset of 100 recorded MS-AS ground motion pairs is obtained from the PEER NGA database and used to conduct nonlinear time-history analyses. To capture the statistical dependence among mainshock intensity, aftershock intensity, and structural demand, a C-vine copula approach is implemented to construct probabilistic fragility surfaces. These fragility relationships are subsequently integrated with FEMA-based recovery functions to evaluate time-dependent functionality and determine the resilience index. The results demonstrate that aftershock events significantly increase the probability of structural damage and reduce resilience, particularly when soil stiffness deteriorates due to liquefaction. Seismic isolation generally reduces the conditional damage probability and improves resilience under the examined scenarios. For example, when both the MS and AS PGAs are 1.0 g, the conditional collapse probability of Pile E decreases from 79% for the CW to 16% for the IW.