A hybrid LSTM-MPHI2 approach for time-dependent reliability analysis of long-span PC bridges

Long-span prestressed concrete (PC) bridge is a high-dimensional and strongly nonlinear system, and their long-term limit-state functions often deviate from Gaussian assumptions. Combined with the high computational cost of finite element analysis (FEA), these factors make existing time-dependent reliability analysis (TDRA) methods difficult to apply in practice. To address these challenges, this study develops an FE-driven surrogate TDRA framework that integrates a long short-term memory (LSTM) neural network with the moment-based PHI2 (MPHI2) method. First, a high-fidelity 3D FEA model is constructed using an implicit solver to capture the coupled effects of creep, shrinkage, cracking, and prestress loss. Based on the FEA dataset, a long short-term memory (LSTM) neural network is trained to efficiently approximate the nonlinear time-dependent responses, which are subsequently incorporated into the MPHI2 method for evaluating the TDRA of an in-service long-span PC box bridge. The results show that the predicted time-dependent failure probabilities (TDFPs) for both the deflection limit state (DLS) and prestress-loss limit state (PLLS) agree well with Monte Carlo simulation results, with errors within 6 % while significantly reducing computational cost. Sensitivity analysis indicates that the creep- and shrinkage-strain coefficients dominate the DLS and PLLS, respectively. Moreover, over a 100-year design life, the TDFP increases by approximately six times for the DLS as the deflection criterion changes from Δd = l /250 to Δd = l /500, whereas the corresponding increase for the PLLS is about two times as the prestress-loss threshold changes from 10.0 % to 7.5 %. The proposed LSTM–MPHI2 approach provides an efficient and accurate tool for the TDRA of long-span PC bridges.