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Railway alignment optimization in earthquake-prone mountainous (EPM) regions should quantify and trade off construction investments and seismic risks. Unfortunately, slight attention has been previously devoted to this trade-off. To this end, based on the FEMA-P58 methodology, a net present value (NPV) model of risk avoidance is presented and solved. In the model, alignment alternatives are first segmented into structural groups with different probabilistic seismic fragility curves, which are then used to generate structural repair cost and repair time curves. Afterward, a probabilistic seismic hazard curve is introduced to estimate the expected annual repair cost and time for computing railway direct and indirect seismic losses. Hence, the railway total annual loss caused by seismic activity can be obtained. Next, a benefit–cost analysis is performed to combine construction cost and seismic loss as the risk-cost NPV. To optimize this objective function, a particle swarm algorithm is used as the basic approach. For implementing the probabilistic seismic performance analysis, a Monte Carlo simulation (MCS) is employed as the risk assessment module. Furthermore, due to the computationally intensive nature of MCS, a CPU-based parallelization is embedded into the algorithm to expedite the search. Finally, the proposed model and method are applied to a representative real-world railway case in an EPM region. Their effectiveness is discussed and verified in five experiments, including algorithm convergence analysis, alignment solution comparison, seismic risk interpretation, computational efficiency test, and a specific sensitivity analysis.
Song et al. (Mon,) studied this question.