A stochastic vulnerability analysis method for armored vehicles with APS was proposed. A two-processes threat-target interaction, including an interception process and a damage process, replaced the one-process of threat-target interaction in the traditional vulnerability method. Depending on the vulnerability results of the incoming threat, various residues-after-interception because of detection or interception failure, deflection, explosion and/or decomposition of the threat and collateral damage was generated and treated as input in the damage process. After randomization of the interception point, the residual penetrator deflection, warhead performance, behind armor debris, and component vulnerability characterization, a stochastic vulnerability analysis was performed. The stochastic model could provide damage states of all the critical components of interest, more practical and informative compared to the expected model.

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In order to address the difficulty in determining the seismic damage probability of continuous girder bridges under construction, the seismic vulnerability analysis method of the construction state is proposed in this study. Firstly, taking a long-span prestressed concrete composite box girder bridge with corrugated steel webs (OSW) as an example, the finite element models (FEMs) of dynamic calculation in different phases of cantilever construction are simulated by OpenSEES. Secondly, by selecting reasonable seismic waves and seismic intensity measures, the non-linear time-history analysis is carried out, followed by the demand parameters and damage indexes suitable for the construction state proposed. Finally, the probabilistic seismic demand model (PSDA) of the continuous box girder bridge during the construction stage is constructed by using the “cloud method”, and the seismic vulnerability curves of the piers and temporary bearings are established to evaluate the seismic performance during the construction stage. The results indicate that the damage probability of piers and temporary bearings increases with the progress of construction. The initial formation of the cantilever structure and the sudden change in the size of the construction segmental girder correspond to a high probability of damage, and seismic protection measures should be strengthened during this construction state. Moreover, significantly higher damage probability of the components under construction compared to the completed bridge after it is built.

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