Computational Methods in Engineering

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Bridges are potentially one of the most seismically vulnerable structures in the highway system during earthquake events. It is known that the seismic performance of transportation systems plays a key role in the post-earthquake emergency management. Hence, it is necessary to evaluate both physical and functional aspects of bridge structures. The physical aspects of the seismic performance of bridges are evaluated by seismic fragility functions or damage probability matrices of transportation facilities. The fragility curves represent the probability of structural damage due to various levels of ground shaking. The fragility curve describes a relationship between a ground motion and a level of damage. In this paper, the fragility curves (F.C) are developed. The vulnerability of a railway prestreed concrete bridge is assessed using fragility curves derived from dynamic nonlinear finite element analysis. A software package is developed in MATLAB to study the results obtained. Modeling of the bridge using 3D nonlinear models and modeling of abutments, bearings, effect of falling of girder on its bearings, and nonlinear interaction of soil-structure are some of the advantages of this research compared to previous ones. Reliability curves developed in this study are unique in their own kind. The proposed method as well as the results are presented in the form of vulnerability and structural reliability relations based on two damage functions.

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The computational burdens and more accurate approximations for the estimation of the failure probability are the main concerns in the structural reliability analyses. The Monte Carlo simulation (MCS) method can simply provide an accurate estimation for the failure probability, but it is a time-consuming method for complex reliability engineering problems with a low failure probability and may efficiently approximate the failure probability. In this paper, the efficiency of MCS for the computations of the performance function is improved using a random-weighted method known as the random-weighted MCS (RWMC) method. By using the weighted exponential function, the weights of random data points generated by MCS are  adjusted by selecting the random point in the design space. The convergence performances including the computational burdens for evaluating the limit sate function and the accuracy of failure probabilities of RWMC are compared with MCS by using several nonlinear and complex mathematical and structural problems with normal and no-normal random variables. The results indicate that the proposed RWMC method can estimate the accurate results with the less computational burdens, about 100 to 1000 times faster than MCS