Seismic Reliability of Stone Arch Bridges Considering the Uncertainty of Material Properties Based on the Response Surface Method

Masonry arch bridges are built using masonry materials such as brick or stone with or without mortar. Their mechanical properties due to the variety of materials used, the quality of construction, and the effect of the passage of time can be inconstant and have significant uncertainties. Therefore, to ensure the ability and performance of the structure against the loads, especially earthquakes, adopting more accurate modeling methods and considering these uncertainties is fundamental issue of structural engineering. For a stone arch bridge of Iran's railway network, the mechanical properties of the materials including the normal and shear stiffness coefficient of the stone block joint as well as the internal friction angle of the joints were considered as quantities with uncertainty and as random variables. According to the discrete environment of the bridge, incremental dynamic analysis has been performed under the influence of eleven selected earthquake records using the discrete element method. After analyzing more than 2,600 bridge samples with different material properties, based on the response surface method, the limit state functions of the bridge failure in terms of three random variables have been determined for all records. Using FORM and MSC reliability methods, the reliability index and probability of bridge failure were calculated. The results showed that for the selected earthquake records, the spectral acceleration of the bridge collapse threshold were reduced by 30% to 50% considering the uncertainties compared to the case where the uncertainty in the materials is not considered.