Rockfall disasters pose a significant threat to bridge structures in mountainous areas. Most of the destroyed bridge structures in mountainous regions are impacted by rockfalls to different degrees. Reinforced concrete (RC) columns with circular and square cross-sections are extensively used in bridge structures as typical alternatives, because of their advantages of easy construction and good performance. Although their seismic behaviors have been extensively investigated, limited studies have been devoted to exploring their dynamic responses and vulnerability to rockfall impacts. To this end, detailed finite element (FE) models were established in this study, to investigate the dynamic behavior and vulnerability of bridge structures with different cross-sections subjected to rockfall impact loading. Key modeling issues, such as modeling RC columns under both impact loading and the initial permanent loads prior to impact, were examined and addressed by high-resolution FE simulations. The effects of the rockfall diameter, impact velocity, and impact height on the dynamic behaviors of the columns, such as the impact force, lateral displacement, and residual axial capacity, were carefully investigated by using the calibrated FE models. Comparison of the dynamic behaviors of the circular and square columns indicated that the impact-resistance performance of the former was remarkably superior to that of the latter, for the same amount of materials used. A vulnerability analysis procedure based on the response surface model and Monte Carlo simulations was proposed, to investigate the probability of various damage levels for both the circular and square columns under rockfall impacts. Good agreement was achieved for the impact-induced responses obtained from the high-resolution FE simulations and the surrogate response surface models. The vulnerability analysis results further confirmed the disadvantage of the square columns for application in mountainous areas, owing to a relatively high risk of rockfall impact. The vulnerability analysis procedure proposed in this paper will assist researchers to investigate the damage and vulnerability of RC column structures subjected to impact loading.

落石灾害对山区的桥梁结构构成了重大威胁。山区大多数被破坏的桥梁结构都受到落石的不同程度的影响。具有圆形和正方形横截面的钢筋混凝土（RC）柱由于其易于施工且性能优良的优点而广泛用于桥梁结构中。尽管已经对其地震行为进行了广泛研究，但有限的研究致力于探索其动力响应和对落石冲击的脆弱性。为此，在本研究中建立了详细的有限元（FE）模型，以研究承受落石冲击载荷的不同横截面桥梁结构的动力特性和易损性。关键建模问题 例如，通过高分辨率有限元模拟来检查和解决诸如在冲击载荷和冲击之前的初始永久载荷下对RC柱建模的问题。使用校准的有限元模型仔细研究了落石直径，冲击速度和冲击高度对立柱动力学行为的影响，例如冲击力，横向位移和残余轴向承载力。比较圆柱和方柱的动力学行为表明，在使用相同数量的材料的情况下，前者的耐冲击性能明显优于后者。提出了基于响应面模型和蒙特卡洛模拟的脆弱性分析程序，调查在落石冲击下圆形和方形圆柱体遭受各种破坏的可能性。从高分辨率有限元模拟和替代响应面模型获得的冲击诱导响应已达成良好协议。易损性分析结果进一步证实了方柱在山区的应用的缺点，因为落石撞击的风险相对较高。本文提出的脆弱性分析程序将有助于研究人员研究承受冲击载荷的RC柱结构的损伤和脆弱性。易损性分析结果进一步证实了方柱在山区的应用的缺点，因为落石撞击的风险相对较高。本文提出的脆弱性分析程序将帮助研究人员研究承受冲击载荷的RC柱结构的损伤和脆弱性。易损性分析结果进一步证实了方柱在山区的应用的缺点，因为落石撞击的风险相对较高。本文提出的脆弱性分析程序将有助于研究人员研究承受冲击载荷的RC柱结构的损伤和脆弱性。