## 1 Introduction  
Arch bridges are one of the oldest types of man-made structures and are still widely used when constructing roads in areas with deep ravines. Reinforced concrete (RC) arch bridges are both aesthetic and economic alternatives to large-span structures and thus perform a useful role in the hierarchy of major bridges. Over the past three decades, the introduction of high-strength materials and the development of new emotion techniques have led to a significant increase in the number of RC arch bridges [1; 2; 3; 4]. Concrete arch bridges take one of the following forms: tied-arch bridges, deck arch bridges, and through arch bridges [5]. Among these, the deck arch bridge is the most widely favored because the arch resists gravity load in compression. The main components of a deck arch bridge are its arch, piers, and superstructure. The arch can be constructed in a number of different cross-section configurations using various materials and techniques, including a single or multicell-box, box-ribs, a solid cross-section, and composite concrete filled by steel tubes [1]. Because of the high torsional rigidity and vital bending capacity required for most such structures, closed-form cross-sections tend to be more popular for arch bridges. The bridge piers that connect the superstructure to the arch consist of either single rectangular wall-shape columns or a pair of rectangular RC piers aligned with the edges of the deck. The main focus of this study is on the dynamic characteristics of deck arch bridge with pairs of rectangular RC columns, but the results would also be applicable to bridges with wall-shaped columns. The seismic behavior of an arch bridge is complex. The structure's ductile capacity will be significantly reduced due to the large axial forces acting on the arch components [6; 7]. The high complexity and widely varying load experienced by individual bridge members during a seismic event make it essential to improve our understanding of the ductility capacity of the structure under normal circumstances and hence support a realistic estimation of the ductility demand during an earthquake. There are several reports in the literature that focus on the seismic response of arch bridges and suggest potential retrofitting techniques to help them withstand seismic events [8; 9; 10; 11; 12; 13]. Most of the previous researchers adopted a displacement-based approach based on incorporating state-of-the-art design concepts such as performance-based design procedures for steel arch bridges under seismic loads. Pushover analyses to determine the ultimate state, taking into account the failure criterion proposed for thin walled steel members, were used to determine the displacement capacities of individual bridge components. [PERSON] et al. [14] and [PERSON] et al. [15] investigated the seismic responses of reinforced concrete arch bridges under particular ground motions. A state-of-art review of the vulnerability and structural damage suffered by RC arch bridges during the bridge life-cycle performed by [PERSON] and [PERSON] [16] classified the characteristics and rules for the various types of distress suffered by such bridges, along with the reasons for their occurrence, providing a useful reference to guide their design, construction and maintenance. [PERSON] et al. [17] developed a new design approach based on direct displacement-based seismic factors for RC arch bridges, proposing new expressions for the yield drift and deformation capacity of bridge columns, while [PERSON] and [PERSON] [18] performed a comparative study on 55 existing arch bridges and developed empirical trends to describe the properties and geometrical ratios related to important attributes such as their proportions, stiffness, slenderness, and efficiency. The current seismic design practices issued by bodies such as AASHTO [19] and the California Department of Transportation [18] recommend the application of modal response spectrum or equivalent static analyses to design RC arch bridges categorized as irregular bridges.