## 2 Structure of the Representative Bridge Used in the Case Study  
An upper-deck RC arch bridge design was designed for the case study analyses (Figure 1). A response spectrum analysis (RSA) was performed when designing the bridge components based on the AASHTO [19] specifications and the _Caltrans Seismic Design Criteria_[20]. The design spectrum provided in the AASHTO specification for a peak ground motion of 0.35 g, which is representative of a strong earthquake intensity level, and a site class of D was selected. The reinforced concrete arch of the bridge consists of a double cell-box cross-section with a constant outer dimension (\(b\times h\)) of 10 m \(\times\) 3 m (Figure 2). The total length of the bridge was taken to be 400 m, with a reinforced concrete arch length of 212 m and a rise at the crown of 52 m, giving a rise-to-span ratio of 0.25. A triple-box cross-section was utilized close to the arch abutments in order to enhance the shear and bending stiffness of the bridge structure. Vertical RC diagrams were incorporated inside the RC arch at the point where the columns rest on the arch. Figure 2 shows the transverse section of the model bridge. The composite superstructure, which is 21 m wide and 2.10 m high, consists of a 25 cm reinforced concrete deck-plate supported by two steel box-shaped girders placed 4 m apart. Fixed supports are assumed at the springings of the arch and at the bottom of piers P2, P11 and P13 to represent the foundation over a bedrock site. This is a widely accepted approach used for the majority of arch bridges; the effect of soil-structure interactions are also generally neglected [11; 12; 13]. The composite deck is supported on longitudinal movable bearings located at the abutments and at the stiff short central piers P5-P8 and P12 (Figure 1). As shown in Figure 2, two types of movable bearing are modeled, namely pinned connections and sliding bearings that support the vertical action only. The bridge deck is highly flexible and may thus experience significant horizontal displacement  
Figure 1: Longitudinal view of the model RC arch bridge designed for this study. All measurements are in m.  
Figure 2: Cross section of the composite deck and RC arch at the P6 position. All measurements are in cm. during a major earthquake event. Any large displacement will result in adverse impacts on all the fixed bearings; hence, viscous dampers of the type developed by [PERSON] et al. [24] as shown in Figure 3, each with a 2000 KN capacity, are included in the model at both ends of the deck in order to reduce the seismic response of the bridge. These nonlinear Fluid Viscous Dampers (NFVD) were modeled here using the following practical relationship between the internal force acting on the damper, \(F(N)\), and the Velocity, \(V\) (in m/s) derived experimentally by [PERSON] and [PERSON] [25]:  
\[F=CV^{n}sgn(V) \tag{1}\]  
where \(C\) (\(N\)(sm\({}^{-1}\))\({}^{n}\)) is the damping constant; velocity exponent, \(n\), defines the type of device and introduces the nonlinearity of viscous damper; and \(sgn\) is sign or signum function which is used for defining the sign of a real number. The mechanical characteristics of the damper [24] used in the present study are modeled with \(n\) and \(V\) values of 0.40 and 0.34 (m\(\cdot\)s\({}^{-1}\)), respectively. Figure 3 shows a fluid viscus damper of the type typically used in bridge abutments. A total of 13 double columns, shown in cross-section in Figure 4, were defined to support the composite deck. The transverse distance between the columns is 7.60 m, which matches the girder spacing in the superstructure. Figure 4: Cross section of the double piers in the model RC arch bridge. All measurements are in cm. Figure 3: Typical nonlinear fluid viscous damper [24]. European concrete classes [26] C45/55 and C35/45, with strengths in compression of 45 MPa and 35 MPa, respectively, were utilized for the arch and columns. The modulus of elasticity for both concrete materials was 3600 GPA.