# Influence of Multiple-Support Excitation on Seismic Response of Reinforced Concrete Arch Bridges
## 1 Introduction  
Improvement of seismic design methods always follows new observations and analyses of damage and collapse due to major earthquakes. Conducted studies identified spatial variation of ground motion as a frequent cause of unfavorable response of long-span bridges, e.g., [1; 2], but this phenomenon is usually not taken into account in seismic design to simplify the calculation procedure. Since length and spans of larger bridges are comparable to the seismic wavelength, it is obvious that all bridge supports cannot be excited simultaneously. Additional differences in the seismic input to different supports arise from changes in the frequency content and amplitude of the seismic waves propagating from the base rock to the ground surface. Simple examples of multiple-support excitations include the unseating of the superstructure due to differential displacements of its supports [2; 3; 4]. The pioneering studies of the phenomenon of ground motion spatial variation occurred in the 1960s [5], while significant improvements in the understanding of the phenomenon may be attributed to data recorded in strong-motion arrays such as SMART-1 (Strong Motion Array in Taiwan--Phase 1) [6], El Centro Differential Array, Thessaloniki in Greece, Pinyon Flat in the USA, among others [7; 8]. The main causes of spatial variability in ground motions are attributed to coherency loss (loss of coherency of seismic waves due to reflections and refractions of waves in the heterogeneous medium of the ground and due to superposition of waves arriving from a seismic source), wave-passage effect (time delay in arrival of seismic waves to different supports of the structure), attenuation effects (decay of amplitudes and energy of seismic wave propagating through the ground) and local site conditions (different geological conditions at different supports influence frequency content and amplitudes of seismic waves) [9], schematically depicted in Figure 1. The interested reader may refer to [7; 10; 11] for a comprehensive overview of the subject. In general, random vibration methods, response spectrum methods and deterministic methods are used in the study of the multiple-support excitation effect in engineering applications. Although, numerous studies in which response of bridges to multiple-support excitation was analyzed using different methods may be found in literature (e.g., [2; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]), very little research has been devoted to arch bridges. Some detailed studies dealt with arch structures in general (e.g., [23; 24; 25]), while studies of arch bridges mostly considered steel bridges [26; 27; 28]. The most important conclusions from some of those studies will be summarized below. The results of the stochastic response of incompressible circular arches to multiple-support excitation presented in [23] showed that neglecting multiple-support excitation effect can underestimate, but also overestimate the response, depending on the properties of the arches, response quantities and the seismic excitation. The author concluded that wave-passage effect was more detrimental than the loss of coherence. However, [PERSON] et al. [26] studied the responses of two-deck steel arch bridges of large span and showed that the coherency loss is also very important for response in addition to wave-passage effect. Authors concluded that uniform excitation is in general unacceptable for considered bridges. In the research [28] in which deck steel arch bridges were analyzed, it was concluded that the response to the multiple-support excitation was less detrimental than to the uniform one in the vertical and transverse directions, whereas in the longitudinal direction the multiple-support excitation significantly affects the response and should not be neglected. Very limited investigations of concrete arch bridges found in literature are those in [29; 30; 31; 32; 33]. The seismic response of an existing reinforced concrete arch bridge of 150 m span to uniform and multiple-support excitation was investigated in [29].