# Investigation of the Structural Dynamic Behavior of the Frontiuns Gate
## 1 Introduction  
The Hellenistic and Roman city of Hierapolis in Phrygia is one of the most important archaeological sites known from the Roman world. Hierapolis of Phrygia is located in southwestern Anatolia about 200 km east of Izmir and the Aegean coast. The urban area stretches over a traverting shelf looking onto the broad and fertile valley of the Curiksu River, the ancient Lykos [1; 2; 3; 4]. The city was probably established by [PERSON] of Pergamum in 190 BC [1; 2; 3]. In Roman times, Hierapolis was an important Asian city characterized by many buildings in traverting and marble; during the Early Byzantine period the city became the metropolis of Phrygia, a very important site due to the presence of the tomb of the Apostle [PERSON] [5]. The region has a high seismic activity due to a fault line running right below the city for more than a kilometer, applying a NE-SW horizontal stretching to the area [6]. In the first century BC, several earthquakes are known to have caused heavy damage. However, the city was rebuilt during the reign of the Roman emperor [PERSON] in AD 14-37. After a major earthquake in the middle of the seventh century AD, the city was severely damaged, but it survived until a new major earthquake in 1354. During the following centuries, Ottoman houses and small farms were constructed in the ruins of the urban area [5]. Between 1653 and 1889, the region faced six devastating earthquakes which caused serious damage [7; 8; 9; 10]. Under the auspices of the Flavian proconsul [PERSON], a monumental gate was built at the northern edge of the city, in the first century AD, and the adjacent part of the main street was extended and framed by a Doric colonnade [11]. The gate has three openings in squared tavertine blocks, with masonry arches, flanked by two round towers. Under the directorship of [PERSON] from the Turin Polytechnic Institute, the Missione Archeologica Italiana (MAIER) was set up in 1957, and restorations on the Frontiuns Gate progressed [12]. Archaeological surveys have been carried out in the urban area and in the territory surrounding the ancient city to collect information [13]. The Frontinus Gate, which is the monumental entrance to Hierapolis (Figure 1), suffered damage from earthquakes in the fourth and seventh centuries, after which some reconstruction interventions were applied [12; 14]. One of the towers of the opening is still in good condition today. Almost half of the other tower collapsed and was damaged from destructive earthquakes and other natural disasters. Since 1988, the site has been included in the UNESCO World Heritage List with emphasis on the extraordinary natural conditions, the Greco-Roman thermal installations, and the Christian monuments [15]; thus the Frontinus Gate and other monuments at the site have great importance in providing the present generation a connection to its past. The aim of this study is to investigate the dynamic characteristics of the Frontinus Gate and simulate the seismic behavior of the structure under the seismic excitations that can be expected at the site, in order to predict the potential damage levels. The tool employed is the discrete element method (DEM), a numerical technique increasingly applied to the analysis of masonry, in particular of historical heritage structures [16]. The analysis of masonry structures may be performed either by equivalent continuum models or by discrete block models [17]. The former, based on the material homogenization approach, are typically preferred for large complex structures, while the discrete (or discontinuum) methods, where DEM is included, were initially applied to components or simple structures, but are presently capable of addressing more complex systems [18]. DEM represents the structure as a system of discrete blocks, thus closely reproducing the physical nature of masonry.