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applied sciences Article Investigation of the Structural Dynamic Behavior of the Frontinus Gate Özden Saygılı 1 and José V. Lemos 2, * 1 Department of Civil Engineering, Yeditepe University, Istanbul 34755, Turkey; ozden.saygili@yeditepe.edu.tr 2 Department of Dams, National Laboratory for Civil Engineering (LNEC), 1700-066 Lisboa, Portugal * Correspondence: vlemos@lnec.pt Received: 28 July 2020; Accepted: 20 August 2020; Published: 22 August 2020 Abstract: The Western Anatolia Region of Turkey is an important region of high seismic activity. The active dynamics of the region are shaped by a compression and expansion mechanism. This active mechanism is still ongoing and causes strong seismic activity in the region. The Frontinus Gate is a monument in the Roman city of Hierapolis of Phrygia located in southwestern Anatolia. The aim of this study is to investigate the seismic behavior of this stone masonry structure using discrete element modeling. For this purpose, nonlinear dynamic analyses were performed to simulate the structural response of the gate under seismic excitation. Deformation, damage, and failure patterns induced in the masonry gate for different levels of seismic action are evaluated and discussed. An earthquake with a return period of 475 years is expected to cause some damage, but no collapse, while for a return period of 2475 years, the models indicate collapse of the monument. Keywords: stone masonry; discrete element modeling; nonlinear dynamic analysis 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 travertine shelf looking onto the broad and fertile valley of the Çürüksu River, the ancient Lykos [1–4]. The city was probably established by Eumenes II of Pergamum in 190 BC [1–3]. In Roman times, Hierapolis was an important Asian city characterized by many buildings in travertine 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 St Philip [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 Tiberius 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 [7–10]. Under the auspices of the Flavian proconsul Sextus Iulius Frontinus, 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 travertine blocks, with masonry arches, flanked by two round towers. Under the directorship of Paolo Verzone from the Turin Polytechnic Institute, the Missione Archeologica Italiana (MAIER) was set up in 1957, and restorations on the Frontinus 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]. Appl. Sci. 2020, 10, 5821; doi:10.3390/app10175821 www.mdpi.com/journal/applsci
columns [20], to the more recent analyses of towers [21], obelisks [22], and stone minarets [23]. More complex geometries are now being addressed, such as arch bridges [24], domes [25], various types of buildings [26,27], or archaeological structures [28]. Comparisons of DEM results with the behavior observed in shaking table tests of scaled models have provided a progressive validation of its performance. Appl. Sci. 2020, 10,Experiments 5821 with marble drum columns provided the earlier assessment of DEM 2 of 16 representations [29]. Extensive shaking table tests of single stone blocks rocking under harmonic and seismic records have confirmed the good performance of the numerical method [30]. Comparisons The Frontinus with tests of more Gate, which structures complex is the monumental entrance have also been to Hierapolis undertaken, namely(Figure masonry1), suffered walls underdamage out- from earthquakes in the fourth and seventh centuries, after which some reconstruction of-plane loads [31,32], or the scaled model of a mosque [33]. DEM has been applied to many historical interventions were applied structures, [12,14]. namely One of thecolumns the Parthenon towers [20,29], of the opening is still walls the Colosseum in good [26],condition a Roman today. temple Almost [27], an half of the other tower collapsed and was damaged from destructive earthquakes obelisk [22], historical minarets [23], or the dome of Florence cathedral [25]. In the present and other natural study, the disasters. Since 1988, the site has been included in the UNESCO World Heritage List effect of the wall curvature on the stability of the round towers is an issue to be examined. The DEM with emphasis on the extraordinary models presented herein natural conditions, are intended not the onlyGreco-Roman thermal under for safety assessment installations, and the large seismic Christian actions, but monuments [15]; thus the Frontinus Gate and other monuments at the site have also as a means to quantify the damage to the structure that can be expected from lower intensity,great importance in providing more likelythe present generation a connection to its past. events. The Frontinus Figure 1. The Frontinus Gate Gate in Hierapolis. 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. It is capable of simulating the nonlinear phenomena of slip and separation along the joints, which are typically observed in masonry structures under seismic loads, allowing the analysis to proceed into the large displacement range to follow the processes of damage and progressive collapse [19]. DEM models have been frequently applied to tall, slender structures, from the early work on the Parthenon columns [20], to the more recent analyses of towers [21], obelisks [22], and stone minarets [23]. More complex geometries are now being addressed, such as arch bridges [24], domes [25], various types of buildings [26,27], or archaeological structures [28]. Comparisons of DEM results with the behavior observed in shaking table tests of scaled models have provided a progressive validation of its performance. Experiments with marble drum columns provided the earlier assessment of DEM representations [29]. Extensive shaking table tests of single stone blocks rocking under harmonic and seismic records have confirmed the good performance of the numerical method [30]. Comparisons with tests of more complex structures have also been undertaken, namely masonry walls under out-of-plane loads [31,32], or the scaled model of a mosque [33]. DEM has been applied to many historical structures, namely the Parthenon columns [20,29], the Colosseum walls [26], a Roman temple [27], an obelisk [22], historical minarets [23], or the dome of Florence cathedral [25]. In the present study, the effect of the wall curvature on the stability of the round towers is an issue to be examined. The DEM models presented herein are intended not only for safety assessment under large seismic actions, but also as a means to quantify the damage to the structure that can be expected from lower intensity, more likely events.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 16 Appl. Sci. 2020, 10, 5821 3 of 16 2. Seismicity of the Region 2. Seismicity The present of the Region tectonic structure of Turkey has been formed by active interactions developed by the continental The present collision tectonicofstructure the Arabian plate with of Turkey the Eurasian has been formed by plate in the active east, and subduction interactions developed by of the African plate beneath the Aegean [34,35]. These tectonic motions caused the the continental collision of the Arabian plate with the Eurasian plate in the east, and subduction of development of two significant the Africanactive faults, the plate beneath theNorth Aegean Anatolian Fault (NAF) [34,35]. These tectonicand the East motions Anatolian caused Fault (EAF), the development of and two the westward significant activeextrusion faults, theofNorth the Anatolian plate.(NAF) Anatolian Fault Anotherand result the EastofAnatolian the motion Faultis(EAF), the ongoing and the lithospheric scale extension westward extrusion caused byplate. of the Anatolian trenchAnother roll-back in the result of Hellenic the motion subduction zone [36,37]. is the ongoing As a lithospheric consequence scale extension of caused the active tectonic by trench motions, roll-back strong in the extensional Hellenic deformation subduction zone [36,37].developed in western As a consequence Anatolia. of the active tectonic motions, strong extensional deformation developed in western Anatolia. Before Before instrumental instrumental recording recording (1900), (1900), only only earthquakes earthquakes having having magnitudes magnitudes greater greater than than 4.5 4.5 were were reported. reported. One of the reported destructive earthquakes occurred in Hierapolis and Phrygia in 494BC. One of the reported destructive earthquakes occurred in Hierapolis and Phrygia in 494 BC. Then, anotherdevastating Then, another devastatingearthquake earthquake occurred occurred in Laodicea in Laodicea andand Hierapolis Hierapolis in 60 inBC.60Both BC.events Both events caused caused heavy damage heavy damage in the Throughout in the regions. regions. Throughout history, history, similar similar destructive destructive earthquakesearthquakes have occurred have in occurred this regioninand thissurrounding region and areas. surrounding Importantareas. Important historical historical earthquakes withearthquakes magnitudeswith magnitudes between Mw 6.2 between and Mw Mw 6.2 and affected 6.6 heavily Mw 6.6 Laodicea heavily affected Laodicea and and Hierapolis. In 26Hierapolis. In 26 BCwith BC an earthquake an earthquake a magnitude withof aMwmagnitude of Mw 6.2 completely destroyed the ancient city. In 17 BC 6.2 completely destroyed the ancient city. In 17 BC an earthquake with a magnitude of Mw 6.6 an earthquake with a magnitude of Mw 6.6 resulted in damages in 12 ancient cities, resulted in damages in 12 ancient cities, causing surface ruptures and landslides. causing surface ruptures and landslides. Focusing on Denizli’s geologic and tectonic structure (Figure 2), the N-S extension system in Focusing Western Turkey onandDenizli’s geologic the Africa and tectonicunder plate subducting structure (Figure 2), the Anatolian the strongly plate N-S extension affect thesystem Denizliin Western Turkey and the Africa plate subducting under the Anatolian plate strongly region and surrounding areas. The most active grabens in the province are the NW-SE extending Gediz affect the Denizli region grabenandand surrounding the E-W extending areas. Menderes The most graben active grabens (Figure 2).in the The province Denizli basinare the NW-SEclose is situated extending to the Gediz graben confluence of and thesethetwoE-W extending Menderes graben (Figure 2). The Denizli basin is situated close grabens. to the confluence of these two grabens. Figure Figure 2. 2.AAsimplified simplifiedtectonic, tectonic,seismic seismicactivity, activity,and andseismic seismicstation stationmap mapof ofDenizli Denizliand andsurroundings. surroundings.
Appl. Sci. 2020, 10, 5821 Appl. x FOR PEER REVIEW 4 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 16 As seen in Figure 3, the magnitude range of most of the earthquakes in this region is from 2 to 4. This Asindicates As seenin seen inFigure Figure 3,3,the that active the magnitude magnitude crustal rangeof range movements ofmost and most ofofthe numerous theearthquakes earthquakes outflow inin thermal this this region region waters is from 2 to is responsible are from 2 to 4. 4. This This indicates indicates thatthat active active crustal crustal movements movements and and numerous numerous outflow outflow thermal thermal waters waters for high micro-seismic activity. Denizli is one of the most seismic regions in Turkey. Figure 4 shows are are responsible responsible for for number high the high micro-seismic micro-seismic of earthquakesactivity. activity. with Denizli Denizli is one is one depth of most of the distribution thefor most seismic seismic Denizli. regions regions in Turkey. in Turkey. As mentioned, Figure Figure Denizli was 4 shows 4 shows the destroyed the number numberof of earthquakes earthquakes with with depth depth distribution distribution for for Denizli. Denizli. As As mentioned, mentioned, Denizli Denizli by an earthquake with a magnitude of 4.7 on 19 August 1976. Although it was a moderate earthquake, was was destroyed destroyed by by an an earthquake earthquake withwith a a magnitude magnitude of of 4.74.7 on on 1919 August August 1976. 1976. Although Although it resulted in the collapse of 40 houses and heavy damage to 1284 houses [38]. itit was was aa moderate moderate earthquake, earthquake, ititresulted resultedin inthe thecollapse collapseof of40 40houses housesandandheavy heavydamage damageto to1284 1284houses houses[38]. [38]. Figure 3. Distribution of earthquakes with their magnitudes from 2000 to 20 December 2018. Figure 3. Distribution of earthquakes with their magnitudes from 2000 to 20 December 2018. Figure 3. Distribution of earthquakes with their magnitudes from 2000 to 20 December 2018. Figure Figure 4. Number of 4. Number of earthquakes earthquakes with with depth depth distribution distribution for for Denizli Denizli from from 2000 2000 to to 20 20 December December 2018. 2018. Figure 4. Number of earthquakes with depth distribution for Denizli from 2000 to 20 December 2018. 3. Numerical Model 3. Numerical Model 3. Numerical The FrontinusModel Gate has three openings in squared travertine blocks, with masonry arches, flanked The Frontinus Gate has three openings in squared travertine blocks, with masonry arches, by two round towers. ThebyFrontinus Some Gate of three has the blocks aboveinthe openings arches travertine squared collapsed and/or blocks,were withdamaged. masonry One of arches, flanked two round towers. Some of the blocks above the arches collapsed and/or were damaged. the round flanked towers by two of round the opening towers. Someis still in good of theisblocks condition today, standing at a maximum height of One of the round towers of the opening still inabove goodthe arches collapsed condition and/or were today, standing damaged. at a maximum 8.17 m. The One ofofthe external and internal diameter of this tower are 10.20 m and 9.09 m, respectively. Almost height 8.17round m. The towers externalof and the opening is still inofgood internal diameter condition this tower today, are 10.20 standing m and 9.09 m,at respectively. a maximum half of the height of other 8.17 tower has collapsed. This damaged tower is 3.18 m at its highest point, with 8.25 m Almost half ofm. theThe external other towerandhasinternal collapsed.diameter of this tower This damaged tower are is10.20 3.18 m m at andits9.09 m, respectively. highest point, with and 7.11 Almost m external half7.11 of the and internal other tower diameters, respectively. Two of the three masonry segmental arched 8.25 m and m external and has collapsed. internal This respectively. diameters, damaged tower Two is of 3.18themthree at itsmasonry highest point, with segmental doorways 8.25 m andhave 7.11 almost m the same external and dimensions. internal The intrados diameters, are circular respectively. Two but of theless than three a semicircle masonry with segmental arched doorways have almost the same dimensions. The intrados are circular but less than a arched doorways have almost the same dimensions. The intrados are circular but less than a
Appl. Sci. 2020, 10, 5821 5 of 16 4.58 m above ground level [1,2,4,5]. In the literature, there are several archeological, experimental and numerical studies investigating the material characteristics of the stone masonry structures in Hierapolis [8,9,39–42]. Most of these studies emphasize the material properties of travertine stone block masonry and ashlar (regular) masonry based on destructive and nondestructive testing procedures. The Frontinus Gate has traces of damage to the stones at round towers and arches from earthquakes or from other natural disasters. The average mechanical properties of the Frontinus Gate were determined using information inferred from previous studies mentioned above and considered obvious damage. In this study, elasticity and shear modulus were assumed as 2800 MPa and 860 MPa, respectively. The numerical model was created with the discrete element method code 3DEC [43], widely used in masonry models [20–33]. 3DEC represents the discontinuous medium as an assemblage of discrete blocks, with the discontinuities treated as interfaces between the blocks. 3DEC allows large displacements and rotations of blocks, thus being able to simulate structural collapse. In this study, rigid blocks have been employed, as often done in the analysis of structures made of strong stone units, for which deformation and failure modes are governed by sliding or separation along discontinuities [19]. The solution is based on the integration of the equations of motion of the blocks, using an explicit time-stepping algorithm. The 3 translational equations of motion of a rigid block center of mass may be expressed as: .. . m ui + α m ui = fi (1) where ui denotes the displacement vector of the block center; m, the block mass; and α, the mass-proportional viscous damping parameter, which reproduces the energy losses in the system beyond frictional dissipation. The force vector fi is the sum of the applied forces, including self-weight, and the contact forces, which are a function of the relative block displacements, and therefore includes the elastic forces. The 3 rotational degrees of freedom are governed by Euler’s equations, expressed in the principal axes of inertia of the block as: . I1 ω1 + α I1 ω1 + (I3 − I2 ) ω3 ω2 = m1 . I2 ω2 + α I2 ω2 + (I1 − I3 ) ω1 ω3 = m2 (2) . I3 ω3 + α I3 ω3 + (I2 − I1 ) ω2 ω1 = m3 where ωi denotes the rotational velocity vector; Ii , the principal mass moments of inertia. The moment mi is the sum of moments produced by the contact forces and the applied forces. The 3DEC model is shown in Figure 5a. The geometry was based on drawings of the structure. Some simplifications were adopted, for example the smaller blocks around the tower openings were not considered. In order to reproduce the correct structural deformability, the joint stiffnesses are based on the dimensions of the blocks adjacent to the joint. The normal joint stiffness is given by kn = E/d, where E is the Young’s modulus and d the average of the dimensions normal to the joint of the 2 blocks in contact; the shear stiffness is given by ks = G/d, where G is the shear modulus. These formulas were applied to assign the stiffness to each group of joints (e.g., bed joints and vertical joints of each layer of the towers, joints of the pillars, and arched gates). A Coulomb friction law was adopted as the joint constitutive model, assuming a friction angle of 30◦ , zero cohesion, and zero tensile strength. This friction angle is a conservative estimate, in the lower range of the available data. The material properties are summarized in Table 1.
In 3DEC, static solutions under gravity loading are first obtained by a relaxation solution algorithm. Then, the dynamic analysis is performed by prescribing the seismic input motion at the base block. The time step required for stability of the explicit algorithm was in the order of 10-5 s, which allows an accurate representation of the block motion and contact updates. Histories of Appl.velocity, displacement, Sci. 2020, 10, 5821 and normal and shear stresses were recorded at the locations shown in Figure 6 of 16 5b, where larger movements are to be expected. (a) (b) Figure Figure 5. (a) 5. (a) Numerical Numerical model model of of FrontinusGate Frontinus GateininHierapolis; Hierapolis;(b) (b) history history locations. locations. 4. Nonlinear Dynamic Analysis Table 1. Material properties. Seismic behavior of the Frontinus Unit Gate weightwas simulated 24 through kN/m3non-linear dynamic analyses. The objective is to discuss the dynamic Young’sglobal response of the2800 modulus masonry MPa gate to an earthquake ground motion which is consistent with Shear themodulus earthquake hazard 860 MPa in accordance with the Turkish levels, Joint friction angle 0 Building Seismic Code 2019. The first seismic input was given30 by a recorded earthquake, the velocity Joint cohesion 0 records of the event that occurred in Dinar (Mw 6.0) on Oct 10, 1995 downloaded from ground PEER Joint tensile strength 0 NGA strong motion database. In addition to the real ground motion, four synthetic acceleration time series were generated. First, for the coordinates of the Frontinus Gate, target response spectrums were In 3DEC, static established solutions for two groundunder gravity motion loading levels. Theare first first obtained by earthquake a relaxation ground motion solution algorithm. level has a 2% Then, the dynamic probability to beanalysis exceeded is performed in 50 years,by prescribing with a return the seismic period input of 2475 motion years (levelat1).theThe base block. second earthquake ground motion level has a 10% probability to be exceeded in 50 years, The time step required for stability of the explicit algorithm was in the order of 10 s, which allows an -5 with a return period of 475representation accurate years (level 2). of Forthe each target block response motion and spectrum, two acceleration contact updates. Historiestime series were of velocity, generated displacement, and based normal on and inter shear plate regimes stressesand linear were site effect. recorded at the locations shown in Figure 5b, where larger movements Selected are toand be created expected. earthquakes were best fit with the adopted target spectrums. Comparison of the response spectrum of the Dinar earthquake (Mw 6.0) on Oct 10, 1995, with the target spectrum for groundDynamic 4. Nonlinear motion level 2, is shown in Figure 6. Comparisons of the response spectrum of synthetic Analysis loadings with corresponding target spectrums are plotted in Figure 7. Seismic behavior of the Frontinus Gate was simulated through non-linear dynamic analyses. These real and synthetic ground motions were applied as base excitation to the numerical model. The objective is to discuss the dynamic global response of the masonry gate to an earthquake ground It is assumed that the structure is subjected to earthquakes in both horizontal directions. Due to the motion fact which is seismic that the consistent withinthe effects twoearthquake orthogonalhazard levels, directions arein accordance unlikely withtheir to reach the maximum Turkish Building value Seismic at theCode same2019. time,The thefirst seismic orthogonal 30 percent input was given loading byrule a recorded earthquake, is applied. Since thethe twovelocity records time series wereof the event that occurred in Dinar (Mw 6.0) on Oct 10, 1995 downloaded from ground generated for each ground motion level, 100% of the synthetic earthquake is combined with 30% of PEER NGA strong motion the database. In addition other synthetic groundtomotion the realinground motion, four the orthogonal synthetic direction. For acceleration ground motion timelevel series 1, were two generated. First, for the coordinates of the Frontinus Gate, target response spectrums were established for two ground motion levels. The first earthquake ground motion level has a 2% probability to be exceeded in 50 years, with a return period of 2475 years (level 1). The second earthquake ground motion level has a 10% probability to be exceeded in 50 years, with a return period of 475 years (level 2). For each target response spectrum, two acceleration time series were generated based on inter plate regimes and linear site effect.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 16 Appl. Sci. 2020, 10, 5821 7 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 16 dynamic analyses were performed, as for 100% of the first synthetic earthquake combined with 30% of dynamic theSelected second synthetic analyses and ground were created motion, performed, earthquakes as and for were 30% 100% best of fitof thethe the with first first synthetic synthetic adopted earthquake earthquake target combined combined spectrums. with with Comparison 30% of 100% the of the of response the secondsecond synthetic synthetic spectrum of groundground the Dinar motion. motion, The and 30% earthquake same (Mwof6.0) procedure theon first was Octsynthetic applied for 10, 1995,earthquake the dynamic combined with the target with spectrum analysis 100% for groundof of the the second second motion ground synthetic level motion 2, is shown inlevel. ground motion. Figure The same procedure 6. Comparisons was applied of the response spectrumfor of the dynamic synthetic analysiswith loadings of the second ground corresponding motion target level. are plotted in Figure 7. spectrums Figure 6. Comparison of target response spectrum created for ground motion level 2 and response Comparison Figure 6. of spectrum of target response spectrum created for ground motion level 2 and response Figure 6. Dinar, Turkey Comparison of1995 earthquake. target response spectrum created for ground motion level 2 and response spectrum of Dinar, Turkey 1995 earthquake. spectrum of Dinar, Turkey 1995 earthquake. (a) (a) (b) Figure (b) ground motion level 1 with corresponding Figure7.7.(a) (a)Comparison Comparisonofoftarget targetresponse responsespectrum spectrumfor for ground motion level 1 with corresponding synthetic Figure earthquake; synthetic 7.earthquake;(b) (b)Comparison (a) Comparison Comparison ofoftarget target of target response response response spectrum spectrum forspectrumfor forground levelmotion ground ground motion 1 with level motion level22with with corresponding corresponding corresponding synthetic earthquake. synthetic (b) synthetic earthquake; earthquake. Comparison of target response spectrum for ground motion level 2 with corresponding synthetic earthquake. Identifying the synthetic These real and dynamic ground characteristics motions of theapplied were masonry structures as base under excitation thenumerical to the assumption of model. elastic behavior It is assumed is that an the important structure first is step subjected in the to study, as earthquakes it provides in both a good horizontal understanding directions. Identifying the dynamic characteristics of the masonry structures under the assumption of Due of tothe the dynamic fact elastic response that behavior the seismicisunder effects low in two an important intensity first stepground orthogonal shaking, indirections the study, are ituntil as unlikely nonlinear to reach provides phenomena their a good maximum become understanding value of the dominant. The first ten natural frequencies and eigenmodes of vibration dynamic response under low intensity ground shaking, until nonlinear phenomena become were calculated for the rigid dominant. The first ten natural frequencies and eigenmodes of vibration were calculated for the rigid
Appl. Sci. 2020, 10, 5821 8 of 16 at the same time, the 30 percent orthogonal loading rule is applied. Since the two time series were generated for each ground motion level, 100% of the synthetic earthquake is combined with 30% of the other synthetic ground motion in the orthogonal direction. For ground motion level 1, two dynamic analyses were performed, as for 100% of the first synthetic earthquake combined with 30% of the second synthetic ground Appl. Sci. 2020, 10, x FORmotion, and 30% of the first synthetic earthquake combined with 100%8 ofof16the PEER REVIEW second synthetic ground motion. The same procedure was applied for the dynamic analysis of the block second Appl. ground model. Sci. 10,The motion 2020, kinematic level. x FOR variables of the system of rigid blocks are the six degrees of freedom PEER REVIEW 8 of of 16 each block as three translations and three rotations. The global stiffness Identifying the dynamic characteristics of the masonry structures under the assumption of matrix for the rigid block systemmodel. block elastic behavior is assembled, is an based on Theimportant kinematic thestep first system variables ofinthe deformability system the study, of as governed rigid by a blocks are it provides the the joint stiffnesses. six degrees good The mass of freedom understanding ofofthe matrix each is obtained block as threefrom block masses translations and and threerotational rotations.inertia terms [36]. The global Vibration stiffness matrixmode shapes for the rigidasblock well dynamic response under low intensity ground shaking, until nonlinear phenomena become dominant. as their iscorresponding system assembled, based frequencies were determined. on the system deformability Frequencies governed for fivejoint by the dynamic eigenmodes stiffnesses. The massare The first ten natural frequencies and eigenmodes of vibration were calculated for the rigid block model. given inisTable matrix obtained 2. The fromshapes blockofmasses modesand 1, 3,rotational and 5 areinertia plotted in Figures terms 8 to 10. mode shapes as well [36]. Vibration The kinematic variables of the as their corresponding system were frequencies of rigid blocks are determined. the six degrees Frequencies for five of freedom dynamic of each block eigenmodes are as threegiven translations and three in Table 2. The shapes Tablerotations. The 2. Frequencies of modes global 1, 3, and for stiffness 5 dynamic 5 are matrix plotted eigenmodes. for the in Figures 8 to 10. rigid block system is assembled, based on the system deformability governed by the joint stiffnesses. The mass matrix is Mode Frequency (Hz) obtained from block masses and Table 2. Frequencies rotational inertia 1 for 5 dynamic terms eigenmodes.mode shapes as well as their [36]. Vibration 11.60 corresponding frequencies were determined. Mode2 Frequencies 12.00for Frequency five dynamic eigenmodes are given in (Hz) Table 2. The shapes of modes 1, 3, and 5 are 13plotted in 11.60 Figures 18.32 8–10. 24 19.98 12.00 Table 2. Frequencies 35 for 5 dynamic 22.64 eigenmodes. 18.32 4 19.98 Mode Frequency (Hz) The first period is approximately 0.09 5 seconds,22.64 corresponding to a bending mode shape on the horizontal plane. Mode 3 involves1 shear and torsional 11.60 movements, and mode 5 mostly the larger tower. TheIt first can period be seenis from approximately2 the displacement 0.09 seconds, 12.00 contourstofor magnitude corresponding mode 3mode a bending and mode 5 that shape on the displacements horizontal increase plane. Modealong 3 involves 3 shearofand the height the round 18.32 tower. torsional movements, and mode 5 mostly the larger 4 tower. It can be seen from the displacement 19.98 contours for mode 3 and mode 5 that magnitude 5 22.64 displacements increase along the height of the round tower. Figure8.8.First Figure Eigenmode. First Eigenmode. Figure 8. First Eigenmode. Figure9.9. Eigenmode Figure . Eigenmode 33. Figure 9. Eigenmode 3.
Appl. Sci. 2020, 10, 5821 9 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 16 Figure 10. Eigenmode 5. Figure 10. Eigenmode 5. The first period is approximately 0.09 seconds, corresponding to a bending mode shape on the In the analysis of the response under seismic action, the nonlinear properties of the joints were horizontal plane. Mode 3 involves shear and torsional movements, and mode 5 mostly the larger tower. applied. First, static analysis was carried out under self-weight. Then, nonlinear dynamic analyses It can bewereseenperformed from theunder displacement magnitude seismic loading. contours For the for mode Dinar, Turkey 19953earthquake and modewith 5 that displacements a duration of 29 increases along the height of the round tower. and increments of 0.005 s, the masonry gate model experienced the seismic excitations in horizontal In and the analysis of the response vertical directions under seismic simultaneously. action,response The structural the nonlinear properties of the numerical of the model joints were subjected to applied.theFirst, Dinar earthquake static analysisin terms of contour was carried outdiagram of the final displacement under self-weight. magnitude Then, nonlinear is presented dynamic analyses in Figure 11. were performed As isseismic under seen in loading. this figure,For thethe displacements increase Dinar, Turkey 1995along the height earthquake of the with round tower a duration of 29 s and the maximum displacement of 7.1 cm is obtained, particularly in areas and increments of 0.005 s, the masonry gate model experienced the seismic excitations in horizontal where the normal stresses are low. The connection of the round tower with the arched gate is also a critical location. and vertical directions simultaneously. The structural response of the numerical model subjected to In the following runs, for each ground motion level the numerical model subjected to synthetic the Dinar earthquake in terms of contour diagram of the final displacement magnitude is presented in earthquakes Appl. Sci. 2020, 10,seen in two horizontal x FORinPEER directions with a duration of 11 s. A total of four dynamic analyses Figure 11. were Asperformed is this REVIEW under figure, synthetictheloading displacements increase combination. alongtothe According theheight results of the round obtained fromtower ground 10 of 16 and the maximum motion displacement level 1, under of 30% 7.1ofcmtheis first obtained, particularly synthetic earthquakeincombined areas where the normal stresses are sliding on horizontal bed joints, which are associated with shear behavior.with It is100% of the seen that thesecond observed low. The connection synthetic groundof the round motion, thetower highest with roundthe tower arched gate is also collapsed, a critical while location. the three masonry gate arches openings have a pattern which would cause typical diagonal cracking. were able to sustain such a large action (PGA about 1g). Representative responses of this analysis in terms of the contour diagram of final displacement magnitude are depicted in Figure 12. For the second combination as 100% of the first synthetic earthquake combined with 30% of the second synthetic ground motion, some small blocks fell and the highest round tower was very close to collapse, a result consistent with the previous run. For ground motion level 2, a lower level of seismic input, under the first case as 100% of the first synthetic earthquake combined with 30% of the second synthetic ground motion, the maximum displacement was 0.16 m (Figure 13), whereas under the second combination the tower experienced maximum displacement of 0.13 m. Again, the top of the higher tower showed more displacements, but no collapse was observed for this lower seismic level. In addition to the displacements, the normal and shear stresses observed from dynamic analyses were evaluated. Considering the stresses, a much better seismic response was observed under the Dinar earthquake than for the synthetic seismic excitations. Figure 14 shows some damage patterns as openings and dislocation of stones under the Dinar, Turkey 1995 earthquake and the synthetic earthquakes. The results predicted by the model for the Dinar earthquake are compatible with the available data which indicate that no major damage was detected in the structure after this seismic Figure event. It canFigure 11.Displacement 11. be concluded magnitude that when Displacement under the numerical magnitude Dinar, Dinar,Turkey undermodel isTurkey 1995 subjected earthquake. 1995toearthquake . real or synthetic seismic excitations, the main damage was observed in the higher elevations of the round towers, around the In door the following openings, runs, and also forextending each ground to themotion level the arch intrados. numerical These model results show subjected that to synthetic the expected forms earthquakes in two horizontal of structural damage to directions with this gate due to aseismic duration of 11 s. A excitations aretotal of four sliding, dynamicand dislocation analyses falling were of performedstones mostly under along the synthetic towers loading when the horizontal combination. Accordinginertial to theforces resultsexceeded obtained certain from limits. groundUnder motion both combination level 1, under 30% of theof synthetic first earthquake synthetic for ground earthquake motion combined withlevel 1, the 100% of highest the secondtensile stresses ground synthetic were observed along the round tower, which would have resulted in a flexural failure motion, the highest round tower collapsed, while the three masonry gate arches were able to sustain mechanism. As shown in representative figures (Figure 14), openings and dislocation of stones took place due to the such a large action (PGA about 1g). Representative responses of this analysis in terms of the contour diagram of final displacement magnitude are depicted in Figure 12. For the second combination as 100% of the first synthetic earthquake combined with 30% of the second synthetic ground motion, some small blocks fell and the highest round tower was very close to collapse, a result consistent with the previous run. For ground motion level 2, a lower level of seismic input, under the first case as 100% of the Figure 12. Displacement magnitude for ground motion level 1, under 30% of the first synthetic
Appl. Sci. 2020, 10, 5821 10 of 16 first synthetic earthquake combined with 30% of the second synthetic ground motion, the maximum displacement Appl. Sci. 2020, 10,was x FOR 0.16 m (Figure PEER REVIEW 13), whereas under the second combination the tower experienced 10 of 16 maximum displacement of 0.13 Appl. Sci. 2020, 10, x FOR PEER REVIEW m. Again, the top of the higher tower showed more displacements, 10 of 16 but no collapse sliding was observed on horizontal for which bed joints, this lower seismic level. are associated withInshear addition to the It behavior. displacements, is seen that thethe normal observed and shear openings sliding on stresses have observed a pattern horizontal from which bed dynamic joints,would analyses which cause were evaluated. typical diagonal are associated with shear Considering cracking. the stresses, a much behavior. It is seen that the observed better seismic openings have response a patternwas observed which undertypical would cause the Dinar earthquake diagonal cracking.than for the synthetic seismic excitations. Figure 14 shows some damage patterns as openings and dislocation of stones under the Dinar, Turkey 1995 earthquake and the synthetic earthquakes. The results predicted by the model for the Dinar earthquake are compatible with the available data which indicate that no major damage was detected in the structure after this seismic event. It can be concluded that when the numerical model is subjected to real or synthetic seismic excitations, the main damage was observed in the higher elevations of the round towers, around the door openings, and also extending to the arch intrados. These results show that the expected forms of structural damage to this gate due to seismic excitations are sliding, dislocation and falling of stones mostly along the towers when the horizontal inertial forces exceeded certain limits. Under both combination of synthetic earthquake for ground motion level 1, the highest tensile stresses were observed along the round tower, which would have resulted in a flexural failure mechanism. As shown in representative figures (Figure 14), openings and dislocation of stones took place due to the sliding on horizontal bed joints, which are associated with shear behavior. It is seen that theFigure observed Figure11. openings 11.Displacement Displacementhave a pattern magnitude magnitude which under under would Dinar, Dinar, cause Turkey Turkey typical 1995 1995 earthquake earthquake . . diagonal cracking. Figure 12. Displacement magnitude for ground motion level 1, under 30% of the first synthetic Figure12.12.Displacement Figure Displacement magnitude magnitude for for ground ground motion level 1, under under 30% 30% of of the the first firstsynthetic synthetic earthquake combined with 100% of the second synthetic ground motion. earthquake combined with 100% of the second synthetic ground motion. earthquake combined with 100% of the second synthetic ground motion. Figure Figure 13. 13. Displacement Displacement magnitude magnitude forfor ground ground motion motion level level 2,2,under underthe thefirst firstcase caseasas100% 100%of ofthe thefirst first synthetic synthetic earthquake earthquake combined combined with with 30% 30% of the second synthetic ground motion . Figure 13. Displacement magnitude for of the second ground motionsynthetic level 2, ground under themotion. first case as 100% of the first synthetic earthquake combined with 30% of the second synthetic ground motion.
Appl. Sci. 2020, 10, 5821 11 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 16 Figure14. Figure Damagepatterns 14.Damage patternsunder underthe theDinar, Dinar,Turkey Turkey1995 1995earthquake earthquakeand andsynthetic syntheticearthquakes. earthquakes. Under real and synthetic earthquakes, time histories of displacements relative to the base of the model were evaluated at five points, shown in Figure 15. It is obvious from these that under the Dinar earthquake and the synthetic motions, the round towers and the gate show quite different movements, with the arched gate displaying lower values. The maximum values of displacements relative to the
Appl. Sci. 2020, 10, 5821 12 of 16 model base during dynamic analyses for real and synthetic earthquakes for the five points shown in Figure 15 are given in Table 3. We can see that point 4, located at the masonry arch, experienced relatively lower displacements under real and synthetic loadings. Although point 1 is at the highest point, in some runs, the maximum displacement occurred at point 3 (near the gate-tower junction) under the real earthquake and three of four synthetic loadings, showing that this area is subject to intense motion. Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 16 Figure15.15. Figure Time Time histories histories of displacements of displacements relative relative to thetobase the under base under the Turkey the Dinar, Dinar, 1995 Turkey 1995 earthquake earthquake and and the the synthetic synthetic earthquakes. earthquakes. Under real and synthetic earthquakes, time histories of displacements relative to the base of the model were evaluated at five points, shown in Figure 15. It is obvious from these that under the Dinar earthquake and the synthetic motions, the round towers and the gate show quite different movements, with the arched gate displaying lower values. The maximum values of displacements relative to the model base during dynamic analyses for real and synthetic earthquakes for the five points shown in Figure 15 are given in Table 3. We can see that point 4, located at the masonry arch, experienced relatively lower displacements under real and synthetic loadings. Although point 1 is at
Appl. Sci. 2020, 10, 5821 13 of 16 Table 3. Maximum displacement relative to base. Maximum Relative Displacement (m) Point 1 0.0416 Point 2 0.0826 Dinar, Point 3 0.1024 Turkey 1995 Earthquake Point 4 0.0226 Point 5 0.0440 Point 1 0.3472 Ground motion level 1 Point 2 0.7614 Case 1: Point 3 0.9380 100% of the first synthetic earthquake combined with Point 4 0.2090 30% of the second synthetic earthquake Point 5 0.2853 Point 1 0.6616 Ground motion level 1 Point 2 collapsed Case 2: Point 3 collapsed 30% of the first synthetic earthquake combined with Point 4 0.1890 100% of the second synthetic earthquake Point 5 0.6338 Point 1 0.0621 Ground motion level 2 Point 2 0.1444 Case 1: Point 3 0.1298 100% of the first synthetic earthquake combined with Point 4 0.0440 30% of the second synthetic earthquake Point 5 0.0709 Point 1 0.0906 Ground motion level 2 Point 2 0.1841 Case 2: Point 3 0.1981 30% of the first synthetic earthquake combined with Point 4 0.0488 100% of the second synthetic earthquake Point 5 0.0438 5. Discussion The Frontinus Gate in Hierapolis in Denizli, Turkey has a very long history. This monumental masonry gate is composed of three openings in squared travertine blocks, with masonry arches, flanked by two round towers. It is difficult to investigate the structural health of existing masonry monuments using seismic code requirements that are prepared for new masonry constructions. The work carried out was aimed at getting a better insight on the seismic response of the Frontinus Gate. To accomplish this objective, a discrete element model was created using the present geometry of the structure. Dynamic nonlinear analyses were performed under real earthquakes and synthetic ground motions. Interpretation of the numerical model results lead to the following conclusions: 1. Modal analysis, assuming elastic behavior, is a very useful first step to obtain insight into the dynamic characteristics of the structure. 2. The nonlinear dynamic analyses indicate that the Frontinus Gate, in the current state, under an earthquake with a magnitude of 6, would be expected to suffer moderate damage. Under the synthetic earthquake with a return period of 475 years, the observed structural response and damage patterns are serious although it does not mean the collapse of the monument. 3. In the case of occurrence of an earthquake with a return period of 2475 years, the models show that the monument would not be able to withstand it, resulting in a large number of blocks collapsing completely. 4. Considering the seismic sensitivity of the Frontinus Gate, the results obtained are consistent with the present state of the structure, with the round towers having more seismic damage potential than the masonry arches.
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