Investigation of seismic damage propagation in historical masonry mosque; example of Uşak Ulu Mosque

Investigation of seismic damage propagation in historical masonry mosque; example of Uşak Ulu Mosque | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Investigation of seismic damage propagation in historical masonry mosque; example of Uşak Ulu Mosque Soner SEKER, Hakki SAHIN This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7316208/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Historical buildings are symbols of our cultural heritage and richness. They are an important part of our heritage, transmitting many of their characteristics to next generations. As Turkey, one of the most important symbols of our cultural heritage are Ulu Mosques. Historical mosques built in Anatolia during the Seljuk, Principalities and Ottoman periods, especially for Friday and Eid prayers, are called “Ulu Mosques”. Ulu Mosques were generally built in city squares and in places that can be called quite easy to reach. Ulu mosques in Turkey are also considered a symbol of “power and independence”. These structures are evidence that show the history and reflect the behaviour of the people and the culture of the past as well and they need to be safely passed on to next generations. Earthquakes over the years have caused great damage to these structures. In order to protect historical masonry mosques against earthquakes, 3D finite element models should be created and nonlinear analysis should be performed. In this paper, linear and nonlinear time domain analyses of the historical masonry Ulu Mosque in Uşak province are carried out. As a result of the analyses, the dynamic behavior of the selected historical masonry structure under earthquake load is investigated. Concrete Damage Plasticity (CDP) model was used in the nonlinear time domain analysis of the structure. Physical sciences/Engineering Humanities/History Social science/History Historical Masonry Mosques Linear and Time Domain Nonlinear Analysis Concrete Damage Plasticity Model Seismic behavior Damage Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Introduction Historic buildings are an important part of our cultural heritage and need to be preserved and passed on to the future. The geography of Anatolia, in which Turkey is located, is very rich in terms of historical buildings, which are part of the cultural heritage. However, since the region has major earthquake zones, earthquakes pose the most important destructive threat to historical buildings in the region. Although historic mosques built of stone reflect the architectural and engineering wisdom of the past, they pose significant structural risks when exposed to natural disasters such as earthquakes. Throughout history, it is seen that many structures exposed to earthquakes have collapsed or suffered major damage. Therefore, some necessary precautions should be taken to minimize the damage to the buildings due to earthquake effects. Understanding the behaviour of historic masonry structures during seismic events is important for predicting potential damage and taking the necessary precautions. Unconsidered restoration and reinforcement works carried out on historic masonry buildings cause significant physical and cultural damage to these buildings. Historic buildings have to be worked on carefully in order to have a safe transition into the future. Seismic simulation of historic buildings should be performed using realistic 3D modelling, appropriate analysis methods, equivalent seismic and material parameters. There are studies determining the seismic behavior of many historical buildings by finite element (FE) method. Erdik ve Durukal inverstigated the behavior of Hagia Sophia under seismic effects. A finite element model of the structure was created and the model was refined through environmental vibration experiments. In determining the actual dynamic behaviour of Hagia Sophia, data from the 1992 Karacabey earthquake played an important role. The results showed that the dynamic analysis and the environmental vibration tests were consistent 1 . Akan and Özen studied the Green Mausoleum in the province of Bursa and carried out a structural analysis. The SAP2000 programme was used to model the mausoleum for the structural analysis. As a result of the analyses, it was seen that the parts of the masonry structure exposed to compressive stresses were in sufficient strength, but they were not in sufficient strength against tensile stresses. Due to tensile stresses, it was observed that the strengths were insufficient at the corners of the door and window openings 2 . The Harput Ulu Mosque was selected as a case study in the study by Tanyıldızı and Sayın and seismic analyses were performed. As a result of the analyses, the shear stresses in two directions (x and y) were calculated and it was determined that the shear stress values were sufficient and the structure was safe against seismic effects 3 . In the study by Dabanlı, Hırka-i Şerif Mosque was investigated and the earthquake performance of the structure was investigated by static and dynamic analyses through the creation of a 3D FE model of the structure. As a result of the analyses, it was found that the damage to the bases, where the minarets join the structure, was similar to the damage that had actually occurred 4 . In the study by Er Akan, the seismic behaviour of Ahi Elvan Mosque, which is one of the most important examples of historical wooden column mosques in Anatolia, was investigated by creating a 3D finite element (FE) model. It was found that the mosque was expected to crack but was unlikely to collapse 5 . Akdeniz's study investigated the behaviour of the Malatya Grand Mosque, a 1224 masonry structure, using linear and nonlinear analyses. The mosque was macro-modeled and analysed using ANSYS finite element analysis software. It was observed that the cracks in the mosque were concentrated in the arch-wall joints, wall joints and the wall-foundation joint interface 6 . In the study by Bayraktar et al., the dynamic parameters of the newly restored historic stone Sundura Mosque in Artvin/Hopa and its minaret reconstructed with natural stone materials were determined using the operational modal analysis method. Since the restoration of the mosque and the construction of the minaret are new, the calculated dynamic values can be used as a reference criterion for the undamaged state. In the following time, measurements can be repeated and changes in dynamic characteristics can be observed. These values can be used to improve finite element models of the structures, and for health monitoring and safety analysis 7 .Uçak et al. carried out Operational Modal Analysis (OMA) method to determine the dynamic characteristics of a historic masonry dome and improve the FE model by considering experimental data. Two different historical masonry structures, Hamza Pasha Tomb and Kavak Square Fountain, were selected as application examples. As a result of the analysis, it was found that changes in dimensions such as the thickness and height of the dome drum had an effect on the analysis result 8 . In the study of Korkmaz et al., Tokat Yağıbasan Madrasah has been taken as a sample model and the seismic behaviour of the madrasah has been investigated in detail. The structure was modelled in three dimensions in SAP2000 and dynamic analyses were performed with different earthquake acceleration records. The values of base shear, base displacement and base stress obtained from the analyses are compared and evaluated 9 . Çarhoğlu et al. investigated the earthquake behaviour of Kars Kümbet Mosque in his study. The 3D finite element model of the historic mosque was prepared in SAP2000 programme, and the dynamic analysis was performed in the time domain with 20 earthquake acceleration records. As a result of the analyses, it was observed that the compressive and tensile stress values of the structure in both directions were close to each other 10 . Çakır et al. developed a three-dimensional finite element model of the Lala Paşa Mosque, which is located in the city center of Erzurum and was constructed in 1562, in order to investigate its structural behavior. Both static and dynamic analyses were conducted on the model to evaluate the mosque’s response under seismic loading. To ensure realistic analysis results, experimental studies including compression and three-point bending tests were carried out on the building materials, and the obtained data were incorporated into the model. The analyses revealed that the most critical structural components of the mosque are the dome, the drum, and the support regions of the main arches that carry the central dome 11 . Köseoğlu and Canbay investigated a single domed mosque built in the Ottoman architectural style 12 . Nohutcu et al. investigated the seismic damage and collapse mechanism of the historical stone masonry minaret of Hafsa Sultan Mosque, which was built in 1522. They investigated the causes of structural damage to the mosque and proposed methods for its retrofitting 13 . In the study conducted by Çalık et al., Büyük Mosque was selected as an example and the dynamic characteristics of the building before and after restoration were determined using the environmental vibration test method. In the studies, the effects of restoration applications on the dynamic characteristics of the structure were investigated and it was found that restoration works significantly increased the stiffness of the structure 14 . The effect of model calibration on the seismic behaviour of the historic masonry Hafsa Sultan Mosque was investigated by Demir et al.. Seismic analyses of calibrated and uncalibrated numerical models were performed using the acceleration records of the 1999 Kocaeli earthquake. The results of the analyses show that the damage condition of the structure can be determined more accurately by calibrating the dynamic properties of the structure with the OMA method 15 . In his master’s thesis, Jaıhoon conducted a numerical analysis of the Sille Ak Mosque, built in 1864 in Konya and holding significant importance in Turkish-Islamic art, according to the 2018 Turkish Building Earthquake Regulation (TBDY). The numerical analyses were carried out using SAP2000, a software commonly used in civil engineering. The results of the analysis revealed that the areas of the building most stressed in its static condition were the edges of door and window openings, the junctions of the walls, and the points where the walls connect with the floor slabs 16 . Aşıkoğlu et al. developed two structural analysis models of the Kütahya Kurşunlu Mosque as reinforced and unreinforced. A 3D nonlinear pushover analysis of the mosque was performed. The finite element model was calibrated with the ambient vibration measurements of the mosque, and more realistic results were obtained 17 . In his study, Çakır focused on a displacement-based simplified assessment method, considering the absence of a standardized and well-defined approach for evaluating the seismic performance of historical structures. Using this method, the seismic performance of the Kaya Çelebi Mosque, which sustained damage during the 2011 Van earthquake, was investigated. The findings indicated that the ‘’Simplified Assessment Method’’ could serve as an effective and practical tool for evaluating the seismic performance of historical buildings, particularly in cases where data limitations and modeling challenges are prevalent 18 . Ural and Çelik investigated the structural condition of the Tahtani (Leylek) Mosque, built in the 18th century in Gaziantep. In their study, structural analyses were conducted using the Finite Element Method (FEM) with the LUSAS software, focusing on both the current condition of the mosque and its condition after restoration. Load and earthquake spectrum analyses were performed as part of this process. The study identified the causes of the mosque’s structural damage and provided recommendations for correcting the restoration errors made in previous works 19 . The seismic performance of four historical mosques under earthquake ground motions was investigated by Kocaman and Kazaz. They carried out an evaluation for the mosques in terms of the mode shapes, the maximum stress values, the maximum displacement values, the damage distributions and the collapse mechanisms 20 . Cosgun et al. conducted a study to evaluate the seismic behavior of the historic timber hypostyle Atabey Gazi Mosque, originally constructed in 1273, following its restoration. The mosque complex consists of three distinct structures: the main prayer hall, a minaret, and a mausoleum. A numerical model of the mosque was developed based on architectural survey drawings obtained during the restoration process. The study involved linear analysis, displacement-controlled nonlinear analysis, and kinematic limit analysis to identify potential damage mechanisms. Results of the linear analysis demonstrated that the structures exhibit adequate shear strength performance under DD3 and DD2 seismic ground motions, corresponding to return periods of 72 and 475 years, respectively. Furthermore, the nonlinear analysis results indicated that the structures satisfy the interstory drift limits defined for seismic performance assessment 21 . Kocaman examined the Adıyaman Ulu Mosque, which was completely destroyed during the February 6, 2023 Kahramanmaraş earthquakes. In this context, nonlinear time-history analyses of the mosque were conducted using four different ground motion records. The damage mechanisms identified through numerical simulations showed a high degree of correlation with the actual damage observed on site. Furthermore, the damage thresholds derived from the dynamic analyses were found to be significantly lower than the limits prescribed by current seismic design codes, in light of the observed structural performance 22 . Kocaman et al. investigated the collapse mechanism of the renovated Malatya Yeni Mosque before the Kahramanmaraş earthquake on 6 February 2023. As a result of the study, it was found that the domes are the most vulnerable parts in historical mosques and are exposed to more displacement compared to the main structure. It was emphasised that the seismic performance of the domes should be improved 23 . Seismic damages in mosques The mechanical properties of the materials used in the structure, the type of soil on which the structure is built, the magnitude of the earthquake and many other factors determine the type of damage that will occur in a structure 24 . Historic masonry mosques, like other historic buildings, are vulnerable to earthquakes. It is known that the materials used in these structures are resistant to compressive stresses and cannot provide sufficient strength in tension. Therefore, it is predicted that they can be damaged more easily in earthquakes than other structures. Damages in mosques are generally concentrated at critical points such as the intersection of rigid and flexible structural elements, at the bearing areas of stone columns due to excessive rotation of rigid components, or at the dome areas of mosque structures, which have relatively lower stiffness compared to the load-bearing walls. Tapan et al.and. Korkmaz et al. investigated the seismic behavior of Akdamar Church in Van/Gevaş 25 . The Hüsrev Paşa Mosque was damaged in the 2011 Van earthquake, the Malatya New Mosque in the 2020 Elazığ earthquake, the Niyazi Mısri Mosque and the Arasa Mosque in the 6 February 2023 Kahramanmaraş earthquake. The damage is usually to the dome and to the arches that support the domes, or to both of them. Images of the damaged state of the mosques are shown in Fig. 1. History of Uşak Ulu Mosque The date of construction of the Uşak Ulu Mosque (Turkey), located in the central district of Uşak province, is not clearly known. Among the buildings that have survived from the past to the present in Uşak, the most remarkable in terms of historical and architectural features is undoubtedly the Great Mosque. The mosque is reflecting the characteristic features of Anatolian Seljuk and first period Ottoman architecture. There is an inscription in Arabic on the entrance door of the mosque. This inscription, which belongs to a well, gives some information about the date of construction of the mosque. The inscription reads: "Yakup Bey, son of Suleyman the Magnificent, ruler of the Germiyan provinces, had it built in 1419 and brought its water". Uşak Ulu Cami reflects the architecture of the Principality period and the Ottoman transition. The Uşak Ulu Mosque, which has a history of more than 600 years, has been exposed to many earthquakes during the time it has been in use. The building was repaired twice in the 19th century, once before 1955 and once in 1970 by the General Directorate of Foundations. In the 19th century, it was decorated in the Empire style. In this period, the last meeting place was added in front of the mosque. In 2016, the General Directorate of Foundations of Kütahya initiated a comprehensive project to renovate the Great Mosque of Uşak, which lasted for two years. The mosque was strengthened both architecturally and statically. Cavities in the foundation and walls of the mosque were filled with injection moulding. The walls supporting the dome were reinforced with steel connections. The lead coating on the dome was completely renewed and the mosque was made physically resilient. The foundation of the mosque is 4.5 metres below ground level and most of the foundation was opened up and renewed. Drainage work was carried out to prevent water from entering the foundation. The mosque's minaret was also strengthened. Figure 2 shows the pictures of the mosque before restoration and Fig. 3 shows the pictures of restoration works. Architectural features of Uşak Ulu Mosque Uşak Ulu Mosque, like many historical buildings, was built with hewn stone. The mosque looks like a whole with its place of worship and the last meeting place, which was added later in the 19th century. The courtyard of the mosque is a few metres below the level of the road due to the construction of the road and the landscaping around it from the past to the present. There is a historic cemetery in the courtyard towards the mihrab of the mosque. The last sanctuary is covered by five domes with eight corner pulleys and pendentives. The entrance from the outside to the inside is provided by three doors. The prayer hall is formed by pointed arches resting on thick stone columns. The entrance to the place of worship is through a door decorated in the Empire style. The place of worship has a rectangular floor plan measuring 18.50 x 22.00 metres and is divided into 3 areas. In front of the entrance is the entrance hall, covered by a pointed vault, and behind this area is the main area of worship, which is covered by a magnificent dome with a diameter of 10 metres. The 10-metre diameter dome is supported on the surrounding walls by wide arches and stone columns. Each side of the main dome is covered by three smaller domes. During the restoration of the mosque, the minbar and the stone carved mihrab were removed from their original appearance. During the restoration, some historical pieces of the old minbar were added to the new one. The general view of the mosque has been presented in Fig. 4 . Although the architecture of the Uşak Ulu Mosque is unique, it is similar to other mosques that were built in the same period. It is very similar to the Old Mosque of Edirne, the Grand Mosque of Sofia and the Friday Mosque of Plovdiv. Geometric Features of Uşak Ulu Mosque The mosque has a rectangular shape measuring approximately 26.00 x 24.00 m and its height is approximately 10 m from the ground; it consists of a semi-enclosed, porticoed final congregation area and a single room harim. There is a minaret in the south-west corner of the harim, which can be entered from the harim. The mosque has a rectangular floor plan of 18.50 x 22.00 m and is divided into 3 areas. In front of the entrance is the entrance hall, covered by a pointed vault, and behind this area is the main place of worship, covered by a magnificent dome with a diameter of 10 m. The 10 m diameter dome is supported on the perimeter walls by wide arches and stone columns. Each side of the main dome is covered by three smaller domes. Each of these domes is about 5 metres in diameter. The last sanctuary of the mosque is rectangular in shape and measures approximately 6.00 x 22.00 metres. The last sanctuary is covered with five domes. The diameter of the domes is approximately 4 m.. The roleve drawing prepared for the restoration works of the mosque is seen in the Fig. 5 . Finite Element Model of Uşak Ulu Mosque The Finite Element (FE) method, a numerical analysis method that can easily define complex cross-sectional and material parameters of structural elements with different geometric shapes, was used for the analysis of the Uşak Ulu Mosque. First of all, a three-dimensional solid model of the mosque was created in the AutoCAD program according to the measurements taken from the survey studies. The three dimensional solid model of the mosque is shown in Fig. 6 . The FE analysis method was utilised in the analysis of the Uşak Ulu Mosque. This method is a theoretical and numerical technique through which structural elements with different geometric shapes and various material parameters can be easily defined. In order for the FE model of the mosque to be realistic, the building survey drawings prepared in 2018 were used. The solid and FE model of the mosque was prepared in 3D in the Autocad drawing programme, with the dimensions taken from the building survey drawings. For the purposes of analysis, the 3D solid model, which was prepared in the Autocad drawing programme, was transferred to the ABAQUS programme as a 'sat' file 26 . Determining the number of nodal points is a critical process in the finite element method (FEM). The elevated quantity of nodes in the finite element method (FEM) analysis facilitates the determination of the earthquake behaviour of the structure with the greatest possible fidelity to reality. In the FE model of the mosque, 177677 nodes and 107241 tetrahedral C3D10 type elements were utilised. The C3D10 element is defined as a general-purpose tetrahedral element. Determining the number of nodal points is an important process in FE method. The high number of nodes in FEM analysis allows the earthquake behaviour of the structure to be determined in the closest way to the reality. In the FE model of the mosque, 177677 nodes and 107241 tetrahedral C3D10 type elements were utilised. The C3D10 element is defined as a general-purpose tetrahedral element. Before starting the FE analysis, the optimal mesh size should be determined. The initial mesh size for the mosque was selected as 0.60 m and frequency analyses were performed at different mesh sizes up to 0.20 m with a difference of 0.10 m. Different analyses were performed for each mesh size. In the FE analysis, the appropriate mesh size was determined as 0.60 m. The values obtained as a result of the analyses are given in Table 1 . The convergence analysis graph in Fig. 7 . was obtained by utilising the values given in Table 1 . Table 1 Mesh values, number of elements, and mode 1 frequency values Mesh Spacing (m) Number of Elements Mode 1 Frequency Values 0.6 107241 3,4153 0.5 166059 3,3462 0.4 292585 3,2308 0.3 626026 3,1254 0.2 1198967 3,0937 As shown in Fig. 8., in the FE model, the part of the mosque floor resting on the ground is defined as a fixed support in y and z directions. The first five numerical frequency values and mode shapes of the mosque structure were obtained using modal analysis method as shown in Table 2 and Fig. 9. Table 2 FE model frequency values In the initial five modes, it is evident that there is a clear observation of deformations in the domes of the mosque. It is evident that the main structure of the mosque exhibits significant deformations between the 8th and 20th modes. Number of Modes 1. 2. 3. 4. 5. Frequency Values (Hz) 3.4153 3.4368 5.4908 5.5158 8.7718 As illustrated in Table 3 , the frequency values ranging from mode 8 to mode 20 are presented. As demonstrated in Fig. 10, this figure presents the visual representation of shape changes between the 15th and 20th modes. Table 3 FE model frequency values for the mosque after the 8th mode Number of Modes 8. 9. 10. 11. 12. 13. 14. Frequency Values (Hz) 13.968 14.618 16.864 18.236 18.928 19.610 20.167 Number of Modes 15. 16. 17. 18. 19. 20. Frequency Values (Hz) 21.062 21.217 21.534 21.679 24.886 26.818 Material Properties The structure of Uşak Ulu Cami is made entirely of cut stone. It has a monolithic architectural design, which is characteristic of Islamic religious buildings. Since the structure is a historical building, destructive material tests are not allowed in the structure, so the mechanical properties of the materials are based on the values used in the studies conducted in the literature. The mechanical properties of the materials are given in Table 4 . 6 , 27 – 29 Table 4 Mechanical properties of materials Material Density (kg/m³) Modulus Of Elasticity(Mpa) Poisson Ratio (v) Stone 2300 8856 0.24 The Concrete Damage Plasticity (CDP) model is a continuous damage model on the basis of plasticity. The CDP model is based on two main damage mechanisms. These damage mechanisms are the tensile cracking and the compressive fracture. The CDP model is designed for dynamic and cyclic loading. It is particularly suitable for dynamic analyses under loading and unloading conditions and applications where the material is damaged 27 . As shown in Fig. 11, different inelastic behaviour can be shown in tension and compression 30 .The CDP model can also be used for the non-linear behaviour of a masonry structure, provided that the appropriate parameters are used. The material properties such as dilatation angle, eccentricity, σ bo /σ co , K and viscosity are determined as 10, 0.1, 1.166, 0.666 and 0.001 respectively that are used in the concrete damage plasticity model. Beside, stress and inelastic strain values used in the concrete failure plasticity model for masonry are presented in Table 5 27 . Table 5 Stress and inelastic strain values used in the concrete failure plasticity model for masonry 27 σ c (MPa) Plastic strain σ t (MPa) Plastic strain 2 0 0.2 0 2 0.0015 0.02 0.0025 0.2 0.005 0.02 0.01 Damage in compression Damage in tension d c Plastic strain d t Plastic strain 0 0 0 0 0.95 0.005 0.95 0.005 The Movement of Ground In the time-history analysis of the mosque, the possibility of an earthquake with a magnitude of Mw = 7.0 in Uşak was considered. Acceleration records from the 1999 Kocaeli earthquake (Mw: 7.4) were used. The maximum acceleration value of the 1999 Kocaeli earthquake was approximately 0.4 g. The acceleration-, velocity- and displacement-time graphs for the 1999 Kocaeli earthquake are presented in Fig. 12 . Nonlinear Analysis Results of Uşak Ulu Mosque The seismic damage and collapse mechanism of the Uşak Ulu Mosque were determined using nonlinear FE models in the ABAQUS programme. In investigating the nonlinear behaviour of the mosque in the time domain using the Concrete Damage Plasticity (CDP) model, the material parameters to be used in the analysis are given in Table 4 . The results of the nonlinear analysis of the mosque are presented in figures and tables. The maximum and minimum S33 stress values in the mosque are given in Table 6 and Fig. 13. S33 refers to the stress component of the xy plane in the z direction that extends along the z axis. The results of the nonlinear analysis of the mosque are presented in figures and tables. Stress values for S13 are given in Table 7 and Fig. 14. As the z-axis is assumed to be the vertical axis in the model, the shear stress due to earthquake forces is the S13 stress, provided it is in the direction of the earthquake loading. The principal stress values Smax and Smin are given in Table 8 and Fig. 15. Figure 16 shows the compression and tension damage zones. Table 9 shows the number of elements exceeding the damage limit. Table 7 S 13 stress values (MPa) Max (Tensile ) Min (Compressive) S 33 Stress Values -8.828 + 5.646 Table 6 S 33 stress values (MPa) Max (Tensile) Min (Compressive) S 13 Stress Values -18.18 + 10.06 Table 8 Principal stress values (MPa) Max (Tensile ) Min (Compressive) Principal Stress 33.96 -36.34 Table 9 Number of elements exceeding damage limit Max (Tensile ) Min (Compressive) Over 0.95 Number of Damaged Elements 3560 7095 Figure 13 S 33 stress values due to tensile ( a )S 13 stress due to tensile stress ( b ) S 13 stress due to compressive stress Figure 14 S 13 stress damage regions Figure 15 Principal stress values Figure 16 Regions of compressive and tensile damage As can be seen in Fig. 15, Smax and Smin principal stresses are concentrated in the dome parts, upper parts of arches and upper parts of openings. Figure 16 shows the tensile and compressive damage regions and Table 9 shows the number of damaged elements in these regions. As can be seen from the figure and the table, there is a high level of damage in and around the main dome. The majority of the damage has been caused by stresses in the tensile direction. Results and Discussions In this study, the FE model of the historical Uşak Ulu Mosque, which was built during the reign of Germiyanoğulları, is investigated in the Abaqus programme. The study performed both frequency analysis and nonlinear behaviour of the structure. The nonlinear analyses of the mosque were performed by considering the CDP model. The CDP analyses closely examined the behaviour of the structure under tension and compression. In 1999, a high intensity and destructive earthquake such as the Kocaeli earthquake is expected to cause damage to some structural parts of the mosque. The results obtained from the analyses carried out in the study show that most of the damage is expected to occur in the areas affected by tensile stresses. Analyses of the mosque revealed that the general damage was to the upper parts of openings, arches supporting the main dome, domes and places near the domes. It is understood that the most of the damage is located in the elements that support the main dome and in the upper parts of the windows that are under the main dome. Stress limits were exceeded in these areas. The main factor in damage occurrence is tensile stress. This is due to the resistance of the masonry structures to compressive stresses. The tensile stress is approximately 28 times the S33 stress limit. The compressive stress is approximately 4.5 times the limit value and for S13 stress these values vary 50 times for tensile stress and 9 times for compressive stress. For principal stresses, these values vary 170 times for tension and 19 times for compression. In general, if the number of damaged elements caused by the compressive and tensile stresses is analysed, it can be seen that the number of damaged elements caused by the tensile stress is 2 times higher than the number of damaged elements caused by the compressive stress. There are many studies in the literature on the damage zones of historical mosques under the effects of earthquakes. The results of this study show that the expected damage zones in the literature can be realised in Uşak Ulu Mosque, and that the damage zones of the mosque in Uşak Ulu Mosque are in accordance with the results of the literature. Declarations Author Contribution Soner SEKER : Writing – review & editing, Supervision, , Validation, Methodology, Investigation,Formal analysis, Conceptualization. Hakki SAHIN: – Writing – original draft, Visualization , Validation , Investigation,Formal analysis, Acknowledgement The title "funding declarations" was added as a subheading after the references in the article. Data Availability The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.The earthquake records of the Kocaeli earthquake used in the study can be accessed at the url address "https://www.strongmotioncenter.org/vdc/scripts/event.plx?evt=510". References Erdik, M. & Durukal, E. Aya Sofya’nin deprem davranisi, 2 (Ulusal Deprem Mühendisligi Konferansi, 1993). Akan, A. E. & Özen, Ö. Bursa yeşil türbe’nin sonlu elemanlar yöntemi ile deprem analizi (Deprem Sempozyumu, Kocaeli, 2005). Tanyıldızı, H. & Sayın, E. Harput Ulu Camisinin Deprem Güvenliğinin Belirlenmesi, Yapısal Onarım ve Güçlendirme Sempozyumu, 440–443, 7–8 December, Denizli, Turkey. (2006). Dabanlı, Ö. Determination of the earthquake performance of historical masonry structures, (Master’s dissertation, İstanbul Technical University, Turkey) (2008). Er Akan, A. 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Effect of model calibration on seismic behaviour of a historical mosque. Struct. Eng. Mech. 60 (5), 749–760 (2016). Jaihoon, E. H. TBDY 2018’e Göre Tarihi Yığma Yapıların Analizi ve Bġr Örnek Sille Ak Camii, (Master’s dissertation, Konya Technical University, Turkey) (2019). Aşıkoğlu, A., Avşar, Ö., Lourenco, P. B. & Silva, L. C. Effectiveness of seismic retrofitting of a historical masonry structure: Kütahya Kurşunlu Mosque, Turkey. Bull. Earthq. Eng. Volume . 17 , 3365–3395 (2019). Çakır, F. Tarihi yapıların deprem performansının belirlenmesi için basitleştirilmiş bir yöntem: Kaya Çelebi Cami örneği. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi . 36 (3), 1643–1656. https://doi.org/10.17341/gazimmfd.754183 (2021). Ural, A., Çelik, T., Kocaman, İ. & Kazaz, İ. Gaziantep Nizip Tahtani (Leylek) Cami Yapisal Analiz ve Değerlendirmesi, Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, 26(1), 79–96., (2023), Collapse mechanism of historical masonry mosques under strong ground motions, Engineering Failure Analysis, Volume 144, 106983, https://doi.org/10.1016/j.engfailanal.2022.106983 (2021). Çoşgun, T. et al. Post-Restoration Seismic Performance Assessment Of A Historic Hypostyle Mosque In Anatolia (13th Century Ad). Case Stud. Constr. Mater. ,18. https://doi.org/10.1016/j.cscm.2023.e01849 (2023). Kocaman, İ. Examination of the damage limits and collapse mechanism of Adıyaman Ulu Mosque with finite element model, Structures, 70. https://doi.org/10.1016/j.istruc.2024.107787 (2024). Kocaman, İ., Mercimenk, Ö., Gürgüz, M., Erbaş, Y. & Anıl, Ö. The effect of Kahramanmaraş earthquakes on historical Malatya Yeni Mosque. Eng. Fail. Anal. 161 , 108310 (2024). Şeker, S. & Şahin, H. Numerical Investigation of A Historic Masonry Minaret Subjected To Seismic Excitation. Iran. J. Sci. Technol. Trans. Civil Eng. 48 , 2249–2262 (2024). Tapan, M. et al. Failures of structures during the October 23, 2011 Tabanlı (Van) and November 9, 2011 Edremit (Van) earthquakes in Turkey. Eng. Fail. Anal. 34 , 606–628. https://doi.org/10.1016/j.engfailanal.2013.02.013 (2013). Korkmaz, K. A., Çarhoğlu, A. I., Usta, P. & Toker, S. Tarihi kiliselerin deprem davranışlarının Van Akdamar kilisesi örneğinde incelenmesi. SDU Int. J. Technological Sci. , 5 (2). (2013). Abaqus v10. Dassault Systèmes Simulia Corp., Providence, Rhode Island, USA (2010). Hökelekli, E. & Al-Helwani, A. Effect of soil properties on the seismic damage assessment of historical masonry minaret–soil interaction systems. Struct. Des. Tall Special Build. 29 (2), e1694 (2019). Altiok, T. Y. Tarihi minarelerin dinamik özelliklerinin deneysel ve nümerik yöntemler ile araştırılması (Master's dissertation, Manisa Celal Bayar University, Manisa). (2019). Şahin, H. Güçlendirilmiş Tarihi Yığma Bir Yapının Doğrusal Olmayan Analiz Yöntemi İle İncelenmesi, (Master's dissertation, Uşak University, (2022). Öztürk, H. Betonarme Kısa Kirişlerde Kesme Dayanımının Çapraz Kesme Donatıları İle İyileştirilmesi, (PhD dissertation, Sakarya University,Turkey) (2016). Additional Declarations No competing interests reported. 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SEKER","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYDADCQYGxgdA2gCKidPCDFMOxAnEaWGTIEqLfHvvwccVDHVyku29z6p5/tgZM7A3b5Ng/HEPpxaDM+eSDc8wHDaW5jludpu3LdmMgedYmQRDQjFuLRI5ZpINDAcS50mksd3mbWC2YQCKALXgdpn8jBzznw0MdfXz5J+xFfP8qbdhkH+DXwvDjRwzxgYG5gRpCTY2Zh62w2YMEjz4tRicOWMs2WBw2HBmTxqz5Ny248ZsPGnFFglpeBzW3mP4saGiTl7i+DHGD2/+VBv2sx/eeOODDR6HQexCYrOBCEIaRsEoGAWjYBTgBwAmXUV6B3P81AAAAABJRU5ErkJggg==","orcid":"","institution":"Usak University","correspondingAuthor":true,"prefix":"","firstName":"Soner","middleName":"","lastName":"SEKER","suffix":""},{"id":505450061,"identity":"b144b41b-034d-4208-8835-b00c9a0c66a4","order_by":1,"name":"Hakki SAHIN","email":"","orcid":"","institution":"Usak University","correspondingAuthor":false,"prefix":"","firstName":"Hakki","middleName":"","lastName":"SAHIN","suffix":""}],"badges":[],"createdAt":"2025-08-07 08:08:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7316208/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7316208/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90044618,"identity":"38c9c784-d0f8-441f-8037-8e767645c7a7","added_by":"auto","created_at":"2025-08-27 17:53:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1061716,"visible":true,"origin":"","legend":"\u003cp\u003eDamages on Mosques\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/2484d167f08aedf89a0f57fc.png"},{"id":90044053,"identity":"352a64df-85b2-412b-a4cf-9a61b287c229","added_by":"auto","created_at":"2025-08-27 17:45:58","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":101235,"visible":true,"origin":"","legend":"\u003cp\u003eUşak Great Mosque before restoration\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/5ad9b148e74459562c75a1a7.jpg"},{"id":90044617,"identity":"debfbddb-03da-4561-9762-59e35b74527f","added_by":"auto","created_at":"2025-08-27 17:53:58","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1054899,"visible":true,"origin":"","legend":"\u003cp\u003eRestoration works of Uşak Ulu Mosque\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/3020885af53dbcad6f222ac2.png"},{"id":90044052,"identity":"2e63f01a-cb91-463e-949d-efb8cb7a4ac8","added_by":"auto","created_at":"2025-08-27 17:45:58","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":191865,"visible":true,"origin":"","legend":"\u003cp\u003eView of Uşak Ulu Mosque\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/5beb41c756db3aa62182e69c.png"},{"id":90044057,"identity":"d3d78b59-5c98-4d60-b3a4-5fb397d61b8e","added_by":"auto","created_at":"2025-08-27 17:45:58","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":72635,"visible":true,"origin":"","legend":"\u003cp\u003eGeometric features of Usak Ulu Mosque\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/2085333ce74c946b0bbe9940.png"},{"id":90044059,"identity":"a68d80fc-4982-456c-b43a-2a26de0284bd","added_by":"auto","created_at":"2025-08-27 17:45:58","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":160876,"visible":true,"origin":"","legend":"\u003cp\u003e3D Solid Model of Usak Ulu 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mosque\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/f2e7b8714803ea9d0c202f33.png"},{"id":90044627,"identity":"cab9337a-6a8c-43a5-bcbd-757e8cca9d6f","added_by":"auto","created_at":"2025-08-27 17:53:59","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":620724,"visible":true,"origin":"","legend":"\u003cp\u003eInitial 5 mode Shape and Frequency Values\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/5c58989c5d44de71e1f7d1c3.png"},{"id":90045750,"identity":"1f616feb-f33d-4032-9a45-86731e8e593f","added_by":"auto","created_at":"2025-08-27 18:09:59","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":790868,"visible":true,"origin":"","legend":"\u003cp\u003eMode shape and frequency values between 15th and 20th modes for the mosque\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/fcdde272a469bf873bf31bac.png"},{"id":90044062,"identity":"f4c14861-45d5-47a5-8d9e-abfc10ca88e2","added_by":"auto","created_at":"2025-08-27 17:45:59","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":67751,"visible":true,"origin":"","legend":"\u003cp\u003eCDP compressive and tensile graphs restoration\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/f5b162e21f05f5a08f2c6f30.png"},{"id":90045174,"identity":"64b35e75-f4bd-4c6e-b987-e54fd77fe005","added_by":"auto","created_at":"2025-08-27 18:02:00","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":45158,"visible":true,"origin":"","legend":"\u003cp\u003eKocaeli earthquake (a)acceleration-time, (b) velocity-time and (c) displacement-time graphs\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/27c4d0bd8ddfbdc19d95481d.png"},{"id":90044122,"identity":"9c25e5bf-0f12-4f33-b5b1-6893beb2fd6d","added_by":"auto","created_at":"2025-08-27 17:45:59","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":663134,"visible":true,"origin":"","legend":"\u003cp\u003eS\u003csub\u003e33\u003c/sub\u003e stress values due to tensile\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/9b70082be0651e00cb310197.png"},{"id":90044640,"identity":"c645e522-edcb-488f-8076-ce665fb4192c","added_by":"auto","created_at":"2025-08-27 17:54:00","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":604702,"visible":true,"origin":"","legend":"\u003cp\u003eS\u003csub\u003e13\u003c/sub\u003e stress damage regions\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/030ba861fd717316b5a75df4.png"},{"id":90044624,"identity":"81291762-9bf0-4385-b33b-55a92a9d0418","added_by":"auto","created_at":"2025-08-27 17:53:59","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":417223,"visible":true,"origin":"","legend":"\u003cp\u003ePrincipal stress values\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/2648bac458ec24e875616005.png"},{"id":90044065,"identity":"1e265e59-8290-477e-8f21-a6acb24865df","added_by":"auto","created_at":"2025-08-27 17:45:59","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":306493,"visible":true,"origin":"","legend":"\u003cp\u003eRegions of compressive and tensile damage\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/cce3a1ee9e6ed7f26b7fe5b5.png"},{"id":90046009,"identity":"be073774-84b4-4ae1-a807-80dc4df56207","added_by":"auto","created_at":"2025-08-27 18:18:02","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7174585,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7316208/v1/55b31e9d-20d8-455c-a841-005ddfe94873.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Investigation of seismic damage propagation in historical masonry mosque; example of Uşak Ulu Mosque","fulltext":[{"header":"Introduction","content":"\u003cp\u003eHistoric buildings are an important part of our cultural heritage and need to be preserved and passed on to the future. The geography of Anatolia, in which Turkey is located, is very rich in terms of historical buildings, which are part of the cultural heritage. However, since the region has major earthquake zones, earthquakes pose the most important destructive threat to historical buildings in the region. Although historic mosques built of stone reflect the architectural and engineering wisdom of the past, they pose significant structural risks when exposed to natural disasters such as earthquakes. Throughout history, it is seen that many structures exposed to earthquakes have collapsed or suffered major damage. Therefore, some necessary precautions should be taken to minimize the damage to the buildings due to earthquake effects.\u003c/p\u003e\u003cp\u003eUnderstanding the behaviour of historic masonry structures during seismic events is important for predicting potential damage and taking the necessary precautions. Unconsidered restoration and reinforcement works carried out on historic masonry buildings cause significant physical and cultural damage to these buildings. Historic buildings have to be worked on carefully in order to have a safe transition into the future. Seismic simulation of historic buildings should be performed using realistic 3D modelling, appropriate analysis methods, equivalent seismic and material parameters.\u003c/p\u003e\u003cp\u003eThere are studies determining the seismic behavior of many historical buildings by finite element (FE) method. Erdik ve Durukal inverstigated the behavior of Hagia Sophia under seismic effects. A finite element model of the structure was created and the model was refined through environmental vibration experiments. In determining the actual dynamic behaviour of Hagia Sophia, data from the 1992 Karacabey earthquake played an important role. The results showed that the dynamic analysis and the environmental vibration tests were consistent \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Akan and \u0026Ouml;zen studied the Green Mausoleum in the province of Bursa and carried out a structural analysis. The SAP2000 programme was used to model the mausoleum for the structural analysis. As a result of the analyses, it was seen that the parts of the masonry structure exposed to compressive stresses were in sufficient strength, but they were not in sufficient strength against tensile stresses. Due to tensile stresses, it was observed that the strengths were insufficient at the corners of the door and window openings \u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. The Harput Ulu Mosque was selected as a case study in the study by Tanyıldızı and Sayın and seismic analyses were performed. As a result of the analyses, the shear stresses in two directions (x and y) were calculated and it was determined that the shear stress values were sufficient and the structure was safe against seismic effects \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. In the study by Dabanlı, Hırka-i Şerif Mosque was investigated and the earthquake performance of the structure was investigated by static and dynamic analyses through the creation of a 3D FE model of the structure. As a result of the analyses, it was found that the damage to the bases, where the minarets join the structure, was similar to the damage that had actually occurred \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. In the study by Er Akan, the seismic behaviour of Ahi Elvan Mosque, which is one of the most important examples of historical wooden column mosques in Anatolia, was investigated by creating a 3D finite element (FE) model. It was found that the mosque was expected to crack but was unlikely to collapse \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Akdeniz's study investigated the behaviour of the Malatya Grand Mosque, a 1224 masonry structure, using linear and nonlinear analyses. The mosque was macro-modeled and analysed using ANSYS finite element analysis software. It was observed that the cracks in the mosque were concentrated in the arch-wall joints, wall joints and the wall-foundation joint interface\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. In the study by Bayraktar et al., the dynamic parameters of the newly restored historic stone Sundura Mosque in Artvin/Hopa and its minaret reconstructed with natural stone materials were determined using the operational modal analysis method. Since the restoration of the mosque and the construction of the minaret are new, the calculated dynamic values can be used as a reference criterion for the undamaged state. In the following time, measurements can be repeated and changes in dynamic characteristics can be observed. These values can be used to improve finite element models of the structures, and for health monitoring and safety analysis \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e .U\u0026ccedil;ak et al. carried out Operational Modal Analysis (OMA) method to determine the dynamic characteristics of a historic masonry dome and improve the FE model by considering experimental data. Two different historical masonry structures, Hamza Pasha Tomb and Kavak Square Fountain, were selected as application examples. As a result of the analysis, it was found that changes in dimensions such as the thickness and height of the dome drum had an effect on the analysis result \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. In the study of Korkmaz et al., Tokat Yağıbasan Madrasah has been taken as a sample model and the seismic behaviour of the madrasah has been investigated in detail. The structure was modelled in three dimensions in SAP2000 and dynamic analyses were performed with different earthquake acceleration records. The values of base shear, base displacement and base stress obtained from the analyses are compared and evaluated \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. \u0026Ccedil;arhoğlu et al. investigated the earthquake behaviour of Kars K\u0026uuml;mbet Mosque in his study. The 3D finite element model of the historic mosque was prepared in SAP2000 programme, and the dynamic analysis was performed in the time domain with 20 earthquake acceleration records. As a result of the analyses, it was observed that the compressive and tensile stress values of the structure in both directions were close to each other \u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. \u0026Ccedil;akır et al. developed a three-dimensional finite element model of the Lala Paşa Mosque, which is located in the city center of Erzurum and was constructed in 1562, in order to investigate its structural behavior. Both static and dynamic analyses were conducted on the model to evaluate the mosque\u0026rsquo;s response under seismic loading. To ensure realistic analysis results, experimental studies including compression and three-point bending tests were carried out on the building materials, and the obtained data were incorporated into the model. The analyses revealed that the most critical structural components of the mosque are the dome, the drum, and the support regions of the main arches that carry the central dome \u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. K\u0026ouml;seoğlu and Canbay investigated a single domed mosque built in the Ottoman architectural style \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Nohutcu et al. investigated the seismic damage and collapse mechanism of the historical stone masonry minaret of Hafsa Sultan Mosque, which was built in 1522. They investigated the causes of structural damage to the mosque and proposed methods for its retrofitting \u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. In the study conducted by \u0026Ccedil;alık et al., B\u0026uuml;y\u0026uuml;k Mosque was selected as an example and the dynamic characteristics of the building before and after restoration were determined using the environmental vibration test method. In the studies, the effects of restoration applications on the dynamic characteristics of the structure were investigated and it was found that restoration works significantly increased the stiffness of the structure \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. The effect of model calibration on the seismic behaviour of the historic masonry Hafsa Sultan Mosque was investigated by Demir et al.. Seismic analyses of calibrated and uncalibrated numerical models were performed using the acceleration records of the 1999 Kocaeli earthquake. The results of the analyses show that the damage condition of the structure can be determined more accurately by calibrating the dynamic properties of the structure with the OMA method \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. In his master\u0026rsquo;s thesis, Jaıhoon conducted a numerical analysis of the Sille Ak Mosque, built in 1864 in Konya and holding significant importance in Turkish-Islamic art, according to the 2018 Turkish Building Earthquake Regulation (TBDY). The numerical analyses were carried out using SAP2000, a software commonly used in civil engineering. The results of the analysis revealed that the areas of the building most stressed in its static condition were the edges of door and window openings, the junctions of the walls, and the points where the walls connect with the floor slabs \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Aşıkoğlu et al. developed two structural analysis models of the K\u0026uuml;tahya Kurşunlu Mosque as reinforced and unreinforced. A 3D nonlinear pushover analysis of the mosque was performed. The finite element model was calibrated with the ambient vibration measurements of the mosque, and more realistic results were obtained \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. In his study, \u0026Ccedil;akır focused on a displacement-based simplified assessment method, considering the absence of a standardized and well-defined approach for evaluating the seismic performance of historical structures. Using this method, the seismic performance of the Kaya \u0026Ccedil;elebi Mosque, which sustained damage during the 2011 Van earthquake, was investigated. The findings indicated that the \u0026lsquo;\u0026rsquo;Simplified Assessment Method\u0026rsquo;\u0026rsquo; could serve as an effective and practical tool for evaluating the seismic performance of historical buildings, particularly in cases where data limitations and modeling challenges are prevalent \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Ural and \u0026Ccedil;elik investigated the structural condition of the Tahtani (Leylek) Mosque, built in the 18th century in Gaziantep. In their study, structural analyses were conducted using the Finite Element Method (FEM) with the LUSAS software, focusing on both the current condition of the mosque and its condition after restoration. Load and earthquake spectrum analyses were performed as part of this process. The study identified the causes of the mosque\u0026rsquo;s structural damage and provided recommendations for correcting the restoration errors made in previous works \u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. The seismic performance of four historical mosques under earthquake ground motions was investigated by Kocaman and Kazaz. They carried out an evaluation for the mosques in terms of the mode shapes, the maximum stress values, the maximum displacement values, the damage distributions and the collapse mechanisms \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eCosgun et al. conducted a study to evaluate the seismic behavior of the historic timber hypostyle Atabey Gazi Mosque, originally constructed in 1273, following its restoration. The mosque complex consists of three distinct structures: the main prayer hall, a minaret, and a mausoleum. A numerical model of the mosque was developed based on architectural survey drawings obtained during the restoration process. The study involved linear analysis, displacement-controlled nonlinear analysis, and kinematic limit analysis to identify potential damage mechanisms. Results of the linear analysis demonstrated that the structures exhibit adequate shear strength performance under DD3 and DD2 seismic ground motions, corresponding to return periods of 72 and 475 years, respectively. Furthermore, the nonlinear analysis results indicated that the structures satisfy the interstory drift limits defined for seismic performance assessment \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Kocaman examined the Adıyaman Ulu Mosque, which was completely destroyed during the February 6, 2023 Kahramanmaraş earthquakes. In this context, nonlinear time-history analyses of the mosque were conducted using four different ground motion records. The damage mechanisms identified through numerical simulations showed a high degree of correlation with the actual damage observed on site. Furthermore, the damage thresholds derived from the dynamic analyses were found to be significantly lower than the limits prescribed by current seismic design codes, in light of the observed structural performance \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. Kocaman et al. investigated the collapse mechanism of the renovated Malatya Yeni Mosque before the Kahramanmaraş earthquake on 6 February 2023. As a result of the study, it was found that the domes are the most vulnerable parts in historical mosques and are exposed to more displacement compared to the main structure. It was emphasised that the seismic performance of the domes should be improved \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Seismic damages in mosques","content":"\u003cp\u003eThe mechanical properties of the materials used in the structure, the type of soil on which the structure is built, the magnitude of the earthquake and many other factors determine the type of damage that will occur in a structure \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Historic masonry mosques, like other historic buildings, are vulnerable to earthquakes. It is known that the materials used in these structures are resistant to compressive stresses and cannot provide sufficient strength in tension. Therefore, it is predicted that they can be damaged more easily in earthquakes than other structures. Damages in mosques are generally concentrated at critical points such as the intersection of rigid and flexible structural elements, at the bearing areas of stone columns due to excessive rotation of rigid components, or at the dome areas of mosque structures, which have relatively lower stiffness compared to the load-bearing walls. Tapan et al.and. Korkmaz et al. investigated the seismic behavior of Akdamar Church in Van/Gevaş \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe H\u0026uuml;srev Paşa Mosque was damaged in the 2011 Van earthquake, the Malatya New Mosque in the 2020 Elazığ earthquake, the Niyazi Mısri Mosque and the Arasa Mosque in the 6 February 2023 Kahramanmaraş earthquake. The damage is usually to the dome and to the arches that support the domes, or to both of them. Images of the damaged state of the mosques are shown in Fig.\u0026nbsp;1.\u003c/p\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003eHistory of Uşak Ulu Mosque\u003c/h2\u003e\n\u003cp\u003eThe date of construction of the Uşak Ulu Mosque (Turkey), located in the central district of Uşak province, is not clearly known. Among the buildings that have survived from the past to the present in Uşak, the most remarkable in terms of historical and architectural features is undoubtedly the Great Mosque. The mosque is reflecting the characteristic features of Anatolian Seljuk and first period Ottoman architecture. There is an inscription in Arabic on the entrance door of the mosque. This inscription, which belongs to a well, gives some information about the date of construction of the mosque. The inscription reads: \"Yakup Bey, son of Suleyman the Magnificent, ruler of the Germiyan provinces, had it built in 1419 and brought its water\". Uşak Ulu Cami reflects the architecture of the Principality period and the Ottoman transition. The Uşak Ulu Mosque, which has a history of more than 600 years, has been exposed to many earthquakes during the time it has been in use. The building was repaired twice in the 19th century, once before 1955 and once in 1970 by the General Directorate of Foundations. In the 19th century, it was decorated in the Empire style. In this period, the last meeting place was added in front of the mosque.\u003c/p\u003e\n\u003cp\u003eIn 2016, the General Directorate of Foundations of K\u0026uuml;tahya initiated a comprehensive project to renovate the Great Mosque of Uşak, which lasted for two years. The mosque was strengthened both architecturally and statically.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCavities in the foundation and walls of the mosque were filled with injection moulding. The walls supporting the dome were reinforced with steel connections. The lead coating on the dome was completely renewed and the mosque was made physically resilient. The foundation of the mosque is 4.5 metres below ground level and most of the foundation was opened up and renewed. Drainage work was carried out to prevent water from entering the foundation. The mosque's minaret was also strengthened. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows the pictures of the mosque before restoration and Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows the pictures of restoration works.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Architectural features of Uşak Ulu Mosque","content":"\u003cp\u003eUşak Ulu Mosque, like many historical buildings, was built with hewn stone. The mosque looks like a whole with its place of worship and the last meeting place, which was added later in the 19th century. The courtyard of the mosque is a few metres below the level of the road due to the construction of the road and the landscaping around it from the past to the present. There is a historic cemetery in the courtyard towards the mihrab of the mosque. The last sanctuary is covered by five domes with eight corner pulleys and pendentives. The entrance from the outside to the inside is provided by three doors. The prayer hall is formed by pointed arches resting on thick stone columns. The entrance to the place of worship is through a door decorated in the Empire style. The place of worship has a rectangular floor plan measuring 18.50 x 22.00 metres and is divided into 3 areas. In front of the entrance is the entrance hall, covered by a pointed vault, and behind this area is the main area of worship, which is covered by a magnificent dome with a diameter of 10 metres. The 10-metre diameter dome is supported on the surrounding walls by wide arches and stone columns. Each side of the main dome is covered by three smaller domes. During the restoration of the mosque, the minbar and the stone carved mihrab were removed from their original appearance. During the restoration, some historical pieces of the old minbar were added to the new one. The general view of the mosque has been presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAlthough the architecture of the Uşak Ulu Mosque is unique, it is similar to other mosques that were built in the same period. It is very similar to the Old Mosque of Edirne, the Grand Mosque of Sofia and the Friday Mosque of Plovdiv.\u003c/p\u003e"},{"header":"Geometric Features of Uşak Ulu Mosque","content":"\u003cp\u003eThe mosque has a rectangular shape measuring approximately 26.00 x 24.00 m and its height is approximately 10 m from the ground; it consists of a semi-enclosed, porticoed final congregation area and a single room harim. There is a minaret in the south-west corner of the harim, which can be entered from the harim. The mosque has a rectangular floor plan of 18.50 x 22.00 m and is divided into 3 areas. In front of the entrance is the entrance hall, covered by a pointed vault, and behind this area is the main place of worship, covered by a magnificent dome with a diameter of 10 m. The 10 m diameter dome is supported on the perimeter walls by wide arches and stone columns. Each side of the main dome is covered by three smaller domes. Each of these domes is about 5 metres in diameter. The last sanctuary of the mosque is rectangular in shape and measures approximately 6.00 x 22.00 metres. The last sanctuary is covered with five domes. The diameter of the domes is approximately 4 m.. The roleve drawing prepared for the restoration works of the mosque is seen in the Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"Finite Element Model of Uşak Ulu Mosque","content":"\u003cp\u003eThe Finite Element (FE) method, a numerical analysis method that can easily define complex cross-sectional and material parameters of structural elements with different geometric shapes, was used for the analysis of the Uşak Ulu Mosque. First of all, a three-dimensional solid model of the mosque was created in the AutoCAD program according to the measurements taken from the survey studies. The three dimensional solid model of the mosque is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eThe FE analysis method was utilised in the analysis of the Uşak Ulu Mosque. This method is a theoretical and numerical technique through which structural elements with different geometric shapes and various material parameters can be easily defined. In order for the FE model of the mosque to be realistic, the building survey drawings prepared in 2018 were used. The solid and FE model of the mosque was prepared in 3D in the Autocad drawing programme, with the dimensions taken from the building survey drawings. For the purposes of analysis, the 3D solid model, which was prepared in the Autocad drawing programme, was transferred to the ABAQUS programme as a 'sat' file \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. Determining the number of nodal points is a critical process in the finite element method (FEM). The elevated quantity of nodes in the finite element method (FEM) analysis facilitates the determination of the earthquake behaviour of the structure with the greatest possible fidelity to reality. In the FE model of the mosque, 177677 nodes and 107241 tetrahedral C3D10 type elements were utilised. The C3D10 element is defined as a general-purpose tetrahedral element. Determining the number of nodal points is an important process in FE method. The high number of nodes in FEM analysis allows the earthquake behaviour of the structure to be determined in the closest way to the reality. In the FE model of the mosque, 177677 nodes and 107241 tetrahedral C3D10 type elements were utilised. The C3D10 element is defined as a general-purpose tetrahedral element. Before starting the FE analysis, the optimal mesh size should be determined. The initial mesh size for the mosque was selected as 0.60 m and frequency analyses were performed at different mesh sizes up to 0.20 m with a difference of 0.10 m. Different analyses were performed for each mesh size. In the FE analysis, the appropriate mesh size was determined as 0.60 m. The values obtained as a result of the analyses are given in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The convergence analysis graph in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. was obtained by utilising the values given in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eMesh values, number of elements, and mode 1 frequency values\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMesh Spacing (m)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eNumber of Elements\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMode 1 Frequency Values\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e107241\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3,4153\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e166059\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3,3462\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e292585\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3,2308\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e626026\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3,1254\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1198967\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3,0937\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAs shown in Fig.\u0026nbsp;8., in the FE model, the part of the mosque floor resting on the ground is defined as a fixed support in y and z directions. The first five numerical frequency values and mode shapes of the mosque structure were obtained using modal analysis method as shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig.\u0026nbsp;9.\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eFE model frequency values In the initial five modes, it is evident that there is a clear observation of deformations in the domes of the mosque. It is evident that the main structure of the mosque exhibits significant deformations between the 8th and 20th modes.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eNumber of Modes\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e1.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e2.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e3.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e4.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e5.\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eFrequency Values (Hz)\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.4153\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.4368\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5.4908\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5.5158\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8.7718\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAs illustrated in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e, the frequency values ranging from mode 8 to mode 20 are presented. As demonstrated in Fig.\u0026nbsp;10, this figure presents the visual representation of shape changes between the 15th and 20th modes.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab3\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eFE model frequency values for the mosque after the 8th mode\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eNumber of Modes\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e8.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e9.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e10.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e11.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e12.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e13.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e14.\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eFrequency Values (Hz)\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e13.968\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e14.618\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e16.864\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e18.236\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e18.928\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e19.610\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e20.167\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eNumber of Modes\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e15.\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e16.\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e17.\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e18.\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e19.\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e20.\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eFrequency Values (Hz)\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21.062\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21.217\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21.534\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21.679\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e24.886\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e26.818\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e"},{"header":"Material Properties","content":"\u003cp\u003eThe structure of Uşak Ulu Cami is made entirely of cut stone. It has a monolithic architectural design, which is characteristic of Islamic religious buildings. Since the structure is a historical building, destructive material tests are not allowed in the structure, so the mechanical properties of the materials are based on the values used in the studies conducted in the literature. The mechanical properties of the materials are given in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab4\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eMechanical properties of materials\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDensity (kg/m\u0026sup3;)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eModulus Of Elasticity(Mpa)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePoisson Ratio (v)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eStone\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8856\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.24\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe Concrete Damage Plasticity (CDP) model is a continuous damage model on the basis of plasticity. The CDP model is based on two main damage mechanisms. These damage mechanisms are the tensile cracking and the compressive fracture. The CDP model is designed for dynamic and cyclic loading. It is particularly suitable for dynamic analyses under loading and unloading conditions and applications where the material is damaged \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eAs shown in Fig.\u0026nbsp;11, different inelastic behaviour can be shown in tension and compression\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e .The CDP model can also be used for the non-linear behaviour of a masonry structure, provided that the appropriate parameters are used.\u003c/p\u003e\n\u003cp\u003eThe material properties such as dilatation angle, eccentricity, \u0026sigma;\u003csub\u003ebo\u003c/sub\u003e/\u0026sigma;\u003csub\u003eco\u003c/sub\u003e, K and viscosity are determined as 10, 0.1, 1.166, 0.666 and 0.001 respectively that are used in the concrete damage plasticity model. Beside, stress and inelastic strain values used in the concrete failure plasticity model for masonry are presented in Table\u0026nbsp;5 \u003csup\u003e27\u003c/sup\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab5\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eStress and inelastic strain values used in the concrete failure plasticity model for masonry 27\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u0026sigma;\u003csub\u003ec\u003c/sub\u003e (MPa)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePlastic strain\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u0026sigma;\u003csub\u003et\u003c/sub\u003e (MPa)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePlastic strain\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0015\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.02\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0025\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.005\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.02\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.01\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eDamage in compression\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eDamage in tension\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003ed\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003ePlastic strain\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003ed\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003ePlastic strain\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.95\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.005\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.95\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.005\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003eThe Movement of Ground\u003c/h2\u003e\n\u003cp\u003eIn the time-history analysis of the mosque, the possibility of an earthquake with a magnitude of Mw\u0026thinsp;=\u0026thinsp;7.0 in Uşak was considered. Acceleration records from the 1999 Kocaeli earthquake (Mw: 7.4) were used. The maximum acceleration value of the 1999 Kocaeli earthquake was approximately 0.4 g. The acceleration-, velocity- and displacement-time graphs for the 1999 Kocaeli earthquake are presented in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Nonlinear Analysis Results of Uşak Ulu Mosque","content":"\u003cp\u003eThe seismic damage and collapse mechanism of the Uşak Ulu Mosque were determined using nonlinear FE models in the ABAQUS programme. In investigating the nonlinear behaviour of the mosque in the time domain using the Concrete Damage Plasticity (CDP) model, the material parameters to be used in the analysis are given in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe results of the nonlinear analysis of the mosque are presented in figures and tables. The maximum and minimum S33 stress values in the mosque are given in Table\u0026nbsp;6 and Fig.\u0026nbsp;13. S33 refers to the stress component of the xy plane in the z direction that extends along the z axis. The results of the nonlinear analysis of the mosque are presented in figures and tables. Stress values for S13 are given in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Fig.\u0026nbsp;14. As the z-axis is assumed to be the vertical axis in the model, the shear stress due to earthquake forces is the S13 stress, provided it is in the direction of the earthquake loading. The principal stress values Smax and Smin are given in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e8\u003c/span\u003e and Fig.\u0026nbsp;15. Figure\u0026nbsp;16 shows the compression and tension damage zones. Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the number of elements exceeding the damage limit.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eS\u003csub\u003e13\u003c/sub\u003e stress values (MPa)\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003eMax (Tensile )\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003eMin (Compressive)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003eS\u003csub\u003e33\u003c/sub\u003e Stress Values\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e-8.828\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e+\u0026thinsp;5.646\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eTable\u0026nbsp;6\u003c/b\u003e S\u003csub\u003e33\u003c/sub\u003e stress values (MPa)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c6\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eMax (Tensile)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003e\u003cb\u003eMin (Compressive)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c6\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eS\u003csub\u003e13\u003c/sub\u003e Stress Values\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003e-18.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003e+\u0026thinsp;10.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c6\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePrincipal stress values (MPa)\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMax (Tensile )\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMin (Compressive)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePrincipal Stress\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e33.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-36.34\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eNumber of elements exceeding damage limit\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMax (Tensile )\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMin (Compressive)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOver 0.95 Number of Damaged Elements\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3560\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e7095\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabf\" border=\"1\"\u003e\u003ccolgroup cols=\"15\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c10\" namest=\"c7\"\u003e\u003cp\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c15\" namest=\"c11\"\u003e\u0026nbsp;\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"8\" nameend=\"c10\" namest=\"c3\"\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;13\u003c/b\u003e S\u003csub\u003e33\u003c/sub\u003e stress values due to tensile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c15\" namest=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e\u003cp\u003e( a )S\u003csub\u003e13\u003c/sub\u003e stress due to tensile stress\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c11\" namest=\"c6\"\u003e\u003cp\u003e( b ) S\u003csub\u003e13\u003c/sub\u003e stress due to compressive stress\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c15\" namest=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"11\" nameend=\"c11\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;14\u003c/b\u003e S\u003csub\u003e13\u003c/sub\u003e stress damage regions\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c15\" namest=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"9\" nameend=\"c9\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;15\u003c/b\u003e Principal stress values\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c14\" namest=\"c10\"\u003e\u003cp\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e\u003cp\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c12\" namest=\"c8\"\u003e\u003cp\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c15\" namest=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"11\" nameend=\"c12\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;16\u003c/b\u003e Regions of compressive and tensile damage\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c15\" namest=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eAs can be seen in Fig.\u0026nbsp;15, Smax and Smin principal stresses are concentrated in the dome parts, upper parts of arches and upper parts of openings. Figure\u0026nbsp;16 shows the tensile and compressive damage regions and Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the number of damaged elements in these regions. As can be seen from the figure and the table, there is a high level of damage in and around the main dome. The majority of the damage has been caused by stresses in the tensile direction.\u003c/p\u003e"},{"header":"Results and Discussions","content":"\u003cp\u003eIn this study, the FE model of the historical Uşak Ulu Mosque, which was built during the reign of Germiyanoğulları, is investigated in the Abaqus programme. The study performed both frequency analysis and nonlinear behaviour of the structure. The nonlinear analyses of the mosque were performed by considering the CDP model. The CDP analyses closely examined the behaviour of the structure under tension and compression. In 1999, a high intensity and destructive earthquake such as the Kocaeli earthquake is expected to cause damage to some structural parts of the mosque. The results obtained from the analyses carried out in the study show that most of the damage is expected to occur in the areas affected by tensile stresses.\u003c/p\u003e\u003cp\u003eAnalyses of the mosque revealed that the general damage was to the upper parts of openings, arches supporting the main dome, domes and places near the domes. It is understood that the most of the damage is located in the elements that support the main dome and in the upper parts of the windows that are under the main dome. Stress limits were exceeded in these areas. The main factor in damage occurrence is tensile stress. This is due to the resistance of the masonry structures to compressive stresses. The tensile stress is approximately 28 times the S33 stress limit. The compressive stress is approximately 4.5 times the limit value and for S13 stress these values vary 50 times for tensile stress and 9 times for compressive stress. For principal stresses, these values vary 170 times for tension and 19 times for compression. In general, if the number of damaged elements caused by the compressive and tensile stresses is analysed, it can be seen that the number of damaged elements caused by the tensile stress is 2 times higher than the number of damaged elements caused by the compressive stress.\u003c/p\u003e\u003cp\u003eThere are many studies in the literature on the damage zones of historical mosques under the effects of earthquakes. The results of this study show that the expected damage zones in the literature can be realised in Uşak Ulu Mosque, and that the damage zones of the mosque in Uşak Ulu Mosque are in accordance with the results of the literature.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eSoner SEKER : Writing \u0026ndash; review \u0026amp; editing, Supervision, , Validation, Methodology, Investigation,Formal analysis, Conceptualization. Hakki SAHIN: \u0026ndash; Writing \u0026ndash; original draft, Visualization , Validation , Investigation,Formal analysis,\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe title \"funding declarations\" was added as a subheading after the references in the article.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.The earthquake records of the Kocaeli earthquake used in the study can be accessed at the url address \"https://www.strongmotioncenter.org/vdc/scripts/event.plx?evt=510\".\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eErdik, M. \u0026amp; Durukal, E. \u003cem\u003eAya Sofya\u0026rsquo;nin deprem davranisi, 2\u003c/em\u003e (Ulusal Deprem M\u0026uuml;hendisligi Konferansi, 1993).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAkan, A. E. \u0026amp; \u0026Ouml;zen, \u0026Ouml;. \u003cem\u003eBursa yeşil t\u0026uuml;rbe\u0026rsquo;nin sonlu elemanlar y\u0026ouml;ntemi ile deprem analizi\u003c/em\u003e (Deprem Sempozyumu, Kocaeli, 2005).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTanyıldızı, H. \u0026amp; Sayın, E. Harput Ulu Camisinin Deprem G\u0026uuml;venliğinin Belirlenmesi, Yapısal Onarım ve G\u0026uuml;\u0026ccedil;lendirme Sempozyumu, 440\u0026ndash;443, 7\u0026ndash;8 December, Denizli, Turkey. (2006).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDabanlı, \u0026Ouml;. Determination of the earthquake performance of historical masonry structures, (Master\u0026rsquo;s dissertation, İstanbul Technical University, Turkey) (2008).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEr Akan, A. Determination of Structural Performance of Timber Pillared Historical Mosques by Finite Element Analysis. \u003cem\u003eSDU Int. Technologic Sci.\u003c/em\u003e \u003cb\u003e2\u003c/b\u003e (1), 41\u0026ndash;54 (2010).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAkdeniz, \u0026Ouml;. Tarihi yapıların lineer olmayan dinamik analizi. (Master's dissertation, Fırat University, Elazığ, Turkey) (2011).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBayraktar, A., Altunişik, A. C., Sevim, B. \u0026amp; T\u0026uuml;rker, T. ),Seismic response of a historical masonry minaret using a finite element model updated with operational modal testing. \u003cem\u003eJ. Vib. Control\u003c/em\u003e. \u003cb\u003e17\u003c/b\u003e (1), 129\u0026ndash;149 (2011).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eU\u0026ccedil;ak, Ş., Bayraktar, A., T\u0026uuml;rker, T. \u0026amp; anfd Osmancıklı, G. Finite-Element Model Calibration of Historical Masonry Domes Using Operational Modal Testings. \u003cem\u003eJ. Perform. Constr. 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Betonarme Kısa Kirişlerde Kesme Dayanımının \u0026Ccedil;apraz Kesme Donatıları İle İyileştirilmesi, (PhD dissertation, Sakarya University,Turkey) (2016).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Historical Masonry Mosques, Linear and Time Domain Nonlinear Analysis, Concrete Damage Plasticity Model, Seismic behavior, Damage","lastPublishedDoi":"10.21203/rs.3.rs-7316208/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7316208/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":" Historical buildings are symbols of our cultural heritage and richness. They are an important part of our heritage, transmitting many of their characteristics to next generations. As Turkey, one of the most important symbols of our cultural heritage are Ulu Mosques. Historical mosques built in Anatolia during the Seljuk, Principalities and Ottoman periods, especially for Friday and Eid prayers, are called “Ulu Mosques”. Ulu Mosques were generally built in city squares and in places that can be called quite easy to reach. Ulu mosques in Turkey are also considered a symbol of “power and independence”. These structures are evidence that show the history and reflect the behaviour of the people and the culture of the past as well and they need to be safely passed on to next generations. Earthquakes over the years have caused great damage to these structures. In order to protect historical masonry mosques against earthquakes, 3D finite element models should be created and nonlinear analysis should be performed. In this paper, linear and nonlinear time domain analyses of the historical masonry Ulu Mosque in Uşak province are carried out. As a result of the analyses, the dynamic behavior of the selected historical masonry structure under earthquake load is investigated. Concrete Damage Plasticity (CDP) model was used in the nonlinear time domain analysis of the structure.","manuscriptTitle":"Investigation of seismic damage propagation in historical masonry mosque; example of Uşak Ulu Mosque","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-27 17:45:53","doi":"10.21203/rs.3.rs-7316208/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-03T07:54:23+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-10T09:24:21+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-27T19:30:33+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-25T20:29:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"90523305047294186093623903057015993402","date":"2025-08-21T08:00:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"30712120440025656221633994808824820468","date":"2025-08-19T19:13:14+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"50238048835895413771629611627791944636","date":"2025-08-19T12:54:42+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-19T04:56:03+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-19T04:54:37+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-08-19T04:34:16+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-14T09:53:04+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-08-14T09:48:48+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a2dc6cea-1f1b-4189-a3df-60079fa4df11","owner":[],"postedDate":"August 27th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":53686557,"name":"Physical sciences/Engineering"},{"id":53686558,"name":"Humanities/History"},{"id":53686559,"name":"Social science/History"}],"tags":[],"updatedAt":"2026-05-15T09:09:17+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-27 17:45:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7316208","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7316208","identity":"rs-7316208","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}